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Space is a fascinating place that you have just begun to explore. However, there are eight planets in our Solar System, but astronomers do believe that there are almost billions or even trillions of other planets that are a part of other solar systems in other galaxies.
Here is some amazing facts about the space that will surprise you i’m sure
- Life is known to exist only on our planet, Earth, but NASA found out in 1986 what they thought may be some kind of fossils of microscopic living things in a rock from the planet Mars.
- Glowing nebulae are called so as they usually give off a dim, red light, due to the hydrogen gas present in them gets heated by radiation from the nearby stars.
- The Milky Way galaxy you live in is one among the billions in the space.
- The hottest planet in our solar system is the Venus with a surface temperature of above 450 degrees Celsius.
- The solar system was formed approximately 4.6 billion years ago.
- The Moon appears to have more scars and craters than Earth as it has a lot less natural activity going on. On the other hand, the Earth is persistently reforming its surface through natural activities like erosion, earthquakes, wind, storms, rain, and plants growing on its surface. Moon has very little weather to change of reform its overall appearance.
- A day on Mercury is equivalent to approximately 59 days on the planet earth!
- The opposite of black holes is predicted to be white holes that spray out matter and light-like fountains.
- Footprints and tire tracks left behind by astronauts on the moon will stay there forever owing to the fact that there is no wind to blow them away on the moon.<|endoftext|>
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# How do you solve abs(5x + 10) - 15 = 20?
Aug 2, 2015
$x = - 9 , 5$
#### Explanation:
Rearrange the equation:
$| 5 x + 10 | - 15 = 20$
=>
$| 5 x + 10 | = 35$
Because of the modulus there are two solutions, the first:
$5 x + 10 = 35$ => $x = 5$
The second:
$5 x + 10 = - 35$ => $x = - 9$
Aug 2, 2015
$x = - 9 , 5$
#### Explanation:
$\left\mid 5 x + 10 \right\mid - 15 = 20$
Add $15$ to both sides of the equation.
$\left\mid 5 x + 10 \right\mid = 20 + 15$ =
$\left\mid 5 x + 10 \right\mid = 35$
Rewrite the equation without the absolute value symbol, with one equation positive, and one negative.
$5 x + 10 = 35$ and
$- \left(5 x + 10\right) = 35$.
Positive Equation
$5 x + 10 = 35$
Subtract $10$ from both sides of the equation.
$5 x = 35 - 10$ =
$5 x = 25$
Divide both sides by $5$.
$x = \frac{25}{5}$ =
$x = 5$
Negative Equation
$- \left(5 x + 10\right) = 35$ =
$- 5 x - 10 = 35$
Add $10$ to both sides.
$- 5 x = 35 + 10$ =
$- 5 x = 45$
Divide both sides by $- 5$.
$x = \frac{45}{- 5}$ =
$x = - 9$<|endoftext|>
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6,618 |
This we believe: The school environment is inviting, safe, inclusive, and supportive of all.
According to a nationally representative survey conducted by the National Institute of Child Health and Human Development (NICHD, 2001), approximately 30 percent of American school children in grades 6 through 10 have been bullied or have bullied other children "sometimes" or more often within a semester.
These data are supported by a more recent study in 2010 by Clemson University in which 17% of K–12 students indicated that they had been bullied with some frequency (2–3 times /month) and 10% of students indicated that they had bullied others with a similar frequency. Increased awareness of the problems of bullying in our schools has led most states to introduce new laws regarding bullying. A primary goal for schools in many states is the provision of a safe, secure, and orderly school. However, even with requirements to provide a safe and orderly school, and with new laws about bullying, schools and school districts are often unsure how to take action. Some school communities, especially schools of academic distinction or who have a good reputation in their community, may believe that their schools are safe and that bullying is not a problem. Principals and teachers might not question whether they have effective policies in place for dealing with bullying.
While some schools are safe, principals may more easily assume that their schools are safe places than to have to deal with any negative publicity related to uncovered incidents of bullying. Moreover, some bullying incidences are microcosms of greater societal issues that certain parents and citizens may view as "controversial" or even justified because some groups "deserve it." Such possible controversy makes the challenge for how schools respond even greater. This article describes how one teacher's concerns changed her school's attitude with regard to bullying from assuming that "bullying is not a major problem at our school" to "bullying is a priority issue included in the school improvement plan with a school-wide program to address bullying."
As we explored the complex topic of bullying, we pondered a statement from This We Believe, which states, "The school environment is inviting, safe, inclusive, and supportive of all," (NMSA, 2010). The most obvious connection is the need for schools, and middle schools in particular, to provide a safe environment for all students whose emerging identities often include significant vulnerability. We contend that bullying reaches to the heart of the school culture and specifically the extent to which middle school environments support the physiological, emotional, social, and academic development of adolescents (Scales, 2003). The Association for Middle Level Education (AMLE), formerly National Middle School Association (2010), provides a good description of this preferred environment: "A successful school for young adolescents is an inviting, supportive, and safe place - a joyful community that promotes in-depth learning and enhances students' physical and emotional well-being.…Students and teachers understand they are part of a community where differences are respected and celebrated.…the safe and supportive environment, students are encouraged to take intellectual risks, to be bold with their expectations, and to explore new challenges" (pp.33–34). This description conveys the multiple ways in which school culture impacts student development, especially since young adolescents often spend as much or more time with teachers and peers as with parents or guardians.
Another perspective identifies the importance of this period for student identity development (Anfara, Mertens & Caskey, 2007). The authors state that questions of identity are of great importance to young adolescents. The authors describe that the search for identity and self-discovery can "lead young adolescents to be easily offended and be sensitive to criticism of personal shortcomings" (p. xx). Identity can be affected by "questions about physical changes, relationships with peer and adults, one's place in the world, and global issues (e.g., poverty, racism, and wealth distribution) [which] help shape what adolescents are interested in and how they view the world" (Brinthaupt, Lipka & Wallace, 2007, p. 207). Lane (2005) in her study of girls and aggression notes, "Middle level students' primary concerns are focused on their peers and what others think of them. It is a time of tremendous insecurity for both boys and girls, and most of them experience some kind of rejection or exclusion exactly when being included is of utmost importance" (p. 42).
Finally, Pollock (2006) identifies the challenges faced by adolescents with regard to sexuality: "Adolescents have many issues surrounding their emerging identities, sexual drives and sexual orientation" (p. 31). She notes that too often these are forbidden topics in school. Fostering greater understanding among educators and the community about the emotional needs and identity crises that some students are going through is exactly what influenced us to explore the topic at the school where one author teaches.
Southeastern Middle School
Southeastern Middle School (a pseudonym) is a fairly large middle school with just over 800 students that serves a largely suburban and rural district in southeastern North Carolina. The school population is predominantly white; 13% of students are of color. About 54% of the students receive free and reduced lunch. As one of five middle schools in its district, Southeastern serves students from two feeder elementary schools. During the previous year, a low incidence of crime was reported at the school. For the last five years the school has been classified as a school of distinction by the state. Finally, Southeastern Middle has a relatively low teacher turnover rate, and teacher working conditions surveys suggest the school receives high support from teachers.
All seasoned teachers at the school agree that in comparison to other school settings, students at this school show a high level of respect toward adults in the building; students get along reasonably well with one another. In fact, little evidence of gang or group hostility asserts itself. Southeastern Middle is, in general, an excellent place to teach. However, during Kayce's fourth year as a teacher of grades 6–8 at Southeastern Middle, she started to pay more attention to incidents of bullying that were occurring in the hallways and occasionally in her own classroom. She and other teachers would hear students use negative terms in referring to other students, but they would not always know an appropriate or affirming, impactful way to respond. While some teachers talked often about cultural differences in the curriculum and opposed discrimination against marginalized people, these were individual decisions and were not part of a larger school-wide discussion. Further, while many students and schools have accepted that discrimination based on race or ability, for example, is unacceptable, other groups too often lack such strong support. Students who are lesbian, gay, bisexual, or transgender (LGBT), overweight, and students of lower socioeconomic status are especially and emphatically among those groups who receive little support. So even though Southeastern Middle School has a reputation as being a good and safe school, Kayce wanted to find out about students' experience with bullying, how they felt about their safety at school, and how they perceived teachers' responses to bullying. After all, the research shows that a student's safety and emotional comfort play a huge role in her/his overall progress and development in other areas of middle school life and beyond. Thus Kayce was able to conduct the present study of bullying at her school as part of an independent study toward a graduate degree. Robert Smith, co-author, served as a resource, helped to guide the study, and provided a knowledgeable perspective from outside our school and district. Kayce and Robert worked together to compile the relevant literature and to evaluate the data from surveys at the school.
Research on bullying
Bullying generally is defined as aggressive behavior or intentional harm by an individual or group repeated over time that involves an imbalance of power (National Conference of State Legislatures, 2007). Further, bullying is viewed as falling into three different types of aggression: physical aggression, which includes hitting, kicking, or pushing; verbal aggression, which includes name calling, teasing, or abusive language; and relational aggression, which consists of spreading rumors and social exclusion (Varjas, Henrich, Meyers, & Meyers, 2009). A 2013 Department of Education report on bullying in West Virginia found that students are most likely to be bullied in middle school with middle school students accounting for 56% of all reported incidents of bullying K–12 (Eyre, 2013). In a study of students in grades 7 and 8 in urban, suburban and rural schools, 24% reported either bullying or being bullied; 14% of students reported being called mean names and others reported being hit or kicked, being teased or being threatened (Seals & Young, 2003). In a separate study of students in grades 7 and 8 at three middle schools that differed significantly by race, socioeconomic status, and urbanicity, "being overweight" and "not dressing right" were the most common reasons that identified why a student might be bullied (San Antonio & Salzfass, 2007). The second most common reason, identified at two of the three schools, was being perceived as gay. Based on student responses, one of the main conclusions from the study was that "most students want adults to see what is going on in their world and respond to bullying in caring, effective, and firm ways" (p. 35).
Kayce's initial questions for students revolved around their perceptions of how much bullying occurs at Southeastern Middle, which types of students are bullied, where bullying is occurring, and what support the school is viewed as offering in preventing and responding to bullying. Olweus (1999), who is widely considered the pioneer in bullying research, describes conducting a needs assessment as a way to gather data and inform the process. This approach, which also included focus groups with students, was successfully implemented in a study of bullying at an elementary school (Orpinas, Horne, & Staniszewski, 2003). Surveys concerning student and teacher perceptions regarding bullying have also been used (Beale & Scott, 2001). Based on the different responses to bullying from their study of students at three middle schools, San Antonio and Salzfass (2007) argue that a needs assessment is an important starting point. Their findings coincide with the various researchers who claim that multiple types of reporting and surveying are necessary when diagnosing a school's need for an anti-bullying program (Bowllan, 2011; Varjas, Henrich, Meyers, & Meyers, 2009).
Surveying students and teachers
Kayce read several articles on bullying and searched for existing surveys that would provide greater reliability and address questions with regard to bullying than might have otherwise been considered. In developing questions for the student survey, Kayce was aware of the rural community surrounding the school that might lead to complaints from community members if too much positive attention was focused on gay identifying students.
While the building principal was supportive of such a project, this was also his first year and he wanted to make sure that student surveys had the support of the local school district. The district reviewed the survey and replied that, as it involved student's beliefs, the survey would have to be approved prior to the start of the school year, per a school board policy. The district also suggested that the wording of some of the questions revealed bias. The district's response initially confirmed our fears that bullying can be a politically sensitive topic and school officials would prefer not to have certain controversial aspects of this issue examined.
This response appeared to end the project, at least for that year. However, after further thought we disagreed with the district's interpretation that the survey questions asked about student's beliefs rather than their opinions and observations about bullying and whether bullying occurred at the school. We decided to submit a revised survey, changing the wording of some questions, and we replied that we did not view this as asking about students' beliefs but about students' observations in regard to their daily experience. At this point, district officials said that the decision ultimately remained with the principal. We realized then that a better way to begin data collection on this topic would be to survey the teachers rather than the students. We suspected that the responses from the teachers might help pave the way to survey the students.
The teacher survey included questions about the frequency with which they observed bullying, the locations on campus where bullying occurs in any capacity, and the extent to which they address bullying with their students both formally and informally. Open-ended questions probed teachers' comfort levels with responding to bullying incidences as well as their opinion on whether the school should be doing more to combat bullying. An impressive return rate resulted, with 48 of the school's 55 teachers responding to the survey; 79% of respondents stated that they observed bullying incidences between one and three times per week. In response to questions about the frequency with which particular groups of students were bullied, most answers reported that many of the groups were bullied at a lower frequency of "sometimes." However, six groups had frequency for being bullied with the highest number of respondents who chose "frequently" or "constantly." These included students "with few or no friends" (35%); students who are "overweight" (33%); students who are "poor or perceived to be impoverished" (21%); students "who are gay or rumored to be homosexual" (23%); and students "who act like the opposite gender" (25%). Although 77% of teachers said they were confident in responding to incidences of bullying, 44% of teachers indicated that they would like to receive additional resources or guidance on how to respond to bullying. Finally, 65% of teachers agreed that the school should be doing more to reduce incidences of bullying.
Senseless Bullying Must Stop Task-Force
Teachers' responses indicated both that bullying is an important issue and that the school could be doing more to address bullying. Their responses also supported the need for further investigation. In completing the online survey, teachers could indicate if they were interested in being part of a solution to bullying at Southeastern. Four teachers and the two school counselors volunteered and formed the Senseless Bullying Must Stop Task-Force (the nickname was a student's idea and coincides with the acronym for the school's name). The task force quickly recruited a parent, six students, and two members of our three-member administration to join in our review of the data from the teacher responses and in our discussions to consider our next step(s). At the task force meetings, small groups were created to examine possible solutions to specific problems that emerged from teacher responses. Very quickly the group identified the need for data from students, which could be compared with the teachers' responses. A student survey was created that modeled the survey given to teachers. It included additional questions that were created based on the input of the students on the task force. Four months after the teacher survey was administered, the student survey was completed by 620 students out of a total of 810 students, with a similar number of responses received from all three grade levels. Student responses indicated that approximately one third of students had been bullied, with 13% indicating they were unsure about whether they had been bullied. Eight percent of students (58 total students) indicated they were bullied daily and seven percent (49 students) said they were bullied 2–3 times a week. Eighty percent of students reported that they see bullying occurring at the school, and 18% stated that they see bullying more than once a day. In response to which groups of students experience the most bullying, the following four groups had the highest percentages of students who are frequently or constantly bullied: students who are gay or rumored to be gay (53%), students who are overweight (50%), students with few or no friends (43%), and students who act like the opposite gender (34%). In response to the question asking students if they have a trusted adult at the school that they can talk to about bullying and other problems they might be experiencing, 57% said "yes," 28% said "no," and 14% indicated "unsure"; this large majority view reveals a powerful indicator of the strength of the ideal middle school model's presence at the school. Finally, only 33% of respondents agreed with the statement that "when my teachers respond to bullying, it helps make the situation better."
Students from the task-force met three times with Kayce and the two counselors in a focus group format to review the results. The students provided valuable feedback in understanding some of the responses, and they also brainstormed various short- and long-term goals for our school and group. One of these goals was similar to a strategy that other researchers have described in the creation of a student-run watch group (Crothers, Kolbert & Walker, 2006). This group, which would later be named "Cougar Watch," would be responsible for monitoring bullying and reporting incidences to teachers. Around the same time this student-led brainstorming was happening, the school faculty learned about the most significant results from the student survey, especially those that differed from their own perceptions. This knowledge of students' experience and perspective undoubtedly fostered greater interest and concern on the part of teachers to learn more about what was happening and the different ways they could respond. This is significantly relevant for this middle school as it shows a genuine desire on the part of adults to be a part of a school community where student differences are celebrated and respected (NMSA, 2010).
Creating the cougar watch student group
Equally important to having mechanisms in place in the school community for students' healthy emotional growth is the need for similar strategies that foster their ability to contribute as democratic citizens both in their school and in their future (NMSA, 2010). The formation of the student-run Cougar Watch group coincides with the AMLE proclamation that developmentally responsive middle schools "will promote the growth of young adolescents as scholars, democratic citizens, and increasingly competent, self-sufficient young people" (NMSA, 1995, p. 10). Students in grades 6–8 who submitted applications to participate in Cougar Watch had to receive parent permission as well as teacher recommendations.
This application process served several goals: (1) it informed parents that we were taking steps to do something about bullying at our school, (2) it ensured that teachers were able to provide confidential input as to the character of these applicants, and (3) it let students know that the role was a serious responsibility and an opportunity for leadership. With backing from our principal and assistant principal, we planned training sessions for our 32 new Cougar Watch members. The training focused on being able to clearly define the three different types of bullying and being able to identify whether or not situations are bullying. These students practiced identifying bullying throughout the school for about two weeks by simply observing and recording their observations in a journal. During this time the two counselors, two teacher members of the task force, the school resource officer, and Kayce met with the 32 Cougar Watch members a total of five times.
In small groups, the adults facilitated the discussions in which students shared what they observed and tried to identify as a group whether or not these should be considered bullying. Out of this training experience we drafted and finalized a bullying reporting form that would be available for use during the following school year. The form incorporates student-friendly language and has a checklist format that helps students determine if what they are reporting is indeed bullying.
Planning our approach to bullying prevention
After this training experience and before departing for the summer, the core group of adults from the task force met for a long brainstorming session with the principal. We determined that the best use of the Cougar Watch reporting forms might be to make them available to all students in the school. This decision resulted from the need to protect Cougar Watch members from becoming targets themselves, but it also is consistent with other bullying prevention programs that stress the importance of a whole-school response particularly involving all students (San Antonio & Salzfass, 2007; Brewster & Railsback, 2001)1. We also intend to incorporate the Cougar Watch members' responsibilities as well as the data from the reporting forms to help inform the implementation of Positive Behavior Intervention Support (PBIS) at our school over the next few years. Next, we decided that since our budget ruled out the opportunity to invite an outside expert to train our teachers, this same core group who trained the students would use similar content with modified methods to train the adults in our building. While possibly missing some of the expertise of an outside trainer, benefits accrue from having the adults and students within our school community find answers to our school's challenges.
One of the reasons bullying is such a complex issue is because people have different ideas as to what constitutes bullying. Hence, we knew we needed a clear definition of bullying that could be communicated to all stakeholders in our school community. We established our school's definition—Bullying: (1) is harming another person intentionally, (2) is repeated, (3) involves a power imbalance—based on the multiple but similar definitions provided by different experts, and made it student-friendly with cartoon-like depictions to help clarify. This clear and shared definition has been communicated to staff during their training. It was also professionally printed on posters that are in all teachers' classrooms and throughout the building, and it was shared with parents at the first Open House night of the school year. During this four-hour Open House, teacher and student volunteers offered descriptions of the main types of bullying, shared with parents the school's official definition, and provided them with a pamphlet that included resources on bullying available on the Internet.
Broader connections of bullying
In less than one school year, the topic of bullying at our school has gone from the status of a "non-issue" to being a real priority with strategies included in next year's school improvement plan. Further, one of the district-determined goals for all School Improvement Plans, which coincides with the AMLE stance on positive school culture, is to have a "safe and nurturing school for all students." Our Senseless Bullying Must Stop Task-Force is a perfect strategy to accomplish this goal. Ideally, after some time is spent raising awareness about bullying and learning how to respond to it better, the approach to dealing with bullying at the school will shift to more of a preventative nature. This should be made easier with the implementation of a school-wide PBIS program. PBIS focuses on bringing a culture shift into a school by modeling positive behavior in school-wide routines and explanations and then rewarding subsequent positive behavior. The district has chosen PBIS as a tool to be utilized by all schools in our county, so the work of the Senseless Bullying Must Stop Task-Force should provide a helpful segue from simply reporting and disciplining bullying to changing the school's culture in general on various behaviors including bullying. For more information on PBIS, see http://www.pbis.org/.
Remarkable changes have occurred at Southeastern Middle School in one year. We now have a much better understanding of the groups of students at the school who have been targets of bullying. We have developed widespread interest and support with the teachers and administration, an action plan for creating awareness about bullying among the students and parents, and a visual representation of the different strategies that are available at the school to respond to bullying and bullying-victim behavior.
As we pursued this study, our understanding of bullying also evolved from seeing bullying as a separate problem, to recognizing that it is deeply connected to the whole school culture and draws upon nearly all 16 characteristics identified as keys to educating young adolescents (NMSA, 2010). In seeking to create a school culture that supports the diversity of our students and in which all students feel valued for who they are, we have had to engage our teachers and administration. We have also realized the importance of listening to our students and involving them in helping create a supportive school culture (Lipka & Roney, 2013). Additionally, we have had to involve our students' parents and families so that they too are included in supporting the changes in school culture. There likely will still be difficult issues to respond to, but we are starting the school year informed of the problem and no longer assuming that "bullying is not a problem at our school."
Key points for teacher led change to address bullying
Based on our experience as well as the literature we read about bullying, we offer the following six key points when considering a grassroots approach to raising awareness about bullying at any school:
- Be aware that some bullying incidences are microcosms of greater societal issues that some parents and citizens may view as "controversial." However, do not be deterred by initial responses that may not be supportive, e.g., "we have a safe school," or "bullying is not a problem at our school." Use data to prove objectively why those controversial issues need to be addressed at the middle school age level.
- Find other colleagues within the school, at other schools, and/or in organizations concerned with bullying who are either interested in helping form a group at the school or who can help serve as a resource for you or the group. A group provides a stronger voice than one individual teacher. Also, invite a broad base of representation on the group, e.g., teacher, student, counselor, parent, and administrator.
- Collect student data on their experience and perceptions of bullying at your school. Students know firsthand what is happening with bullying. Include students in any group created to make recommendations on bullying. School-wide action plans should include all students and teachers.
- Be patient. Just when you think you have made changes and done extensive work, you will realize the road is a long one. Eliminating or reducing bullying is not something that happens in one year. No matter what community you are in, it is an ongoing effort and programs or strategies should be continually assessed for their effectiveness.
- Remind your principals that increased reporting will occur when you start to tackle the issue of bullying. This is positive and means people are paying attention. It will be extra work upfront for the principals, but if the school's action plan is successful and effective, these reports should decrease over time.
- Once you determine through your needs assessment that some type of program or plan is necessary at your school, you will likely find that a clear definition of what your school considers as bullying is a great place to start. It gets everyone (students, teachers, parents, and administrators) on the same page when discussing the issue and formulating plans.
- Remind yourself that efforts to eliminate bullying get to the heart of creating a successful middle school. Don't give up!
1 Author's update on the Cougar Watch and reporting forms: In the following school year, the adult task force determined that allowing students to serve as "bullying police" via the Cougar Watch may not be the most effective use of the student run group. Additionally, there was a concern that there would not be sufficient adult human power to monitor, investigate, and respond to the reporting forms if they were completed by all students in the school. Since then, the group's focus has turned more toward awareness for the school and community at large. They meet as an academic club 1-2 times a month, are well-versed in the school's definition of bullying and process for reporting bullying, and are making plans to lead assemblies for each grade level in which they engage students around the definition of bullying, how to respond to it, and how to report it at our school.
Anfara,V., Mertens, S., & Caskey, M. (2007). Introduction. In S. Mertens, V. Anfara & M. Caskey (Eds.) The young adolescent and the middle school (pp. ix–xxxiii). Charlotte, NC: IAP.
Beale, A. V., & Scott, P. C. (2001). Bullybusters: Using drama to empower students to take a stand against bullying behavior. Professional School Counseling, 4, 300–306.
Bowllan, N. M. (2011). Implementation and evaluation of a comprehensive, school-wide bullying prevention program in an urban/suburban middle school. Journal of School Health, 81, 167–173.
Brewster, C., & Railsback, J. (2001). Schoolwide prevention of bullying. Retrieved from http://www.wrightslaw.com/advoc/articles/prevention.of.bullying.pdf
Brinthaupt, T., Lipka, R., & Wallace, M. (2007). Aligning student self and identity concerns with middle school practices. In S. Mertens, V. Anfara & M. Caskey (Eds.) The young adolescent and the middle school (pp. 201–218). Charlotte, NC: IAP.
Clemson University (2010). Retrieved from http://www.growingupglobal.net/blog/?p=402
Crothers, L. M., Kolbert, J. B., & Barker, W. F. (2006). Middle school students' preferences for anti-bullying interventions. School Psychology International, 27, 475–487. doi: 10.1177/0143034306070435
Eyre, E., (2013). Bullying most prevalent in middle school, report finds. Charleston Gazette. Retrieved from http://www.wvgazette.com/News/politics/201307230059
Lane, B., (2005). Dealing with rumors, secrets, and lies: Tools of aggression for middle school girls. Middle School Journal, 36(3), pp. 41–47.
Lipka, R., & Roney, K., (2013). What have we learned and what must we do. In K. Roney & R. Lipka (Eds.) Middle grades curriculum. Voices and visions of the self-enhancing school (pp. 307–309). Charlotte, NC: IAP
National Institute of Child Health and Human Development, (2001). Retrieved from http://www.nih.gov/news/pr/apr2001/nichd-24.htm
National Conference of State Legislatures (2007). Retrieved from http://www.ncsl.org/issues-research/educ/school-bullying-overview.aspx
National Middle School Association. (1995). This we believe: Developmentally responsive middle level schools. Columbus, OH: Author
National Middle School Association. (2010). This we believe: Keys to educating young adolescents. Westerville, OH: Author
Olweus, D. (1999). Bullying prevention program. Boulder, CO: Center for the Study and Prevention of Violence, Institute of Behavioral Science, University of Colorado at Boulder.
Orpinas, P., Horne, A. M., &Staniszewski, D. (2003). School bullying: Changing the problem by changing the school. School Psychology Review, 32, 431–444.
Pollock, S., (2006). Counselor roles in dealing with bullies and their LGBT victims. Middle School Journal, 38(2), 29–36.
San Antonio, D. M., & Salzfass, E., (2007). How we treat one another in school. Educational Leadership, 64(8), 32–38.
Scales, P., (2003). Characteristics of young adolescents. In National Middle School Association, This we believe: Successful schools for young adolescents (pp.43–51). Westerville, OH: Author.
Seals, D., & Young, J. (2003). Bullying and victimization: Prevalence and relationship to gender, grade level, ethnicity, self-esteem, and depression. Adolescence, 38, 735–747.
Varjas, K., Henrich, C. C., Meyers, H., & Meyers, J. (2009). Urban middle school students' perceptions of bullying, cyberbullying, and school safety. Journal of School Violence, 8, 159–176.
Robert William Smith is a professor in the Watson College of Education at the University of North Carolina at Wilmington. E-mail: [email protected]
Kayce Smith teaches middle school in rural North Carolina. E-mail: [email protected]
Published in Middle School Journal
, September 2014.<|endoftext|>
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Jordan12
# 6 Facts About Resources Everyone Thinks Are True
How To Better Understand The Basics Of Working With Fractions
Dealing with numbers is always a challenge even when you are young, and for some doing math and its calculation is something that is characterized with deep analytical thinking and problem solving capacity.
When you add, subtract, multiply, and divide numbers it will be easy if they are whole numbers and it is easy to apply the basic knowledge you learned about math, but when it comes to fractions, the challenge begins there.
It will be easy to go by it if you use online fraction calculator or any device that is capable of solving fractions but when you do have to do it manually, still the basics are needed and a little twist, and you will see it here how to be refreshed with the way fractions are solved.
You know that a fraction is a portion of a whole number, it is a part of an entire picture and it can best be understood when it has illustrations, but there are ways in which you can learn more of the easy and practical way to solve fractions.
If you want to add fractions, like example 1/2 + 1/4 , you have to get the least common denominator that is applicable for both fractions that is divisible in both denominator, and in this case it is 2, then you multiply the fraction with lesser denominator by 2 so it becomes 2/4, add that back to 1/4 then that becomes 3/4 .
When you subtract 1/2 – 1/4 , still you get the least common denominator and multiply that number to the lesser denominator fraction, hence 2/4 – 1/4 is 1/4 , and remember either in addition or subtraction you do not include the denominators.
Now to multiply fraction you simply multiple same level, numerator to numerator and denominator to denominator, therefore for 1/2 * 1/4 it will result to 1/8 , and when you divide 1/2 by 1/4 will you will have to multiply numerator 1 to denominator 2, and denominator 1 to denominator 2 and you will get 4/2 and this number is divisible with its denominator, therefore, you get the result of 2.
These are but simple ones, and you will get the hang of it when you get to practice more often or if not you can always use the online fraction calculator to help you get the immediate answer, but mastery will go with constant practice.
Learning mathematics is fun, and with solving fractions even, just remember the basic solving process and you will be able to pull it off, and get the problem solved in no time at all. These may not be as helpful as it may seem but you just don’t know how convenient it is to learn and understand how to calculate fractions in a fraction of the time.
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Black British Woman is a term which has a racial link to it. Generally it has been often used to refer to any non-white British woman. This term was first used at the fag end of the British Empire, when numerous colonies gained independence and thereby created a new form of national identity. At that time this term was used mainly to describe those women from the former colonies of India, Africa, and the Caribbean or the New Commonwealth countries. Presently it defines a British woman with specifically African ancestral origins, who is identified as Black, African or African-Caribbean. Black British Women also emigrated from other countries like Brazil and the USA.
Black British women had the same aspirations as whites to combine work and family life, and were even more ambitious about their education and future career. Despite high ambitions and investment in education the black British women employees under 35 were experiencing severe penalties when they wanted to work.
This includes higher rate of unemployment, a lower ceiling than fellow white women and lower pay packets. Most of these black British women worked in a restricted range of sectors and jobs. Most of the employers strongly agreed for employing black British women. Many of the young black British women in these groups reported that they had to deal with racism and sexism.
There are many different voices among Black British women they however speak of Black Feminism only. Though divided by language, religion, nationality, and culture, a new politics of solidarity became possible under these new relations of equivalence for the black British women. The black women’s movement in the year 1978 became a landmark in terms of an emerging Black British Feminist consciousness. It revealed the political agency of black women speaking different languages, religions, cultures and classes who consciously constructed a political based identity in response to exclusion of women experiences of racism.
Black British women’s coalitions such as South hall Black Sisters and Women against Fundamentalism have campaigned for black women’s rights since 1970s. These organizations demonstrate the value brought about by heterogeneity and conflict which opens a debate.
Many black British women have found their due place in the annals of history and fame. More and more are still storing their place in the field of literature, fashion entertainment, science and business but their plight continues to remain the same. They are the most unprivileged lot and to find their place they have to put in the extreme efforts, still they get lower income, sometime humiliation and face many other atrocities. When they become successful people praise them but at the hour of need they do not come forward to help them. This is the actual story of the black British woman of the present day. But this lot is marching ahead against all odds to find their sweet destiny. The war is on against the racism world over and specifically in Britain, but it will take time. Meanwhile we should salute the courage of the Black British women.<|endoftext|>
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Honey is a natural sweetener and resistant to microorganism growth, so it should be ideal to make fresh, nutritious hummingbird nectar, right? Wrong! While honey can be delicious, using it in nectar can be dangerous and even fatal to hummingbirds
Honey is a thick, viscous, syrupy liquid produced by insects that break down floral nectar. The exact chemical composition of honey depends on a variety of factors, including…
- The type of insect that produces the honey
- The type of flower nectar or plant sap transformed into honey
- Overall climate type, including humidity and temperature when the honey is produced
The sugars in honey are a combination of glucose and fructose, while the sugar in floral nectar is primarily sucrose. There are trace amounts of glucose and fructose present in floral nectar, depending on the exact flowers, but the concentration is far higher in honey.
Honey is rich and sweet, and is often preferred as a natural sweetener substitute in many cooking and baking recipes instead of adding extra sugar to foods. While honey can be a healthier option for many human foods, it isn’t the best choice for feeding hummingbirds.
Why Honey is Bad for Hummingbirds
There are several reasons why honey isn’t appropriate to feed to hummingbirds, either as a substitute in a sugar water recipe or to offer freely for birds to sip.
- Honey does not have the same chemical composition as floral nectar and is more difficult for hummingbirds to efficiently digest. This means the birds will get less energy and nutritional value from honey than from classic nectar or sugar water. Because hummingbirds need to maximize their energy intake to keep up on their active lifestyles, honey is not an ideal food option.
- Different bacteria and fungus that are naturally present in some types of honey are fatal to hummingbirds. When honey is diluted with water to be the proper consistency to feed birds, the extra water and oxygen in the mixture amplifies the fermentation of the honey so the bacteria and fungus grow much more quickly, infecting birds more easily.
- The sticky, syrupy texture of honey can easily coat the bills and feathers of hummingbirds, causing difficulties for the birds to feed or fly properly. This sticky goo can be difficult to wash away, particularly after it crystallizes, and birds that have gotten coated will be more vulnerable to predators and other threats.
- Honey, even diluted in water, will more easily clog the feeding ports of hummingbird feeders, restricting the flow of nectar and making it more difficult for birds to feed. Clogged ports can also become warped and cracked, leading to more feeder leaks and drips or making the feeder impossible to use properly.
- The sweetness of honey, both its taste and its enticing aroma, will attract other pests to the hummingbird feeder, including wasps, bees, ants, praying mantises and other insects, as well as raccoons and even bears in some areas. These visitors will not only keep hummingbirds from visiting, but can destroy feeders and may even be a danger to any both birds and birders.
With so many reasons why honey is not appropriate to feed hummingbirds, there is never a reason to offer it in hummingbird nectar.
Other Sweeteners to Avoid
In addition to honey, other types of sweeteners should not be used to make hummingbird nectar. Corn syrup, molasses and other sweetening syrups are never suitable, and beet sugar, raw sugar and powdered sugar are also inappropriate because they do not create the same nectar concentration and formula that is preferred by hummingbirds. Artificial sweeteners and zero-calorie sugar substitutes are also unsuitable because they do not provide hummingbirds with the appropriate caloric energy and nutrition they need.
Only plain, white table (granulated) sugar should be used to make homemade hummingbird nectar, or nectar concentrates or mixes that approximate floral nectar can be purchased to create healthy hummingbird nectar. No dyes or added flavors are necessary. With the best high-quality nectar, you’ll soon see more hummingbirds visiting your feeders and you’ll be able to enjoy more of these flying jewels every time you refill your nectar feeders.<|endoftext|>
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Math and Arithmetic
Algebra
Calculus
# What is X squared equals 3X?
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###### 2013-01-10 16:21:07
It is a quadratic equation in X.
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## Related Questions
3x squared - x squared = 2x squared
9x2 + 3x / 3x equals (3x + 1).9x2 + 3x divided by x is 9x + 3 , and then divided by 3 yields the 3x +1.
x2+3x = 7 x2+3x-7 = 0 Using the quadratic equation formula:- x = -4.541381265 or x = 1.541381265
since y = 3x+1 we have y squared =(3x+1) squared x^2 + y^2 = 25 x^2 + (3x+1)^2=25 x^2 + 9x^2+ 6x+1 = 25 10x^2 + 6x + 1 = 25 10x^2 + 6x -24 = 0 solve x from quadratic formula x = 1.28 y = 3x + 1 = 4.83
(3x - 2)(x + 1) are the factors if the equation equals 0, making x = two-thirds or -1.
3X = x2 - 2xsubtract 3X from each sideX2 - 5X = 0factor out an XX(X - 5) = 0=========X = 0--------orX = 5--------
It is a quadratic equation in the variable x.
The points of intersection of the equations 4y^2 -3x^2 = 1 and x -2 = 1 are at (0, -1/2) and (-1, -1)
(3x2 - 6x)/3x = 3x(x-2)/3x = x-2, for x<>0
3x = -111 x = -111 / 3 x = -37 x2 + x = (-37)2 - 37 = 1369 - 37 = 1332
It is a quadratic equation and its solutions are: x = -3/2 and x = 3
If x equals 8, then 3x equals 24. 24-x would equal 16.
(x^2-2) (x^2+3x+5)= x^2(x^2+3x+5) -2(x^2+3x+5)= x^4 +3x^3 +5x^2 -2x^2 -6x -10= x^4 +3x^3 +3x^2 -6x -10
###### Math and ArithmeticAlgebra
Copyright ยฉ 2020 Multiply Media, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.<|endoftext|>
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# Measures of Position in Statistics
In the last tutorials, we have learned about the measures of location and dispersion in detail. In this tutorial, we will learn about the measures of position – another technique for measuring dispersions.
Although the standard deviations are the widely used measure of dispersion that belongs to measures of location. But there are some other methods that also can be applied for measuring the dispersion or variation in a data set. That is the measure of position.
## What is Measures of Position?
The measure of position is actually a tactic for measuring dispersion in a data set. These measurements include quartiles, deciles, and percentiles.
Quartiles divide a set of data into four equal parts. In the quartiles measurement, as the observations are divided into four equals part that’s why it makes three breakdowns in the observations at the position of 25%, 50%, and 75%. And these breakdowns are labeled as Q1, Q2, and Q3.
Deciles divide a set of data into ten equal parts. In the deciles measurement, as the observations are divided into ten equals part that’s why it makes nine breakdowns in the observations at the position of 10%, 20%, 30%, … 90%. And these breakdowns are labeled as D1, D2, D3, …. D9.
Percentiles divide a set of data into a hundred equal parts. In the percentiles measurement, as the observations are divided into a hundred equals part that’s why it makes 99 breakdowns in the observations at the position of every percent (1%, 2%, 3%, …. 99%). And these breakdowns are labeled as P1, P2, P3, …. P99.
## Quartiles vs Deciles vs Percentiles
In the different scenarios of measurement, you will use different methods. When you will measure the average or central tendency of 25%, 50%, or 75%, then using the quartiles method is the best solution. In the same way, if you want to measure 10%, 20%, 70%, etc then obviously deciles will be the best approach.
And in the last situations, if you need to calculate the measures like 17%, 23%, 94%, etc then Percentile comes in handy in this case.
NOTE: Quartiles, deciles, and percentiles are only applicable for ungrouped and numerically sorted data set. Any unsorted data should be sorted before calculations.
## What is next?
In the next subsequent tutorials, we will learn about the quartiles, deciles, and percentiles in detail with their measurement rules, formula, and example math.
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How do you find the x and y intercepts on a graph?
How do you find the x and y intercepts on a graph?
To find the x-intercept of a given linear equation, plug in 0 for ‘y’ and solve for ‘x’. To find the y-intercept, plug 0 in for ‘x’ and solve for ‘y’.
What is the x-intercept in a formula?
To find the x-intercept of an equation, set the value equal to zero and solve for . Subtract from both sides.
How do you find the x-intercept when given two points?
Put the value of the slope in the expression of the line i.e. y = mx + c. Now find the value of c using the values of any of the given points in the equation y = mx + c. To find the x-intercept, put y = 0 in y = mx + c. To find the y-intercept, put x = 0 in y = mx + c.
What is x-intercept of a line?
The x intercept is the point where the line crosses the x axis. The y intercept is the point where the line crosses the y axis.
What is x-intercept example?
The x -intercepts of a function are the point(s) where the graph of the function crosses the x -axis. The x -intercept is often referred to with just the x -value. For example, we say that the x -intercept of the line shown in the graph below is 7 .
What is an example of a y-intercept?
The y -intercept of a graph is the point where the graph crosses the y -axis. When the equation of a line is written in slope-intercept form ( y=mx+b ), the y -intercept b can be read immediately from the equation. Example 1: The graph of y=34x−2 has its y -intercept at −2 .
How do you find y-intercept on a table?
When finding Y Intercept from a graph, you find the point where the graph of the equation crosses the y-axis. When finding Y Intercept from a table, you find the y-value when the x-value is equal to zero. If you do not know what the x-value is equal to when its zero, you must use the slope to go backward to find it.
What is the x-intercept variable?
In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y and an x-intercept is a point where the graph of a function or relation intersects with the x-axis of the coordinate system.
What is x-intercept format?
A linear equation has the form y = mx + b, where M and B are constants. The x-intercept is the point where the line crosses the x-axis. By definition, the y-value of a linear equation when it crosses the x-axis will always be 0, since the x-axis is stationed at y = 0 on a graph.
How do you solve for the x intercept?
Using the Equation of the Line Determine that the equation of the line is in standard form. The standard form of a linear equation is Ax+By=C{\\displaystyle Ax+By=C}. Plug in 0 for y{\\displaystyle y}. The x-intercept is the point on the line where the line crosses the x-axis. Solve for x{\\displaystyle x}.
What is the equation for x – intercept?
X-Intercept. A linear equation has the form y = mx + b, where M and B are constants. The x-intercept is the point where the line crosses the x-axis. By definition, the y-value of a linear equation when it crosses the x-axis will always be 0, since the x-axis is stationed at y = 0 on a graph. Consequently, to find a y-intercept,…
How do you Find X in an equation?
You can find “x” or solve the equation for “x” by isolating the “x” on one side of the algebraic equation. To solve for “x”, you need to understand the basic rules of algebraic operations. Isolate “x” on one side of the algebraic equation by subtracting the sum that appears on the same side of the equation as the “x.”.
How do find the y intercept?
Find the Y intercept. Press the “Trace” button. Press the “0” button. This will move the cursor to the Y intercept where X = 0. Look at the bottom of your screen; the Y-intercept will be displayed there.<|endoftext|>
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# How do you graph y=-x^2+4?
Apr 12, 2017
Point plotting or finding the vertex and axis of symmetry
#### Explanation:
Point plotting:
Create a table of $x$ and $y$ values.
Since $x$ is the independent variable in the equation ($y$ depends on the $x$ variables selected), you can select any $x$ value and find the corresponding $y$ value using the equation $y = - {x}^{2} + 4$
$\text{x|"-3"|"-2"|"-1"| "0"| "1"| "2"| "3"|}$
$\text{y|"-5"| "0"| "3"| "4"| "3"| "0"|"-5"|}$
Plot these points on a coordinate plane and connect the points with an arc.
Finding the vertex and axis of symmetry:
A parabola can be graphed easily when it is in the standard form/vertex form $y = a {\left(x - h\right)}^{2} + k$ where the vertex $= \left(h , k\right)$ and the axis of symmetry is $x = h$
First put the equation in general form $A {x}^{2} + B x + C = 0$
A negative $A$ value means the parabola opens downward, a positive $A$ value means the parabola opens upward.
$h = - \frac{B}{2 A}$
For $y = - {x}^{2} + 4 , \text{ " A = -1, B = 0, C = 4; " } h = \frac{0}{-} 2 = 0$
So the axis of symmetry is $x = 0$
$k = f \left(h\right) = f \left(0\right) = - {\left(0\right)}^{2} + 4 = 4$
So the vertex is $\left(0 , 4\right)$
graph{-x^2+4 [-12.66, 12.66, -6.33, 6.33]}<|endoftext|>
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Manufacturing materials are undergoing a huge change, particularly with the advent of composite materials that include components such as carbon fibre and graphene.
Composite materials have been around since mud and straw were mixed together to build ancient bricks. Concrete and fibreglass are also among the long line of materials that are stronger or more useful combined than in their constituent parts.
“The latest BMW I3 and I7, and about 50 per cent of the Boeing 787 are now made out of carbon fibre composites,” says Dr Nishar Hameed, a Group Leader at Swinburne’s Manufacturing Futures Research Institute and specialist in next generation of ‘smart’ polymers and composite materials.
“Carbon fibre based composites are used because they are eight times lighter than steel.”
These lighter materials for cars and planes – previously made from steel and aluminium – mean that the vehicles use less energy. The reduction in fuel use also reduces costs and carbon emissions. Naturally, the automotive, aerospace, mining, construction and other industries are all deeply interested in the potential of these materials.
Understanding smart composites
The next step is into smart composites.
“Most composites are not smart. They’re just ‘dumb’ materials that don’t share information,” says Dr Hameed.
“We can integrate sensors into smart materials so that we can learn about their performance, durability, structure and whether they are experiencing stress or damage. Smart materials are living materials.”
Graphene is the component that makes composite materials smart. A highly conductive nanomaterial, when graphene is embedded in steel, concrete or fabric – it can conduct electric signals, allowing it to act as a sensor.
Graphene made from graphite can be made into nano-platelets, which means it can be produced in high volume at low cost. The graphene can be added in small amounts to make nearly any composite conductive, sensing and smart.
Exploring the possibilities
Dr Lachlan Hyde, a research engineer, is excited about the possibilities.
“You can put them into liquids. You can paint it on the wall and turn your wall into a sensor. You can add it to carbon fibre and make that a sensing material as well. Think about an aeroplane that can give you real-time feedback on its aerodynamics,” he says.
“The material will be able to tell you about the performance of large structures,” confirms Dr Hameed.
“It will be able to predict when maintenance is required as well as when damage has occurred before it becomes critical.”
Abstract Submission Deadline: 15th of October, 2018<|endoftext|>
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Randomness is the lack of pattern or predictability in events. A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events (or "trials") is predictable. For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than haphazardness, and applies to concepts of chance, probability, and information entropy.
The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in probability theory and the various applications of randomness.
Randomness is most often used in statistics to signify well-defined statistical properties. Monte Carlo methods, which rely on random input (such as from random number generators or pseudorandom number generators), are important techniques in science, as, for instance, in computational science. By analogy, quasi-Monte Carlo methods use quasirandom number generators.
Random selection, when narrowly associated with a simple random sample, is a method of selecting items (often called units) from a population where the probability of choosing a specific item is the proportion of those items in the population. For example, with a bowl containing just 10 red marbles and 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10. Note that a random selection mechanism that selected 10 marbles from this bowl would not necessarily result in 1 red and 9 blue. In situations where a population consists of items that are distinguishable, a random selection mechanism requires equal probabilities for any item to be chosen. That is, if the selection process is such that each member of a population, of say research subjects, has the same probability of being chosen then we can say the selection process is random.
In ancient history, the concepts of chance and randomness were intertwined with that of fate. Many ancient peoples threw dice to determine fate, and this later evolved into games of chance. Most ancient cultures used various methods of divination to attempt to circumvent randomness and fate.
The Chinese of 3000 years ago were perhaps the earliest people to formalize odds and chance. The Greek philosophers discussed randomness at length, but only in non-quantitative forms. It was only in the 16th century that Italian mathematicians began to formalize the odds associated with various games of chance. The invention of the calculus had a positive impact on the formal study of randomness. In the 1888 edition of his book The Logic of Chance John Venn wrote a chapter on The conception of randomness that included his view of the randomness of the digits of the number pi by using them to construct a random walk in two dimensions.
The early part of the 20th century saw a rapid growth in the formal analysis of randomness, as various approaches to the mathematical foundations of probability were introduced. In the mid- to late-20th century, ideas of algorithmic information theory introduced new dimensions to the field via the concept of algorithmic randomness.
Although randomness had often been viewed as an obstacle and a nuisance for many centuries, in the 20th century computer scientists began to realize that the deliberate introduction of randomness into computations can be an effective tool for designing better algorithms. In some cases such randomized algorithms outperform the best deterministic methods.
Many scientific fields are concerned with randomness:
In the physical sciences
According to several standard interpretations of quantum mechanics, microscopic phenomena are objectively random. That is, in an experiment that controls all causally relevant parameters, some aspects of the outcome still vary randomly. For example, if a single unstable atom is placed in a controlled environment, it cannot be predicted how long it will take for the atom to decay—only the probability of decay in a given time. Thus, quantum mechanics does not specify the outcome of individual experiments but only the probabilities. Hidden variable theories reject the view that nature contains irreducible randomness: such theories posit that in the processes that appear random, properties with a certain statistical distribution are at work behind the scenes, determining the outcome in each case.
The modern evolutionary synthesis ascribes the observed diversity of life to random genetic mutations followed by natural selection. The latter retains some random mutations in the gene pool due to the systematically improved chance for survival and reproduction that those mutated genes confer on individuals who possess them.
Several authors also claim that evolution and sometimes development require a specific form of randomness, namely the introduction of qualitatively new behaviors. Instead of the choice of one possibility among several pre-given ones, this randomness corresponds to the formation of new possibilities.
The characteristics of an organism arise to some extent deterministically (e.g., under the influence of genes and the environment) and to some extent randomly. For example, the density of freckles that appear on a person's skin is controlled by genes and exposure to light; whereas the exact location of individual freckles seems random.
As far as behavior is concerned, randomness is important if an animal is to behave in a way that is unpredictable to others. For instance, insects in flight tend to move about with random changes in direction, making it difficult for pursuing predators to predict their trajectories.
The mathematical theory of probability arose from attempts to formulate mathematical descriptions of chance events, originally in the context of gambling, but later in connection with physics. Statistics is used to infer the underlying probability distribution of a collection of empirical observations. For the purposes of simulation, it is necessary to have a large supply of random numbers or means to generate them on demand.
Algorithmic information theory studies, among other topics, what constitutes a random sequence. The central idea is that a string of bits is random if and only if it is shorter than any computer program that can produce that string (Kolmogorov randomness)—this means that random strings are those that cannot be compressed. Pioneers of this field include Andrey Kolmogorov and his student Per Martin-Löf, Ray Solomonoff, and Gregory Chaitin. For the notion of infinite sequence, one normally uses Per Martin-Löf's definition. That is, an infinite sequence is random if and only if it withstands all recursively enumerable null sets. The other notions of random sequences include (but not limited to): recursive randomness and Schnorr randomness which are based on recursively computable martingales. It was shown by Yongge Wang that these randomness notions are generally different.
Randomness occurs in numbers such as log (2) and pi. The decimal digits of pi constitute an infinite sequence and "never repeat in a cyclical fashion." Numbers like pi are also considered likely to be normal, which means their digits are random in a certain statistical sense.
Pi certainly seems to behave this way. In the first six billion decimal places of pi, each of the digits from 0 through 9 shows up about six hundred million times. Yet such results, conceivably accidental, do not prove normality even in base 10, much less normality in other number bases.
In statistics, randomness is commonly used to create simple random samples. This lets surveys of completely random groups of people provide realistic data. Common methods of doing this include drawing names out of a hat or using a random digit chart. A random digit chart is simply a large table of random digits.
In information science
In information science, irrelevant or meaningless data is considered noise. Noise consists of a large number of transient disturbances with a statistically randomized time distribution.
In communication theory, randomness in a signal is called "noise" and is opposed to that component of its variation that is causally attributable to the source, the signal.
In terms of the development of random networks, for communication randomness rests on the two simple assumptions of Paul Erdős and Alfréd Rényi who said that there were a fixed number of nodes and this number remained fixed for the life of the network, and that all nodes were equal and linked randomly to each other.[clarification needed]
The random walk hypothesis considers that asset prices in an organized market evolve at random, in the sense that the expected value of their change is zero but the actual value may turn out to be positive or negative. More generally, asset prices are influenced by a variety of unpredictable events in the general economic environment.
Random selection can be an official method to resolve tied elections in some jurisdictions. Its use in politics is very old, as office holders in Ancient Athens were chosen by lot, there being no voting.
Randomness and religion
Randomness can be seen as conflicting with the deterministic ideas of some religions, such as those where the universe is created by an omniscient deity who is aware of all past and future events. If the universe is regarded to have a purpose, then randomness can be seen as impossible. This is one of the rationales for religious opposition to evolution, which states that non-random selection is applied to the results of random genetic variation.
Hindu and Buddhist philosophies state that any event is the result of previous events, as reflected in the concept of karma, and as such there is no such thing as a random event or a first event.
In some religious contexts, procedures that are commonly perceived as randomizers are used for divination. Cleromancy uses the casting of bones or dice to reveal what is seen as the will of the gods.
In most of its mathematical, political, social and religious uses, randomness is used for its innate "fairness" and lack of bias.
Politics: Athenian democracy was based on the concept of isonomia (equality of political rights) and used complex allotment machines to ensure that the positions on the ruling committees that ran Athens were fairly allocated. Allotment is now restricted to selecting jurors in Anglo-Saxon legal systems and in situations where "fairness" is approximated by randomization, such as selecting jurors and military draft lotteries.
Games: Random numbers were first investigated in the context of gambling, and many randomizing devices, such as dice, shuffling playing cards, and roulette wheels, were first developed for use in gambling. The ability to produce random numbers fairly is vital to electronic gambling, and, as such, the methods used to create them are usually regulated by government Gaming Control Boards. Random drawings are also used to determine lottery winners. Throughout history, randomness has been used for games of chance and to select out individuals for an unwanted task in a fair way (see drawing straws).
Sports: Some sports, including American football, use coin tosses to randomly select starting conditions for games or seed tied teams for postseason play. The National Basketball Association uses a weighted lottery to order teams in its draft.
Mathematics: Random numbers are also employed where their use is mathematically important, such as sampling for opinion polls and for statistical sampling in quality control systems. Computational solutions for some types of problems use random numbers extensively, such as in the Monte Carlo method and in genetic algorithms.
Medicine: Random allocation of a clinical intervention is used to reduce bias in controlled trials (e.g., randomized controlled trials).
Religion: Although not intended to be random, various forms of divination such as cleromancy see what appears to be a random event as a means for a divine being to communicate their will. (See also Free will and Determinism).
It is generally accepted that there exist three mechanisms responsible for (apparently) random behavior in systems:
- Randomness coming from the environment (for example, Brownian motion, but also hardware random number generators)
- Randomness coming from the initial conditions. This aspect is studied by chaos theory and is observed in systems whose behavior is very sensitive to small variations in initial conditions (such as pachinko machines and dice).
- Randomness intrinsically generated by the system. This is also called pseudorandomness and is the kind used in pseudo-random number generators. There are many algorithms (based on arithmetics or cellular automaton) to generate pseudorandom numbers. The behavior of the system can be determined by knowing the seed state and the algorithm used. These methods are often quicker than getting "true" randomness from the environment.
The many applications of randomness have led to many different methods for generating random data. These methods may vary as to how unpredictable or statistically random they are, and how quickly they can generate random numbers.
Before the advent of computational random number generators, generating large amounts of sufficiently random numbers (important in statistics) required a lot of work. Results would sometimes be collected and distributed as random number tables.
Measures and tests
There are many practical measures of randomness for a binary sequence. These include measures based on frequency, discrete transforms, and complexity, or a mixture of these. These include tests by Kak, Phillips, Yuen, Hopkins, Beth and Dai, Mund, and Marsaglia and Zaman.
Quantum Non-Locality has been used to certify the presence of genuine randomness in a given string of numbers.
Misconceptions and logical fallacies
Popular perceptions of randomness are frequently mistaken, based on fallacious reasoning or intuitions.
A number is "due"
This argument is, "In a random selection of numbers, since all numbers eventually appear, those that have not come up yet are 'due', and thus more likely to come up soon." This logic is only correct if applied to a system where numbers that come up are removed from the system, such as when playing cards are drawn and not returned to the deck. In this case, once a jack is removed from the deck, the next draw is less likely to be a jack and more likely to be some other card. However, if the jack is returned to the deck, and the deck is thoroughly reshuffled, a jack is as likely to be drawn as any other card. The same applies in any other process where objects are selected independently, and none are removed after each event, such as the roll of a die, a coin toss, or most lottery number selection schemes. Truly random processes such as these do not have memory, making it impossible for past outcomes to affect future outcomes. In fact, there is no finite number of trials that can guarantee a success.
A number is "cursed" or "blessed"
In a random sequence of numbers, a number may be said to be cursed because it has come up less often in the past, and so it is thought that it will occur less often in the future. A number may be assumed to be blessed because it has occurred more often than others in the past, and so it is thought likely to come up more often in the future. This logic is valid only if the randomisation is biased, for example with a loaded die. If the die is fair, then previous rolls give no indication of future events.
In nature, events rarely occur with perfectly equal frequency, so observing outcomes to determine which events are more probable makes sense. It is fallacious to apply this logic to systems designed to make all outcomes equally likely, such as shuffled cards, dice, and roulette wheels.
Odds are never dynamic
In the beginning of a scenario, one might calculate the probability of a certain event. The fact is, as soon as one gains more information about that situation, they may need to re-calculate the probability.
Say we are told that a woman has two children. If we ask whether either of them is a girl, and are told yes, what is the probability that the other child is also a girl? Considering this new child independently, one might expect the probability that the other child is female is ½ (50%). But by building a probability space (illustrating all possible outcomes), we see that the probability is actually only ⅓ (33%). This is because the possibility space illustrates 4 ways of having these two children: boy-boy, girl-boy, boy-girl, and girl-girl. But we were given more information. Once we are told that one of the children is a female, we use this new information to eliminate the boy-boy scenario. Thus the probability space reveals that there are still 3 ways to have two children where one is a female: boy-girl, girl-boy, girl-girl. Only ⅓ of these scenarios would have the other child also be a girl. Using a probability space, we are less likely to miss one of the possible scenarios, or to neglect the importance of new information. For further information, see Boy or girl paradox.
This technique provides insights in other situations such as the Monty Hall problem, a game show scenario in which a car is hidden behind one of three doors, and two goats are hidden as booby prizes behind the others. Once the contestant has chosen a door, the host opens one of the remaining doors to reveal a goat, eliminating that door as an option. With only two doors left (one with the car, the other with another goat), the player must decide to either keep their decision, or switch and select the other door. Intuitively, one might think the player is choosing between two doors with equal probability, and that the opportunity to choose another door makes no difference. But probability spaces reveal that the contestant has received new information, and can increase their chances of winning by changing to the other door.
- The Oxford English Dictionary defines "random" as "Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard."
- Third Workshop on Monte Carlo Methods, Jun Liu, Professor of Statistics, Harvard University
- Handbook to life in ancient Rome by Lesley Adkins 1998 ISBN 0-19-512332-8 page 279
- Religions of the ancient world by Sarah Iles Johnston 2004 ISBN 0-674-01517-7 page 370
- Annotated readings in the history of statistics by Herbert Aron David, 2001 ISBN 0-387-98844-0 page 115. Note that the 1866 edition of Venn's book (on Google books) does not include this chapter.
- Nature.com in Bell's aspect experiment: Nature
- "Each nucleus decays spontaneously, at random, in accordance with the blind workings of chance." Q for Quantum, John Gribbin
- Longo, Giuseppe; Montévil, Maël; Kauffman, Stuart (1 January 2012). No Entailing Laws, but Enablement in the Evolution of the Biosphere. Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation. GECCO '12. New York, NY, USA: ACM. pp. 1379–1392. arXiv:1201.2069. CiteSeerX 10.1.1.701.3838. doi:10.1145/2330784.2330946. ISBN 9781450311786.
- Longo, Giuseppe; Montévil, Maël (1 October 2013). "Extended criticality, phase spaces and enablement in biology". Chaos, Solitons & Fractals. Emergent Critical Brain Dynamics. 55: 64–79. Bibcode:2013CSF....55...64L. doi:10.1016/j.chaos.2013.03.008.
- Breathnach, A. S. (1982). "A long-term hypopigmentary effect of thorium-X on freckled skin". British Journal of Dermatology. 106 (1): 19–25. doi:10.1111/j.1365-2133.1982.tb00897.x. PMID 7059501.
The distribution of freckles seems entirely random, and not associated with any other obviously punctuate anatomical or physiological feature of skin.
- Yongge Wang: Randomness and Complexity. PhD Thesis, 1996. http://webpages.uncc.edu/yonwang/papers/thesis.pdf
- "Are the digits of pi random? researcher may hold the key". Lbl.gov. 23 July 2001. Retrieved 27 July 2012.
- Laszso Barabasi, (2003), Linked, Rich Gets Richer, P81
- Municipal Elections Act (Ontario, Canada) 1996, c. 32, Sched., s. 62 (3) : "If the recount indicates that two or more candidates who cannot both or all be declared elected to an office have received the same number of votes, the clerk shall choose the successful candidate or candidates by lot."
- Terry Ritter, Randomness tests: a literature survey. ciphersbyritter.com
- Pironio, S.; et al. (2010). "Random Numbers Certified by Bell's Theorem". Nature. 464 (7291): 1021–1024. arXiv:0911.3427. doi:10.1038/nature09008. PMID 20393558.
- Johnson, George (8 June 2008). "Playing the Odds". The New York Times.
- Randomness by Deborah J. Bennett. Harvard University Press, 1998. ISBN 0-674-10745-4.
- Random Measures, 4th ed. by Olav Kallenberg. Academic Press, New York, London; Akademie-Verlag, Berlin, 1986. MR0854102.
- The Art of Computer Programming. Vol. 2: Seminumerical Algorithms, 3rd ed. by Donald E. Knuth. Reading, MA: Addison-Wesley, 1997. ISBN 0-201-89684-2.
- Fooled by Randomness, 2nd ed. by Nassim Nicholas Taleb. Thomson Texere, 2004. ISBN 1-58799-190-X.
- Exploring Randomness by Gregory Chaitin. Springer-Verlag London, 2001. ISBN 1-85233-417-7.
- Random by Kenneth Chan includes a "Random Scale" for grading the level of randomness.
- The Drunkard’s Walk: How Randomness Rules our Lives by Leonard Mlodinow. Pantheon Books, New York, 2008. ISBN 978-0-375-42404-5.
|Wikiversity has learning resources about Random|
|Look up randomness in Wiktionary, the free dictionary.|
|Wikiquote has quotations related to: Randomness|
|Wikimedia Commons has media related to Randomness.|
- QuantumLab Quantum random number generator with single photons as interactive experiment.
- HotBits generates random numbers from radioactive decay.
- QRBG Quantum Random Bit Generator
- QRNG Fast Quantum Random Bit Generator
- Chaitin: Randomness and Mathematical Proof
- A Pseudorandom Number Sequence Test Program (Public Domain)
- Dictionary of the History of Ideas: Chance
- RAHM Nation Institute
- Computing a Glimpse of Randomness
- Chance versus Randomness, from the Stanford Encyclopedia of Philosophy<|endoftext|>
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Optional resources - Week 4
Here are some resources to help you develop your range of questioning techniques. Most of them can be found on the National STEM Learning Centre website. Sometimes registration is required to access specific files - this is quick and easy (and indicated below).
There’s a lot here that you could try out. For example, have a look at:
- Technique 2 – right is right
- Technique 3 – stretch it
- Technique 22 – Cold call
The book this is based on is Teach Like a Champion: 49 techniques that put students on the path to college by Doug Lemov (Jossey-Bass, 2010)
Concept Cartoons: Change of State and Insulation [Registration required]
Concept cartoons are a good way to promote group discussion, or you can use it as a hinge point question with students voting for the viewpoint they believe.
This concept cartoon explores student’s ideas about heat and insulation. A common misconception is that some materials have the property of making things warm. In this case because we have put coats on to keep warm there is a tendency to believe that the coat will also make the snowman warm so that it will melt quickly. In fact the coat acts as an insulator, reducing the movement of energy in either direction.
© National STEM Learning Centre<|endoftext|>
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A clinical trial is a carefully designed research study that uses volunteers to answer specific health questions, such as whether a medication, device or other intervention can improve health outcomes. The study protocol states the study’s purpose, goals of discovery and exactly how the research process must be implemented in each center where the clinical trial is taking place. To ensure that information gained from the study is reliable and valid, the protocol outlines how the= research is conducted safely and consistently.
There are three main types of clinical research studies: prevention trials, interventional trials and observational trials. Each type of study operates according to a protocol and requires informed consent from study participants – whether or not the research involves treatment of a diagnosed disease.
For information about clinical trials offered at UCLA Health, please visit clinicaltrials.ucla.edu.
Informed consent is the process by which potential study participants are given all of the information they need to determine whether or not they wish to voluntarily participate in a clinical trial. Informed consent is an ongoing and dynamic process that keeps participants informed of all study-related information throughout the research process. Potential study participants are educated about the purpose and duration of the study; required procedures; potential risks and benefits; and known side effects of intended treatment (if applicable). All consent-related information will be provided to potential participants in an informed consent form, which participants are given to sign if they so decide. A person is never obligated to participate in clinical research. The informed consent form is not a contract, and the participant may withdraw from the trial at any time – before or during the clinical trial.
There are many different kinds of clinical trials, each with a different design and purpose.
Screening trials may include new techniques for diagnosis, such as new types of diagnostic imaging or lab work that may identify certain genetic markers in people with a particular health issue. Screening trials may also look for ways to identify potential risks people may have for developing a particular health issue, such as brain cancer.
Observational clinical trials address health issues in large groups of people or populations in natural settings and do not involve assigned treatments or interventions. Observational clinical trials may investigate certain genetic factors, symptoms or quality of life for people who are affected by a specific health issues, like brain tumors.
Interventional clinical trials consist of treatment trials and prevention trials. Under strictly controlled circumstances, interventional clinical trials test whether experimental therapies or new formulations of already-approved treatments are safe and effective. They may also examine whether a drug or device is effective at preventing a specific illness or health issue.
Interventional clinical trials are divided into phases in order to extract safety information, determine efficacy and delineate whether or not a new treatment is as good as or better than the currently recognized standard of care. There are several phases of clinical trials.
Clinical trials are separated into four distinct phases.
Phase I clinical trials involving a potential new drug are designed to investigate the safety, side effects and appropriate dosage of a new investigational drug. Participants in phase 1 trials are carefully monitored through lab work, physical exams and imaging tests. If the initial cohort of study participants does not experience any dose-limiting toxicity (serious effects from the drug), the next group of participants then begins a higher dose, predetermined by the study protocol. This process continues until the maximum tolerated dose is identified.
Phase II clinical trials test drug effectiveness. During this phase, the drug or treatment is exposed to a larger number of participants – up to 100 people in some trials. In phase II trials, it is also possible to compare the new drug with another drug already in use, or with a placebo. Most importantly, phase II trials screen out ineffective treatments. If the results of a phase II trial indicate that a new drug is as effective as or more effective than an existing treatment, the new treatment proceeds to phase III.
Phase III clinical trials are large-scale studies that aim to prove that the new drug under investigation is safe, effective and non-inferior to the current standard of care. To do this, the drug is evaluated across a variety of factors, including drug tolerance, effectiveness and side effects, and compared against the same measures in the current standard of care. A secondary objective in a phase III trial is proving that the trial treatment is superior to the standard of care. Examples of treatment superiority include fewer side effects, better quality of life, improved survival, or even decreased need for monitoring. In a phase III trial, several hundred patients may be enrolled over several years and may sometimes involve thousands of patients across many different hospitals and even countries.
Phase IV clinical trials monitor for increased incidence of adverse events associated with a newly approved drug or device. This process is called pharmacovigilance. After a drug is found to be safe, effective and at least as good as the current standard of care, it then goes through a stringent approval process by the Food and Drug Administration (FDA). When the drug comes to market, there are additional observations made for safety reasons. These observations may include whether or not a drug is safe for use in children, pregnant women or nursing mothers, or in individuals with certain health concerns or who are taking other medications. Pharmacovigilance may also identify optimal use or additional uses of an FDA-approved drug.<|endoftext|>
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Diglossia is a situation where a language that has two forms, one a ‘higher' and more prestigious form used by educated speakers in formal situations, and the other a ‘lower', vernacular form used more commonly. Although English is not a diglossic language, it does have a wide variety of dialects, colloquial forms and levels of formality.
Greek, Arabic and Tamil are diglossic languages.
In the classroom
Teachers working with multi-lingual groups may find this is an interesting area to explore if there are learners in the class who speak diglossic languages. Learners can explain the different types of language and the roles they have in society and comparisons can be made with English.<|endoftext|>
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Authors: D. M. Christodoulou, S. G. T. Laycock, D. Kazanas
First Author’s Institution: Lowell Center for Space Science and Technology, University of Massachusetts Lowell, USA
Status: Accepted to MNRAS, open access
What are Be/X-ray Binaries?
Stars are like people — they act very different in company from the way they act alone. Interacting binaries are systems in which two stars orbit close together, so that their evolutions are intrinsically linked. They are the hosts of a plethora of astronomical phenomena: type Ia supernovae, millisecond pulsars, cataclysmic variables, common envelopes, and contact binaries are all only possible in interacting binary systems.
Among these systems are X-ray binaries. These are accreting binaries — systems in which material is flowing from the less massive star (the ‘donor’) onto the more massive star (the ‘accretor’). In the case of X-ray binaries, the star on which the matter is falling is a neutron star or black hole. The infalling material spirals towards the accretor, forming an accretion disc. Friction in the disc heats it up until it is hot enough to produce the bright X-rays that name this type of system. Similar accretion discs are seen throughout astronomy — in cataclysmic variables, active galactic nuclei, and protoplanetary systems, to name a few varieties — but are pretty hard to model, so there’s a great deal of interest in exploring the different varieties they come in.
In the standard X-ray binary model, material is pulled from the atmosphere of the donor star by the accretor’s gravity. Today’s paper is about Be/X-ray binaries, a special case in which the donor star is a Be-type star and the transferred material is a stellar wind. A Be star is a star spinning so fast that it throws some of its own matter off into space. Put a Be star into orbit around a neutron star, and some of that expelled matter will fall towards the neutron star — and voilà, you have your accretion. The orbits of these systems are often elliptical, meaning that at some points in their orbit the stars are close together (resulting in a higher accretion rate and an extra spurt of X-ray emission) and at others they are further apart (causing a dip in the X-ray emission).
If the accretor is a neutron star with a magnetic field, we also see pulses in the brightness of the system caused by the spinning of the neutron star’s magnetic field. This means we can measure how quickly the neutron star spins on its axis — its ‘spin period’. Pulsars spin quickly: the fastest stars in todays paper spin on their axes once every few seconds; the slowest, once every 30 minutes.
Slowing Down or Speeding Up?
The author’s of today’s paper compared results from a catalogue of Be/X-ray binaries in the Small Magellanic Cloud, all of which had their spin periods measured continuously between 1997 and 2014. Over that time, there were 53 binaries in which the spinning of the neutron star noticeably changed — either increasing or decreasing in period.
For those neutron stars whose spin is accelerating, there is a commonly accepted explanation. When the infalling material lands on the neutron star, it transfers any angular momentum it has to the star and spins it up. However, in the sample the authors were studying, they were surprised to find that nearly half of the neutron stars were ‘spinning down’ — their spin was decelerating. The surprise comes from the fact that we don’t know of any mechanism that can change the angular momentum of these stars as efficiently as the accretion process.
To investigate further, the authors compared the spin-up and spin-down rates as a function of the spin period of the neutron stars. You can see their results in Figure 2, in which is plotted the magnitude of the spin up/down against spin period. They found that both groups seem to follow the exact same pattern, but in opposite directions. A neutron star with a long spin period is likely to be either accelerating or decelerating sharply, whereas a neutron star with a short spin period is likely to have a much more gradual acceleration or deceleration. You could fit the same straight line through both populations in Figure 2.
The appearance of the same pattern in both groups of systems implies that the two populations must be linked, and that the processes driving their evolutions must be similar. This would mean that the accretion driving the spin-up in some systems must also drive the spin-down in others. The only way this could work is if those spinning-down systems have accretion discs spinning backwards — accretion discs that rotate in the opposite direction to the spin of the neutron star. The term for this is ‘retrograde’.
Such backwards-spinning accretion discs have been proposed before for a few individual systems, but never for Be/X-ray binaries. If it’s true, it could be very interesting for models of how these systems form and evolve, particularly if — as the authors suggest at the end of their paper — the accretion discs can switch between rotating with and against the neutron star. Today’s paper was only a short letter introducing the idea; it will be exciting to see where this goes next!<|endoftext|>
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Most South Floridians live on porous limestone rock blanketed with a few inches of soil, mere feet above sea level. This, coupled with gradually rising seas, has caused property owners to be rightfully concerned about flooding and property loss.
Over the past 100 years, sea level has risen approximately 8 inches globally. Over the next century, that could increase five-fold.
While flooding in urban areas is always a concern, most South Floridians are utterly unaware of the impact rising sea levels have on the natural landscape of the Everglades. This lack of awareness is, to some degree, understandable. A remarkably resilient ecosystem, the Everglades contains a variety of habitats adapted to a range of flooding from either freshwater or saltwater, so some may wonder why we should be concerned about sea level rise at all in the Everglades.
How the Everglades responds to rising sea levels is a bit complex. The Everglades is a flat, low- lying landscape with a gentle slope — about a 1.5 to 2-inch rise for every mile from the coast. The conventional thinking is that coastal habitats such as mangroves will gradually migrate up this gentle slope with increased penetration of saltwater into freshwater habitats.
This “landward migration” scenario, however, may not necessarily be the rule.
Cape Sable, a span of beach and freshwater wetland shielding the southwest coast of the Florida peninsula, may provide an instructive glimpse into a potential future scenario. In the 1920’s, the dredging of canals accelerated saltwater penetration into this freshwater marsh habitat.
The outcome was less like “landward migration” and more analogous to the land loss situation in coastal Louisiana.
When we deprive Everglades marshes of freshwater, organic soils (known as peat soils) decompose and disappear, resulting in a rapid loss of soil elevation. In severely dried areas, the soils also become vulnerable to fire. Freshwater plants die and soils begin to breakdown resulting in massive nutrient releases to nearshore habitats like Florida Bay.
Ultimately, the outcome is that collapsed areas created by soil loss are often too deep with saltwater for mangroves to become established. Instead, they remain open water habitats and eventually become seagrass habitats. This phenomenon has already shaped the coastlines of Biscayne and Florida Bays, and accelerating this process will also change the future coastline of the entire South Florida region whether we recognize it or not.
This process is particularly significant for the Everglades. Not only is it the source of our drinking water, it is also our most important protection from sea level rise and storm surge. By not offsetting this saltwater intrusion with restoration of freshwater flow, we are effectively leaving our back door open in a rising flood. For this reason and more, Everglades restoration should be our highest priority.
As for what the future South Florida will look like, excellent monitoring and modeling tools are available to us. We know what today and tomorrow – or perhaps even the next 20 years – will be like.
What will happen over the next 50 to 100 years is less certain.
Although South Florida won’t disappear into the sea anytime soon, there is a clear and growing need to educate citizens about the significance of incremental sea level rise. The first step is to acknowledge the problem.
Beyond that, we must continue to monitor changes in the ecosystems we depend on and prioritize the science needed to understand how future Floridians might be affected. While we don’t want to take too long, time and resources are needed to understand the sea level rise problem and develop the most advantageous options, strategies and solutions.<|endoftext|>
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# CAT 2021 Set-2 | Quantitative Aptitude | Question: 6
1 vote
47 views
For a real number $x$ the condition $|3x – 20| + |3x – 40| = 20$ necessarily holds if
1. $9 < x < 14$
2. $6 < x < 11$
3. $7 < x < 12$
4. $10 < x < 15$
retagged
1 vote
Given that, $|3x-20| + |3x-40| = 20 ; x \in \mathbb{R} \quad \longrightarrow (1)$
We know that $,|x| = \left\{\begin{matrix} x\;;&x\geq 0 \\ -x\;; &x<0 \end{matrix}\right.$
We can open mod as positive and negative. There are four such cases.
$\textbf{Case 1:}\;\text{ Positive, Positive}$
$\Rightarrow 3x – 20 + 3x – 40 = 20$
$\Rightarrow 6x – 60 = 20$
$\Rightarrow 6x = 80$
$\Rightarrow \boxed{x = \frac{40}{3} = 13.33}$
$\textbf{Case 2:}\;\text{ Positive, Negative}$
$\Rightarrow 3x – 20 – (3x – 40) = 20$
$\Rightarrow 3x – 20 – 3x + 40 = 20$
$\Rightarrow \boxed{20 = 20\; {\color{Green} {\text{(True)}}}}$
$\textbf{Case 3:}\;\text{ Negative, Positive}$
$\Rightarrow \;– (3x – 20) + 3x – 40 = 20$
$\Rightarrow\; – 3x + 20 + 3x – 40 = 20$
$\Rightarrow \boxed{- 20 = 20\;\color{Red}{\text{(False)}}}$
$\textbf{Case 4:}\;\text{ Negative, Negative}$
$\Rightarrow \;– (3x – 20) – (3x – 40) = 20$
$\Rightarrow \;– 3x + 20 – 3x + 40 = 20$
$\Rightarrow \;– 6x =\; – 40$
$\Rightarrow \boxed{x = \frac{20}{3} = 6.66}$
$\therefore$ $\boxed{7 < x < 12}$
Correct Answer $: \text{C}$
10.1k points 4 8 30
edited
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# The position x of a particle varies with time according to the relation $x={{t}^{3}}+3{{t}^{2}}+2t$. Find velocity and acceleration as functions of time.
Last updated date: 18th Sep 2024
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Hint: First derivative of function ‘x’ with respect to time gives velocity and double derivative of ‘x’ gives acceleration.
The position of the particle is given by variable x, and it varies according to time.
Given the relation$\Rightarrow x={{t}^{3}}+3{{t}^{2}}+2t-(1)$
To find the velocity, which is the rate of change of displacement.
The first derivative of Eqn(1) gives us the velocity and the second derivation will give the acceleration.
$\therefore$Velocity $=\dfrac{dx}{dt}$
\begin{align} & \overrightarrow{v}=\dfrac{d}{dt}\left( x \right)=\dfrac{d}{dt}\left( {{t}^{3}}+3{{t}^{2}}+2t \right) \\ & \Rightarrow \overrightarrow{v}=3{{t}^{2}}+2\left( 3t \right)+2 \\ & \overrightarrow{v}=3{{t}^{2}}+6t+2 \\ \end{align}
The unit of velocity is meter per second (m/sec).
$\therefore \overrightarrow{v}=\left( 3{{t}^{2}}+6t+2 \right)$m/sec.
To find acceleration, which is the rate of change of velocity.
Acceleration, $\overrightarrow{a}=\dfrac{d\overrightarrow{v}}{dt}$
\begin{align} & \overrightarrow{a}=\dfrac{d}{dt}\left( \overrightarrow{v} \right)=\dfrac{d}{dt}\left( 3{{t}^{2}}+6t+2 \right) \\ & \overrightarrow{a}=2\times \left( 3t \right)+6=6t+6 \\ \end{align}
The unit of acceleration is meter per second square $\left( m/{{\sec }^{2}} \right)$.
$\therefore$ $\overrightarrow{a}=\left( 6t+6 \right)m/{{\sec }^{2}}$
$\therefore$Velocity of the function, $\overrightarrow{v}=\left( 3{{t}^{2}}+6t+2 \right)$m/sec.
Acceleration of the function, $\overrightarrow{a}=\left( 6t+6 \right)m/{{\sec }^{2}}$
Note: We know velocity$=\dfrac{Displacement}{time}$and acceleration$=\dfrac{velocity}{time}$, here the velocity is taken as the rate of change of displacement w.r.t the time, so differentiation $\left( \dfrac{dx}{dt} \right)$is done.<|endoftext|>
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It is important to understand that we receive huge amounts of information through the senses of vision, hearing, touch, smell, taste and balance. The brain receives about 11 million bits of information each and every second of our waking day. However, we can only pay attention to around 70 to 80 bits per second, so one of the main functions of the brain is to filter, redirect or delete most information that comes in. Some people are not so good at this and either let too much information through or filter the wrong information out. This can lead to sensory overload and sensitivities, resulting in a range of difficulties, including sometimes 'autistic-like behaviour'. Much of this behaviour is simply a reaction to the unrelenting assault of information on the brain. Improve the sensory filtering and processing in the brain and behaviour will change for the better.
One of the ways the brain filters sensory input is by comparing the signals from the right ear and right field of vision, with those from the left ear and left field of vision. The brain uses these two separate and slightly different signals to, for instance, concentrate on a single sound source or limit our visual awareness. By training the brain to make better and faster connections between the two sides, it is possible to improve the filtering of sensory input, reduce sensitivities and boost attention.<|endoftext|>
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o Early Vedic Religion
o Birth of Hinduism
o Modern Hinduism
o Life and Philosophy of Buddha
o Forms of Buddhism
o Blurring Distinctions between Hinduism and Buddhism
o Religion and Government
Over time the beliefs of the Vedas transformed into a new religion called Hinduism. Some scholars believe that the evolvement of the Vedic religion into Hinduism was a response to the challenges of new competing religions, namely Buddhism and Jainism Whatever the case may be, Vedic religion adjusted to include new beliefs similar to some Buddhist ideas, as well as some aspects of the Dravidian culture. One of the new concepts was the idea of a tripartite godhead. Brahman remained an important part of Hinduism, but now present were Vishnu, the preserver, who incarnated into human forms on several occasions to help mankind, and Shiva, the destroyer. Another new concept was the idea of ethical and social responsibility, or dharma. The principle behind dharma was established in the Vedic age, but as Hinduism developed, it became even more important. The last and perhaps most important new concept that developed was the idea of reincarnation. Never before had the inhabitants of the area believed in the eternal nature of the soul. With the development of Hinduism came the belief in moksha, or liberation from the cycle of rebirths (Bulliet, p. 181-2).
Today Hinduism has spread to many different parts of the world other than India. It is believed that the religion developed in the part of the Indian subcontinent that is modern day Nepal, and in fact Nepal is the first country to establish a government with Hinduism as the official religion (Savada, 1991). While Hinduism is most dominant in its home region of South Asia, large populations of Hindus also live in the United States, Britain, South Africa, and many parts of Southeast Asia, including Indonesia (Ash, 1997, pp. 160-61). The idea of a system of castes has always faced opposition on some level, but in recent years the opposition has grown with the development of human rights organizations like Amnesty International, which mostly fight for the rights of the group known as Untouchables. The caste system has changed greatly over the last couple of centuries, and many modern Hindus regard it only as a formality. Countries where Hinduism is the main religion have long since outlawed discrimination against someone based on caste, but as in the United States, this law does not entirely eliminate discrimination (Daniel, 1999, online).
Buddhism began with the Indian prince Gautama Siddhartha, who was born around 563 B.C.E. into nobility and lived a very sheltered life. At the age of thirty, he left his wife, family, and wealth and turned to a life of meditation. His goal was to find the cause of suffering in the world. One day he was sitting under a tree when he had a realization. His epiphany led to what became known as the four noble truths. The first truth in Buddhism is that all life is suffering. The second truth is that the origin of suffering is desire. The third truth is the idea that suffering can be ended, and the fourth holds that suffering can only be ended by following the eightfold path, which involves right understanding, attitude, action, speech, conduct, effort, attention, and meditation. Siddhartha soon became known as the first Buddha, or enlightened one, and his teachings became known as Buddhism (Jansen, 2000. p.13).
After Buddha’s death, his followers had different ideas on how to interpret his teachings. These differences led to many different forms of Buddhism. The three main forms that still exist today are Theravada, or “the lesser vehicle,” Mahayana, or “the greater vehicle,” and Vajrayana, or “the diamond vehicle.” Each form more or less follows the original ideas of Buddha and the four noble truths, with slight variations in each form. For example, followers of Theravada Buddhism believe that anyone can attain enlightenment, while Mahayana Buddhism maintains that enlightenment can only be attained with the help of an experienced teacher (Jansen, p. 14). Despite the differences, all Buddhists believe in the idea of enlightenment through the eightfold path, which eventually leads to nirvana, or freedom from the cycle of rebirths, a concept also important to Hinduism.
In the early 1990s, Nepal was officially declared a Hindu state. Even though the Nepalese recognize Hinduism as the official religion, Buddhist and Hindu beliefs often combine to form one interfaith ideology. Many people who are regarded as Hindus could just as easily be considered Buddhists. Religious conflict may exist on some level, but it has never been a dominating factor because Hindus sometimes worship in Buddhist temples and vice versa. In many places, Buddhist and Hindu temples are built side by side. Although roughly 87% of the population proclaim themselves to be Hindu, the similarities between the two religions in this area are so subtle that few outsiders can tell the difference. Those who claim to be purely Buddhist are mostly concentrated in the eastern hills near Tibet (Savada, 1991). In general, the mutual respect Hindus and Buddhists feel towards each other in Nepal has helped to create a sense of social and political unity.
The constitution of Nepal was written in 1990. At first there was pressure from many groups to make Nepal a secular state, but the followers of Hinduism eventually won out the opposition to a Hindu state. Although Hinduism is the official religion, the constitution of Nepal aims to establish “harmony amongst the various castes, tribes, religions, languages, races, and communities (BBC, 1998). The government of Nepal is a monarchy, and despite the religious freedom that exists in Nepal, the constitution states that the king must be Hindu. The cow is considered sacred in Nepal, and, as in India, killing a cow is a crime. Again, the idea of cows as sacred is a Hindu philosophy. Although many of the laws of the Nepalese constitution are derived from Hindu religion, the Nepalese people have much religious freedom, and those who choose to engage in Buddhist worship are in no way looked down upon or persecuted.
The differences between Hinduism and Buddhism have often been more compelling to the followers of each religion than the similarities. On many occasions throughout history, tension has existed between Buddhists and Hindus. In fact, Buddhism has been almost completely eliminated in South Asia, the region of its birth, and exists today almost entirely in Southeast Asia. Nepal is an exception to this rule. In modern Nepal, Buddhists and Hindus not only live together and tolerate each other but also share common aspects of worship in many respects. In Nepal, like almost no place else in the world, exists not only a mutual respect for those who practice a different religion, but also a distinctive dual faith situation where two major traditional religions have combined to form one unique belief system.
Bulliet, R. (2001). The earth and its peoples(2nd edition). New York: Houghton Mifflin Company.
Jansen, E. (2000). The book of buddhas(7th edition). Havelte, Holland: Binkey Kok Publications.
Ash, R. (1997). Top 10 of everything. New York: DK Publishing, Incoporated.
Savada, A. (1991). Nepal: a country study. [Online]. Library of Congress. Available: http://memory.loc.gov/frd/cs/nptoc.html#np0056 [November 22, 2001].
Daniel, A. (1999). Caste system in modern India. [Online]. Available: http://adaniel.tripod.com/modernindia.htm [November 24,2001].
BBC. (1998). The Hindu kingdom of Nepal. [Online]. Available: http://www.bbc.co.uk/religion/religions/hinduism/features/nepal.shtml [November 22, 2001].
Andrea Westerbuhr, November 25th, 2001.<|endoftext|>
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### Theory:
The reduction in market price to increase the sale or to dispose of old goods is known as a discount.
Usually, discounts are express as a percentage of the marked price.
The customer or buyer pays the difference between the marked price and the discounted price.
Thus, we have $\mathit{Discount}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\mathit{Marked}\phantom{\rule{0.147em}{0ex}}\mathit{price}\phantom{\rule{0.147em}{0ex}}×\mathit{Discount}\phantom{\rule{0.147em}{0ex}}\mathit{percentage}$.
Example:
Suresh went to purchase a shirt which is discounted like 9 $$\%$$ of it's marked price which is $$₹$$209.
Can you find how much amount is discounted for the shirt that he bought?
We can apply the above formula to find the discount amount.
$\begin{array}{l}\mathit{Discount}\phantom{\rule{0.147em}{0ex}}\mathit{amount}=\phantom{\rule{0.147em}{0ex}}209×9%\\ \\ \mathit{Discount}\phantom{\rule{0.147em}{0ex}}\mathit{amount}=\phantom{\rule{0.147em}{0ex}}209×\frac{9}{100}\\ \\ \mathit{Discount}\phantom{\rule{0.147em}{0ex}}\mathit{amount}=\frac{1881}{100}\\ \\ \mathit{Discount}\phantom{\rule{0.147em}{0ex}}\mathit{amount}=₹\phantom{\rule{0.147em}{0ex}}18.81\end{array}$
Therefore $$₹$$18.81 amount has been discounted from the marked price of 209.
Now can you calculate for how amount Suresh bought that shirt?
Just subtract the marked price by the discounted amount.
That is, $209-18.81$ $$=$$ 190.19.
Therefore he bought the shirt for $$₹$$190.19.<|endoftext|>
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In addition to learning the alphabet and how books work, the path to reading and writing begins with talking! Research has revealed that there is a direct relationship between reading achievement and a child's level of vocabulary. When children learn to read, they draw upon the words they know and hear to make sense of the words they read.
When your child learns a new word, it isn't simply added to her list of known words. Each new word adjusts and refines the meaning and use of these known words. Although research is still exploring just how children develop such a large vocabulary, we know that children need an environment rich in language, filled with lots of words and talk. The type of talk, however, needs to be robust and engaging. Here are a few ideas about how to have rich talk time in your home:
- Establish a "talk time." While riding the bus, preparing breakfast, or during his bath, talk about topics important to your child. These will more than likely be stories about everyday life such as what someone did at school. Listen carefully, and try to use new words in your conversation.
- Read fiction and nonfiction books. Books are a wealth of new words. In addition to reading favorite stories, be sure to share informational children's books. Discussing the book together is also important.
- Play pretend. The talk that happens during playtime tends to be filled with very imaginative exchanges. This is a time to not only use new words but to think creatively about how we use language. The idea of a pink and purple peanut butter pie tends to only come up during playtime.
- Use rare words. Our talk with children is often filled with very common words such as "yes," "go," "wait," and "almost." We need to make sure our conversations are also filled with less common words such as "hurricane," "fortunate," "gloomy," and even "diesel gas."
Remember, a child's vocabulary grows quickly during the preschool and grade school years, although the rate of growth varies among children. Have fun and get talking!<|endoftext|>
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Boston Tea Party
May 10, 1773: Parliament passes the Tea Act;
December 16, 1773: Boston Tea Party;
On May 10, 1773, Parliament passed the Tea Act. The Tea Act was meant to save the East India Tea Company from bankrupcy. It allowed the East India Tea Company to send half a million pounds of tea to America subject only to a three cent per pound tax. This would allow it to undersell smuggled Dutch tea and legally imported tea. The tea was to be delivered to consignees in New York, Charleston, Philadelphia and Boston.
On October 16, the Philadelphia consignees were forced to resign by a committee of citizens. The New York consignees resigned when the Sons of Liberty called them enemies of America. The Charleston shipment arrived on December 2 and the consignees were forced to resign on December 3. The tea was impounded after the 20-day waiting period expired. Three Tea Act ships arrived in Boston on November 27, 1773.
Samuel Adams and the Sons of Liberty prevented the Boston ships from being unloaded. The ships agreed to leave without unloading the tea, but Royal Governor Thomas Hutchinson would not clear them to leave, because he was determined to uphold the law. As the end of the 20-day waiting period neared, the radical patriots decided that seizure would not be a solution either. They felt that the confiscated tea would be sold for customs expenses and thus the illegal tax would still have been paid.
To prevent the tea from being seized and sold, Samuel Adams organized the Boston Tea Party. On the night of December 16, the evening before the 20-day waiting period ending, several thousand colonists gathered near the wharf and encouraged sixty men who were thinly disguised as Mohawk Indians. The men boarded the three tea ships and dumped 342 chests of tea overboard. The tea was valued at over 90,000 pounds.
The Boston Tea Party inspired several other tea parties in New York (April 22, 1774), Annapolis, Maryland (October 19, 1774) and Greenwich, New Jersey (December 22). The British reacted to the Boston Tea Party with the Intolerable Acts, which included closing Boston Harbor and imposing martial law.
2. Boatner, Michael; Encyclopedia of the American Revolution
Topic Last Updated: 8/12/2001
Related Items Available at eBay - Scroll for additional items
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Lesson 2 of 10
by Debi West
Elements! Principles! Media! Art History! Techniques! Careers! In Gwinnett County, art educators have so many objectives to teach students that it can often feel daunting, especially when we consider the vast amount of art vocabulary they are required to master by the time final exams roll around!
With this in mind, I developed a lesson that springboards nicely off of the Sept. 2015 issue’s “Name Designs” that requires each student to design an artwork that defines and illustrates a visual-art vocabulary word.
After seeing the skill level of each intro 2-D art student, I assign them a vocabulary word from the list of words they need to know. Some of the words are simple and some are more complex and challenging. Our visual art vocabulary list is as follows, but you can certainly add more to this list depending on what your district requires:
aesthetic / analogous colors / architect /artist / balance /calligraphy /caricature/ cartoon / chalk /collage / color / complementary colors / composition / contour line / contrast / cool colors /crosshatching / design / elements of design / emphasis / fashion designer / figure ground / foreground / foreshortening / form / genre / graphic designer /harmony/ hatching / hue / implied line / intensity / interior designer / line / linear perspective / mosaic / movement / negative space / neutral colors / one-point perspective / opaque / optical mixing / organic shapes / outline / pattern / perspective /photography /picture plane /pigment / positive space / primary colors/ principles of design / proportion /radial balance /repetition / rhythm / saturation / secondary colors / shade / shape / space / split-complementary / subject matter / tempera / texture / three-dimensional / tint / triadic color scheme/ two-dimensional / two-point perspective / unity / value / vehicle / variety / warm colors / wash
Once students have been given their words, they have to do a bit of research. They have to find the definition, as they are required to creatively add the definition somewhere in their final piece. They need to see how the word is used in the context of visual art and they need to brainstorm ways they can turn the word into its meaning visually to help us build a type of “study guide” word wall in our art hallway.
I love the excitement in the room after students have received their words and they quickly get to work, looking them up and searching for interesting images they can manipulate to graphically illustrate the meanings. The initial sketches are always fascinating to see. After learning about media in their first lesson, and experiencing success with their Name Designs, the students are confident and excited to explore. They really rise to the challenge of this lesson and are ready to WOW!
They have a week to research, plan and create their final piece, which is done on 12″ x 18″ white drawing paper. Each student knows that most of these works will be hung in a semester-long exhibit, becoming a part of the “study-guide” word wall, which motivates them to work extra hard. They are hoping for that acknowledgement and pat on the back every student deserves when they give their best
Each year, our word wall exhibit gets stronger. And, due to these beautiful and well-thought-out works, our county assessment scores have risen. I believe our students learn and retain more when they learn it, create it and then SEE it every day. These visual vocabulary artworks are amazing, and the best part is that language arts teachers have come to us and asked us to help them teach this lesson to their students to prepare for the SAT! Just another great reason why the arts should be integrated into each and every subject!
Next up … Creative Contour Line Studies!
Debi West, Ed.S, NBCT, is Art Department Chair at North Gwinnett High School in Suwanee, Georgia. She is also an Arts & Activities Contributing Editor.
CLICK HERE for resources related to this article.<|endoftext|>
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What are Sequences in Music?
A sequence is the “more or less exact repetition of a passage at a higher or lower level of pitch”. (The Oxford Dictionary of Music, Kennedy, M.).
I am going to explain sequences in music by showing/playing you various examples.
Have a look/listen to the following example of a sequence:
This is a clear example of a sequence.
You can see how the short melodic phrase is played and then repeated at a higher level of pitch.
The same pattern is then repeated again at a higher pitch, etc..
Types of Sequences
There are 2 main types of sequence you will come across in music:
- Melodic Sequence – This is the repetition of a melody (like in the above example)
- Harmonic Sequence – This is a repetition of a series of chords (I will explain this later)
When the word “sequence” is used it generally implies that both melodic and harmonic material is being used.
Examples of Melodic Sequences
In a tonal sequence the intervals between the notes are altered to some extent.
The interval size usually stays the same (i.e. 4th, 5th, etc..).
However, the interval quality changes (e.g. a minor interval may become a major interval) This change in quality is inevitable if the composer wants the key to remain unchanged.
In our example of a sequence you can see that the interval sizes remain the same across the 2 melodies (3rd, 3rd, 2nd, 2nd in the 1st melody stay as 3rd, 3rd, 2nd, 2nd in the repeated melody):
However, the interval qualities change (major 3rd, minor 3rd, major 2nd, minor 2nd in the first melody become minor 3rd, major 3rd, major 2nd, major 2nd in the repeated melody):
These changes in quality continue through all 4 bars of the sequence and so our sequence example is a Tonal Sequence.
In a real sequence there is no change in either the size or quality of the intervals (this will usually mean that the composer has to change the key as the sequence progresses).
If we convert our example of a sequence into a real sequence it would look as follows:
You can see how we have converted the 2 “F” notes to “F sharp” notes so that the interval qualities remain the same.
The full sequence would look and sound like this:
Can you hear how the music sounds like it is changing key (modulating) as the sequence progresses?
A sequence that has several repetitions, some of which are tonal and some of which are real is called a Mixed Sequence.
In the example above you can see that the sequence between the 1st two bars is a real sequence, whilst the remaining bars are tonal sequences.
Examples of Harmonic Sequences
Descending Harmonic Sequences
Descending Circle-of-Fifths Sequence
This sequence gets its name from the fact that each successive chord has a root note that is a fifth lower than the previous chord.
Descending Thirds Sequence
In a descending thirds sequence the chords move down a third for each repetition, hence the name.
Ascending Harmonic Sequences
Ascending Circle-of-Fifths Sequence
In an ascending circle-of-fifths sequence each chord’s root is a 5th higher than the previous chord in the sequence.
Composing Using Sequences
Sequences are an excellent tool for composing music – I use them in a lot of the pieces I write.
You will find lots of examples of sequences in the music you listen to.
A famous example of a descending melodic sequence can be found in the well known Christmas carol “Ding Dong Merrily on High”.
Have a look/listen to this example below:
I hope you have found this lesson on sequences helpful.
My advice would be to try composing/improvising some short melodies and then experiment with repeating them at different transpositions.
I am sure that you will be pleasantly surprised by what you discover!
As always, if you have any questions, please feel free to contact me.<|endoftext|>
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As a candidate for the presidency in 1968, Richard Nixon campaigned in part on a promise to end the war in Vietnam. This speech, delivered eleven months after his inauguration, provided the details of his plan to withdraw the United States from the conflict. Although the military situation had improved for U.S. and South Vietnamese forces, domestic support for the war continued to erode. Echoing his predecessor Lyndon Johnson, Nixon spoke of the need to demonstrate American determination to keep its promises; otherwise, instability and violence would spread globally. He also announced a new policy: Vietnamization or the Nixon Doctrine. According to this policy, the United States would assist in the defense of other nations, but those nations would have to supply the manpower for their defense. The Nixon Doctrine was thus a return to something like the Truman Doctrine (Document 2). It showed a recognition that, contrary to the assumptions of earlier Cold War policies such as NSC 68 (Document 6), and the rhetoric of Kennedy’s Inaugural Address (Document 20), the United States did not have unlimited resources to fight the Cold War. Acknowledging the effect of the anti-war demonstrations and seeking a counterweight, Nixon finished his speech by evoking “the great silent majority of” Americans who, he hoped, would support his efforts to end the war on terms acceptable to the United States. In a swipe at war opponents, the president also remarked, “North Vietnam cannot defeat or humiliate the United States. Only Americans can do that.”
Source: Public Papers of the Presidents of the United States: Richard Nixon, 1969 (Washington, D.C.: U.S. Government Printing Office, 1971), 901–9. Available online at Richard Nixon Presidential Library and Museum. https://goo.gl/WwSY6R.
Good evening, my fellow Americans:
Tonight I want to talk to you on a subject of deep concern to all Americans and to many people in all parts of the world – the war in Vietnam.
. . .
. . . I would like to answer some of the questions that I know are on the minds of many of you listening to me.
How and why did America get involved in Vietnam in the first place?
How has this administration changed the policy of the previous administration?
What has really happened in the negotiations in Paris1 and on the battlefront in Vietnam?
What choices do we have if we are to end the war?
What are the prospects for peace?
Now, let me begin by describing the situation I found when I was inaugurated on January 20.
– The war had been going on for 4 years.
– 31,000 Americans had been killed in action.
– The training program for the South Vietnamese was behind schedule.
– 540,000 Americans were in Vietnam with no plans to reduce the number.
– No progress had been made at the negotiations in Paris and the United States had not put forth a comprehensive peace proposal.
– The war was causing deep division at home and criticism from many of our friends as well as our enemies abroad.
In view of these circumstances there were some who urged that I end the war at once by ordering the immediate withdrawal of all American forces.
From a political standpoint this would have been a popular and easy course to follow. . . .
. . . [but] I had to think of the effect of my decision on the next generation and on the future of peace and freedom in America and in the world.
Let us all understand that the question before us is not whether some Americans are for peace and some are against peace. The question at issue is not whether Johnson’s war becomes Nixon’s war.
The great question is: How can we win America’s peace?
Well, let us turn now to the fundamental issue. Why and how did the United States become involved in Vietnam in the first place?
Fifteen years ago North Vietnam, with the logistical support of Communist China and the Soviet Union, launched a campaign to impose a Communist government on South Vietnam by instigating and supporting a revolution.
In response to the request of the Government of South Vietnam, President Eisenhower sent economic aid and military equipment to assist the people of South Vietnam in their efforts to prevent a Communist takeover. Seven years ago, President Kennedy sent 16,000 military personnel to Vietnam as combat advisers. Four years ago, President Johnson sent American combat forces to South Vietnam. . . .
. . . Now that we are in the war, what is the best way to end it?
In January I could only conclude that the precipitate withdrawal of American forces from Vietnam would be a disaster not only for South Vietnam but for the United States and the cause of peace.
For the South Vietnamese, our precipitate withdrawal would inevitably allow the Communists to repeat the massacres which followed their takeover in the North 15 years before . . .
For the United States, this first defeat in our Nation’s history would result in a collapse of confidence in American leadership, not only in Asia but throughout the world. . . .
For these reasons, I rejected the recommendation that I should end the war by immediately withdrawing all of our forces. I chose instead to change American policy on both the negotiating front and battlefront.
In order to end a war fought on many fronts, I initiated a pursuit for peace on many fronts.
In a television speech on May 14, in a speech before the United Nations, and on a number of other occasions I set forth our peace proposals in great detail.
– We have offered the complete withdrawal of all outside forces within 1 year.
– We have proposed a cease-fire within 1 year.
– We have offered free elections under international supervision with the Communists participating in the organization and conduct of the elections as an organized political force. And the Saigon Government2 has pledged to accept the result of the elections. . . .
Hanoi3 has refused even to discuss our proposals. They demand our unconditional acceptance of their terms, which are that we withdraw all American forces immediately and unconditionally and that we overthrow the Government of South Vietnam as we leave. . . .
Well now, who is at fault?
It has become clear that the obstacle in negotiating an end to the war is not the President of the United States. It is not the South Vietnamese Government.
The obstacle is the other side’s absolute refusal to show the least willingness to join us in seeking a just peace. And it will not do so while it is convinced that all it has to do is to wait for our next concession, and our next concession after that one, until it gets everything it wants. . . .
Now let me turn, however, to a more encouraging report on another front.
At the time we launched our search for peace I recognized we might not succeed in bringing an end to the war through negotiation. I, therefore, put into effect another plan to bring peace – a plan which will bring the war to an end regardless of what happens on the negotiating front.
It is in line with a major shift in U.S. foreign policy which I described in my press conference at Guam on July 25. Let me briefly explain what has been described as the Nixon Doctrine – a policy which not only will help end the war in Vietnam, but which is an essential element of our program to prevent future Vietnams. . . .
. . . – First, the United States will keep all of its treaty commitments.
– Second, we shall provide a shield if a nuclear power threatens the freedom of a nation allied with us or of a nation whose survival we consider vital to our security.
– Third, in cases involving other types of aggression, we shall furnish military and economic assistance when requested in accordance with our treaty commitments. But we shall look to the nation directly threatened to assume the primary responsibility of providing the manpower for its defense.
. . .
The defense of freedom is everybody’s business – not just America’s business. And it is particularly the responsibility of the people whose freedom is threatened. In the previous administration, we Americanized the war in Vietnam. In this administration, we are Vietnamizing the search for peace.
. . . [T]he primary mission of our troops is [now] to enable the South Vietnamese forces to assume the full responsibility for the security of South Vietnam. . . .
. . . As South Vietnamese forces become stronger, the rate of American withdrawal can become greater. . . .
My fellow Americans, I am sure you can recognize from what I have said that we really only have two choices open to us if we want to end this war.
– I can order an immediate, precipitate withdrawal of all Americans from Vietnam without regard to the effects of that action.
– Or we can persist in our search for a just peace through a negotiated settlement if possible, or through continued implementation of our plan for Vietnamization if necessary – a plan in which we will withdraw all of our forces from Vietnam on a schedule in accordance with our program, as the South Vietnamese become strong enough to defend their own freedom.
I have chosen the second course.
It is not the easy way.
It is the right way . . .
And now I would like to address a word, if I may, to the young people of this Nation who are particularly concerned, and I understand why they are concerned, about this war.
I respect your idealism.
I share your concern for peace.
I want peace as much as you do . . .
I have chosen a plan for peace. I believe it will succeed.
If it does succeed, what the critics say now won’t matter. If it does not succeed, anything I say then won’t matter.
I know it may not be fashionable to speak of patriotism or national destiny these days. But I feel it is appropriate to do so on this occasion.
Two hundred years ago this Nation was weak and poor. But even then, America was the hope of millions in the world. Today we have become the strongest and richest nation in the world. And the wheel of destiny has turned so that any hope the world has for the survival of peace and freedom will be determined by whether the American people have the moral stamina and the courage to meet the challenge of free world leadership. . . .
And so tonight – to you, the great silent majority of my fellow Americans – I ask for your support. . . .
Let us be united for peace. Let us also be united against defeat. Because let us understand: North Vietnam cannot defeat or humiliate the United States. Only Americans can do that. . . .
A. Why does President Nixon not immediately end U.S. involvement in Vietnam’s war when he becomes president? According to the president, how and why did the United States become involved in Vietnam? What peace terms does he propose? Who is holding up an agreement? What is the Nixon Doctrine?
B. Compare this speech to Documents 29 and 31: does the United States still have the same goals in Vietnam in 1969 as it did in 1964 – 1965? Does the Nixon Doctrine show a change to the recommendations of Document 6 regarding U.S. support for its allies? If so, how might the war in Vietnam have brought about this change? Compare Nixon’s 1973 speech (Document 37) to this speech: does the United States achieve its goals when the war ends?
- Representatives of the United States and North Vietnam began meeting in Paris in 1968 to negotiate an end to the war, but little progress had been made by the time of President Nixon’s speech.
- The government of South Vietnam.
- The government of North Vietnam. Hanoi was its capital.<|endoftext|>
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Independence Day has a special place in my heart. The American Revolution was the core area of focus of my bachelors degree and is a passion that has continued post-collegiate studies. I’m so enamored by the romance of the time. People giving passionate, eloquent speeches about liberty and unalienable rights – ugh! I just gets me! Some of my favorite movies and tv shows center around this time (have you seen Turn?!) I eat up books and articles on the subject (always accepting recommendations). As a result, I love celebrating this amazing act of treason every year. Today, in honor of this glorious day, I’m sharing with you 7 fun Independence Day facts.
- July 4, 1776 wasn’t what you think it was. Independence from Britain was actually declared on July 2, 1776 but the language of the Declaration of Independence was approved by Congress two days later. The document wasn’t signed until August 2, 1776 with the last signature being added on November 4, 1776 by a representative from New Hampshire.
- The Revolutionary War had only just begun. On July 4, 1776, war had been raging between the Patriots and Red Coats for a little over a year. The war continued for seven more years! * Bonus Trivia: The “American Revolution” does not refer to the fighting that occurred, but rather the philosophical changes among the residents of the colonies against the King and British government. The fighting is referenced as the Revolutionary War or War for Independence.
- The Declaration of Independence was enacted to save their heads. Congress had been formally declared traitors by the British government. Facing charges of treason, these men drafted a document to immediately separate themselves from the King and thus, the legal authority of the British to execute them. Ironically enough, the act of signing the document was the ultimate treasonous offense.
- John Hancock was in charge. Everyone knows John Hancock for his large signature on the Declaration. However, did you also know that he was the first signature on the document because he was the President of the Continental Congress?
- Robert R. Livingston sent a proxy to sign the Declaration. Livingston was a member of the Committee of Five, the five men who were responsible for drafting the Declaration. He was a representative from New York but before he could sign the document, he was recalled by his state. His cousin Philip Livingston signed in his place.
- The first public reading of the Declaration was on July 8, 1776. The Liberty Bell was used to summon the public to Independence Square to hear Colonel John Nixon read the text of the Declaration. At the time, Nixon was militarily responsible for the protection of the city of Philadelphia and would later serve directly under George Washington.
- John Adams and Thomas Jefferson both died on a significant day. Adams and Jefferson were both members of the Committee of Five and eventually US Presidents. Even more interesting is they had a deep friendship that was often tumultuous due to their differing political views. However, remarkably so, Adams and Jefferson both passed away… on Independence Day 1826. True story! They both passed on July 4, 1826 – the 50th Anniversary of the Declaration of Independence
“My, Jen, those were quite interesting facts.”
I know! Share these with your friends over hot dogs and drinks (domestic only!) this holiday weekend!
Finally, for your viewing enjoyment… OneRepublic’s classic “Too Late to Apologize: A Declaration”.<|endoftext|>
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The exact cause of most mental illnesses is not known, but research suggests that a combination of the following factors may be involved.
- Heredity (genetics): Mental illness tends to run in families, which means the likelihood to develop a mental disorder may be passed on from parents to their children.
- Biology: Some mental disorders have been linked to special chemicals in the brain called neurotransmitters. Neurotransmitters help nerve cells in the brain communicate with each other.
- If these chemicals are out of balance or not working properly, messages may not make it through the brain correctly, leading to symptoms. In addition, defects in or injury to certain areas of the brain also have been linked to some mental illnesses.
- Psychological trauma: Some mental illnesses may be triggered by psychological trauma, such as
- severe emotional, physical or sexual abuse;
- an important early loss, such as the loss of a parent;
- Environmental stress: Stressful or traumatic events can trigger a mental illness in a person with a vulnerability to a mental disorder.<|endoftext|>
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## ◂Math Worksheets and Study Guides Kindergarten. Whole Numbers
### The resources above correspond to the standards listed below:
#### Ohio Common Core Standards
OH.CC.CC.K. Counting and Cardinality
Compare numbers.
CC.K.6. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.
CC.K.7. Compare two numbers between 1 and 10 presented as written numerals.
Count to tell the number of objects.
CC.K.4. Understand the relationship between numbers and quantities; connect counting to cardinality.
CC.K.4(a) When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
CC.K.4(b) Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
CC.K.4(c) Understand that each successive number name refers to a quantity that is one larger.
CC.K.5. Count to answer ''how many?'' questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.
Know number names and the count sequence.
CC.K.1. Count to 100 by ones and by tens.
CC.K.2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
OH.CC.G.K. Geometry
Analyze, compare, create, and compose shapes.
G.K.4. Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/''corners'') and other attributes (e.g., having sides of equal length).
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
G.K.1. Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.
G.K.2. Correctly name shapes regardless of their orientations or overall size.
OH.CC.MD.K. Measurement and Data
Classify objects and count the number of objects in each category.
MD.K.3. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.
Describe and compare measurable attributes.
MD.K.2. Directly compare two objects with a measurable attribute in common, to see which object has ''more of''/''less of'' the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
OH.CC.NBT.K. Number and Operations in Base Ten
Work with numbers 11-19 to gain foundations for place value.
NBT.K.1. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
OH.CC.OA.K. Operations and Algebraic Thinking
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
OA.K.1. Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
OA.K.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
OA.K.3. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
OA.K.4. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
OA.K.5. Fluently add and subtract within 5.<|endoftext|>
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Kwanzaa centers around Seven Principles, Nguzo Saba (En-GOO-zoh Sah-BAH), which represent the values of family, community and culture for Africans and people of African descent to live by. The principles were developed by Kwanzaa founder Dr. Maulana Karenga based on the ideals of the first-fruit harvests.
The principles are:
- Umoja (oo-MOE-jah) - Unity - Joining together as a family, community and race
- Kujichagulia (koo-jee-cha-goo-LEE-ah) - Self-determination - Responsibility for one's own future
- Ujima (oo-JEE-mah) - Collective Work and Responsibility - Building the community together and solving any problems as a group
- Ujamaa (oo-JAH-mah) - Cooperative Economics - The community building and profiting from its own businesses
- Nia (nee-AH) - Purpose - The goal of working together to build community and further the African culture
- Kuumba (koo-OOM-bah) - Creativity - Using new ideas to create a more beautiful and successful community
- Imani (ee-MAH-nee) - Faith - Honoring African ancestors, traditions and leaders and celebrating past triumphs over adversity
The principles are illustrated during the Kwanzaa festivities by the Seven Symbols.<|endoftext|>
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Memoni Grammar and Sentence Structure
It is generally recognized that the Memoni language is originate from an ancient Sindhi which is belongs to an Indo-Iranian (North-Western Zone) family of languages.
Like many Indian languages, Memoni nouns are either masculine or feminine and they could have singular and plural forms. The Memons borrow vast majorities of the nouns from Hindustani (mixture of Urdu & Hindi) languages
Nouns is a person, place or thing.
a man - akro maru ; she is a girl - ee akry chockery eye - that is my book - ee meji chopry eye
The pronouns are small words which substitute nouns, he, you, ours, themselves, some, each. In Memoni the pronouns are divided into fewer categories than English
1. Subject Pronouns:
Unlike in English, the 2nd person singular "You" is segregated a polite form use for a respect generally for a stranger, elderly and well respected persons including parent and relatives and the second is informal form use among the friends, parent and elderly relatives addressing to younger family members etc. Furthermore, the third person singular (he, she, it) and plural (they) including demonstrative pronouns (this these, those) are divided into two category one for near object and person and second for far object and person. (more research is needed to support this conclusion)
2. Other Pronouns:
In addition these pronouns are either masculine or feminine and must agree to the object noun.
Unlike English, the Memoni the proposition is generally comes after a noun or a verb
Pakistan may - in Pakistan
Adjectives are words that describe or modify another person or thing in a sentence
Like English, the position of Memoni adjectives nearly always appear
immediately before the noun that they modify.
ARTICLES, DETERMINERS AND QUANTIFIER:
Articles, determiners, and quantifiers are those little words that precede and modify nouns:
Determiners are used in front of nouns
to indicate whether you are referring to something specific or
something of a particular type.
bahuj kum too much work
Verbs carry the idea of being or action in the sentence.
In a Memoni sentence, a verb generally appears at the end of the sentence.
Memoni verb may vary (inflected) in form, (there are very few form) according to many factors, including its tense, aspect, mood and voice. It also agree with the person, gender, and/or number of some of its arguments (subject, object, etc.). Note more research may be needed.<|endoftext|>
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The exact origins of the Nauruans are unclear since their language does not resemble any other in the Pacific. Germany annexed the island in 1888. A German-British consortium began mining the island's phosphate deposits early in the 20th century. Australian forces occupied Nauru in World War I; it subsequently became a League of Nations mandate. After the Second World War - and a brutal occupation by Japan - Nauru became a UN trust territory. It achieved independence in 1968 and joined the UN in 1999 as the world's smallest independent republic.
limited natural freshwater resources, roof storage tanks collect rainwater but mostly dependent on a single, aging desalination plant; intensive phosphate mining during the past 90 years - mainly by a UK, Australia, and NZ consortium - has left the central 90% of Nauru a wasteland and threatens limited remaining land resources
blue with a narrow, horizontal, yellow stripe across the center and a large white 12-pointed star below the stripe on the hoist side; blue stands for the Pacific Ocean, the star indicates the country's location in relation to the Equator (the yellow stripe) and the 12 points symbolize the 12 original tribes of Nauru
Revenues of this tiny island traditionally have come from exports of phosphates. Few other resources exist, with most necessities being imported, mainly from Australia, its former occupier and later major source of support. In 2005 an Australian company entered into an agreement to exploit remaining supplies. Primary reserves of phosphates were exhausted and mining ceased in 2006, but mining of a deeper layer of "secondary phosphate" in the interior of the island began the following year. The secondary phosphate deposits may last another 30 years. The rehabilitation of mined land and the replacement of income from phosphates are serious long-term problems. In anticipation of the exhaustion of Nauru's phosphate deposits, substantial amounts of phosphate income were invested in trust funds to help cushion the transition and provide for Nauru's economic future. As a result of heavy spending from the trust funds, the government faced virtual bankruptcy. To cut costs the government has frozen wages and reduced overstaffed public service departments. Nauru lost further revenue in 2008 with the closure of Australia's refugee processing center, making it almost totally dependent on food imports and foreign aid. Housing, hospitals, and other capital plant are deteriorating. The cost to Australia of keeping the government and economy afloat continues to climb. Few comprehensive statistics on the Nauru economy exist with estimates of Nauru's GDP varying widely.
1 government-owned television station broadcasting programs from New Zealand sent via satellite or on videotape; 1 government-owned radio station, broadcasting on AM and FM, utilizes Australian and British programs (2009)<|endoftext|>
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Future Value of Sum with Continuous Compounding
Simple interest is easy to compute, but most of the time, we want our interest payments to be reinvested. For example, if you put money into your bank savings account, the bank routinely deposits the monthly or quarterly interest payments back into your account. During following periods, interest is earned on a higher balance. If the interest is reinvested, then, in later periods, interest is made on earlier interest. This is compound interest.
Virtually all of the calculations performed in finance assume that interest is compounded. We begin our study of compound interest by finding future balances over multiple periods with annual compounding.
Compound Interest: Future Value over One Year
As we saw in the introduction, if you make a $100 deposit into a bank that pays 5% interest once per year, you’ll have$105 at the end of 1 year. The formula for computing the balance after one period is given in the following equation:
\begin{align}& F{{V}_{1}}=P{{V}_{0}}\times (1+i) \\& F{{V}_{1}}=\100\times(1+0.05)=\105\\\end{align}
This calculation is shown on the timeline in Figure 1. At time period 0, we see a present value of 105. Notice the use of the subscripts in the above formula. The subscript denotes the point on the timeline when the cash flow occurs.
Figure 1: Future Value over a period of time
Compound Interest: Future Value over Two Years
Now suppose that you leave the deposit in the bank to compound for another year, without withdrawing any money. Using the above formula, the balance grows to 110.25: \begin{align}& F{{V}_{2}}=F{{V}_{1}}\times (1+i) \\& F{{V}_{2}}=\105\times(1+0.05)=\110.25\\\end{align} This calculation is shown under period 2 on the timeline in Figure 1. For the period of first year, the account earned5, but during the second year, it earned $5.25. The extra 5.00×0.05=$0.25)—it is compound interest. We can streamline these calculations by observing that FV1 is equal to PV0× (1+i) and then by substituting PV0× (1+i) for FV1 into the equation as given below:
\begin{align}& F{{V}_{2}}=P{{V}_{0}}\times (1+i)(1+i) \\& F{{V}_{2}}=P{{V}_{0}}\times {{(1+i)}^{2}} \\& F{{V}_{2}}=\100\times{{(1+0.05)}^{2}}\\&F{{V}_{2}}=\100\times1.1025=\110.25\\\end{align}
The process of calculating a future balance over multiple periods is termed as compounding because the investor is receiving compound interest.
Compound Interest: Future Value over Multiple Years
Similarly, each subsequent period of compounding increases the exponent by one. The equation to find the future value of a deposit is
$F{{V}_{n~}}=~P{{V}_{0}}~\times ~{{(1+i)}^{n}}$
Where
FVn=the future value of a deposit at the end of the nth period
PV0=the initial deposit
i=the interest rate earned during each period
n= the number of periods the deposit is allowed to compound
Let’s illustrate with an example.
Example 1: Future Value over Multiple Years
Suppose your grandfather gave you 1000 when you graduated from college. Instead of using it to buy clothes, you decided to invest it and to not touch the balance for 40 years, until you retire. If you managed to earn 10% per year, what is the future value of your investment? Solution To work out the future value of 1000 over 40 years compounded at 10: $F{{V}_{n}}=P{{V}_{0}}\times {{(1+i)}^{n}}$ \begin{align}&F{{V}_{40}}=\1,000\times{{(1.10)}^{40}}\\&F{{V}_{40}}=\1,000\times45.25926\\&F{{V}_{40}}=\45,259.26\\\end{align} Calculating Interest Earned For finding the interest earned, we subtract the principal (which is the original amount) from the ending balance as shown below: \begin{align}& Interest~earned=FV-PV \\& Interest~earned=\45,259.26-\1,000=\44,259.26\\\end{align} Simple and Compound Interest Compared If simple interest, rather than compound interest, had been earned in Example 1, then100 per year would have been earned 100. Over a period of 40 years, the total simple interest earned would have been 40 times $100 or$4,000. Since the total amount of interest earned was $44,259.26, the difference 4,000 of$40,259.26 was earned because of compounding. Put another way, \$40,259.26 in interest was earned on interest.
In this example, more interest was earned on the interest than was earned on the original principal! This is the magic of compound interest.
Compounding Rules of Thumb
Here are some rules that will help you think of the theory of compound interest in more meaningful ways.
Future balance increases if periods and/or interest rates increase.
First, as the number of compounding periods increases, the future balance increases. Second, as the interest rate increases, the future balance increases.
Compound interest theory applies to any growth.
One of the more important features of TVM calculations is that the methods can be applied to anything that grows. We can use the same equations to find future sales, if sales grow at a constant rate. The method can be applied to any constant growth situation, whether it be money, sales, profits, or dividends.
Any length of period can be used.
Time does not have to be measured in years. The formula can be used with any length period: days, weeks, months, quarters, or years. This period is called the compounding period or the conversion period. This period is the basic unit of time in all time value of money problems. However, whatever compounding period is used, the interest rate must be defined over the same period.<|endoftext|>
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Birds have been dealing with hurricanes for millions of years and have developed a remarkable ability to survive. Whether it is a type of ESP (extra sensory perception) or not, birds process acute sensory perceptions and sensitivities to changes in air pressure, vibrations and low frequency sound waves that alert them to weather changes such as a coming hurricane. Sensing a storm, birds either hunker down and ride it out, or flee. In some instances, they move in the wrong direction getting trapped inside a hurricane’s eyewall. Here they are forced to move with the storm until it losses strength or they become exhausted and land to ride out the remainder of the storm.
A couple weeks prior to Hurricane Matthew I watched in amazement a Ruby-throated Hummingbird alternately sitting on a small tree branch and flying back and forth to its feeder in 20 to 25 MPH wind. Hummingbirds, as with other song and woodland birds have specially adapted toes that automatically tighten around their perch. This enables them to hold on to branches when they sleep and in high wind. Birds also have the ability to fluff their feathers adding additional protection from the rain and cold. Woodpeckers and other cavity nesting birds may ride out storms in their cavities. However, in the high winds and driving rain of a hurricane such adaptations and behavior may help but can’t explain how they survive. Two days after Hurricane Matthew visited Seabrook Island. the same or perhaps another Rudy-throated Hummingbird was waiting on the same branch watching me put the feeder back up. Had he hunkered down somewhere close-by or flown out of harm’s way?
One of the most written about instances concerning a birds encounter with a hurricane is the story of Machi, a Whimbrel. Fitted with a satellite tracking tag in 2009, Machi had been followed for two years while making seven 2,000 mile trips between her breeding grounds near Hudson Bay to her wintering grounds in the Caribbean Sea. She had traveled a total of over 27,000 miles. Prior to being shot by a Guadeloupe hunter in 2011, Machi on her last trip was tracked traveling hundreds of miles out of her normal migration route as she skirted Tropical Storm Irene.
A tagged gannet approaching the southern shore of New Jersey as Hurricane Sandy made landfall there, made a sharp U-turn and headed back north toward Long Island and out to sea along the continental shelf where it waited out the storm. However not all birds go around a storm. In 2011 another tagged whimbrel, nicknamed Hope, was tracked flying through Tropical Storm Gert off the coast of Nova Scotia, entering at 7 MPH and emerging at nearly 90 MPH.
Shore and ocean-faring birds have been detected in recent years by polarization radar that were trapped in the center of a hurricane. Trying to fly away from the higher winds of such storms these birds enter the back edge and work their way to the calmer center. Here they become trapped, being forced to fly long distance without food or rest. Becoming exhausted, these birds are often forced to take refuge from the storm landing, particularly as the storm passes over a large lake or other water body, and ride-out the rest of the storm.
Called “hurricane birds”, these birds may be transported great distances. Coastal shore birds may be transported hundreds of miles inland and Caribbean Island species may flee to coastal areas of the United States. Birders frequently take advantage of this phenomena and search for new bird sighting following a hurricane. Many first area records occur at such times however unfortunately many of these translocated birds do not survive.
The most important impact of a hurricane on birds may be its impact on the environment. Flooding by a saltwater surge and/or freshwater flooding from accompanying rain may have dramatic short and long term impacts on vegetation. Beach erosion may destroy critical feeding and nesting areas of shore birds. Forest vegetation may be flattened and stripped of leaves making it uninhabitable to many birds. Fruits and berries, nuts, acorns, and other food sources may be lost. Many cavity dwelling birds such as woodpeckers and owls may lose nesting trees as they frequently snap off at the cavities.
In 1989, Hurricane Hugo resulted in the loss of nearly 60% of the remaining population of the endanger Red-cockaded woodpecker as a result of an estimated 90% of the trees with nesting cavities within the Francis Marion National Forest being flattened. The same storm resulted in the loss of 40% of all the known American eagle nests in South Carolina.
Hurricanes do kill birds and change the ecosystem, however, one animal’s loss is another’s gain and healthy populations do survive. Tree top dwelling birds may lose much of their habitat but those requiring lower, shrubby level vegetation such as the whip-poor-will will flourish. Fallen trees, branches and stripped leaves result in increased light and photosynthesis on the forest floor. As the fallen vegetation rots it fertilizes and simulates new growth creating important food sources. Fallen vegetation also creates millions of new nooks and crannies that will become home for many bird species and numerous other forest creatures.
Submitted by: Charles Moore<|endoftext|>
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Education
### Locating the Major Axis of an Ellipse: How-To Guide
You may be thinking, ‘Locating the major axis of an ellipse sounds complicated and time-consuming.’ But fear not, because with this step-by-step guide, you’ll be able to easily determine the major axis of an ellipse in no time.
Whether you’re a mathematics enthusiast or someone who simply wants to understand the concept, this guide will provide you with clear and concise instructions.
So, let’s dive in and explore the fascinating world of ellipses, uncovering the secrets to locating their major axis along the way.
## Understanding the Ellipse Shape
To understand the ellipse shape, imagine a flattened circle that’s stretched or compressed along its major axis. An ellipse is a geometric figure that resembles a closed curve. It’s formed by the set of all points in a plane, in which the sum of the distances from two fixed points, called foci, is constant. The major axis of an ellipse is the longest diameter, which passes through the two foci. This axis divides the ellipse into two equal halves, known as the minor axes. The major axis determines the overall length of the ellipse, while the minor axes determine its width.
When the major axis is stretched, the ellipse becomes elongated, appearing more like an oval shape. On the other hand, when the major axis is compressed, the ellipse becomes more circular in shape. The amount of stretching or compression along the major axis affects the eccentricity of the ellipse. An ellipse with a low eccentricity value is more circular, whereas an ellipse with a high eccentricity value is more elongated.
Understanding the ellipse shape is crucial in various fields, such as astronomy, engineering, and architecture. It allows for accurate measurements and calculations, as well as the design and construction of structures with elliptical shapes.
## Identifying the Center Point
To identify the center point of an ellipse, start by locating the central spot where the two axes intersect. This point is crucial in determining the symmetry and proportions of the ellipse.
### Central Point Identification
How can you accurately identify the center point of an ellipse?
To determine the center point, you need to examine the shape of the ellipse and locate its symmetry.
Start by drawing two imaginary lines that connect opposite points along the major axis of the ellipse. These lines, known as the conjugate diameters, will intersect at the center point.
Measure the distance between the intersection and any point on the ellipse along the major axis. Repeat this measurement for multiple points along the major axis to ensure accuracy.
The center point is where the measurements are equal.
### Locating the Central Spot
In order to accurately locate the center point of an ellipse, you must examine the shape of the ellipse and identify its symmetry. The center point of an ellipse is the point where the two axes intersect.
To identify this point, you need to look for the symmetry of the ellipse. An ellipse has two axes – the major axis and the minor axis. The major axis is the longest diameter of the ellipse and passes through the center point. The minor axis is perpendicular to the major axis and also passes through the center point.
### Finding the Center Point
Examine the shape of the ellipse and identify its symmetry to accurately locate the center point.
An ellipse has two axes: the major axis, which is the longest diameter, and the minor axis, which is the shortest diameter.
The center point of the ellipse is the midpoint of both axes and is the point of symmetry.
To find the center point, measure the major axis and minor axis, and then locate their midpoints. These midpoints will intersect at the center point of the ellipse.
Another way to find the center point is by drawing two lines across the ellipse that pass through opposite vertices. The point where these lines intersect is the center point.
## Determining the Semi-Major Axis Length
To determine the length of the semi-major axis of an ellipse, you need to focus on the longest distance across the ellipse. This distance is known as the major diameter. The major diameter passes through the center of the ellipse and is the line segment that connects two points on the ellipse’s circumference, which are farthest apart.
Once you have identified these two points, measure the length of the major diameter using a ruler or any other measuring tool.
To obtain the semi-major axis length, simply divide the length of the major diameter by 2. This is because the semi-major axis is half the length of the major diameter.
## Finding the Semi-Minor Axis Length
Now it’s time to determine the length of the semi-minor axis. This will allow you to accurately calculate the dimensions of the ellipse.
By understanding how to find the semi-minor axis length, you’ll be able to accurately represent the shape and proportions of the ellipse.
### Determining Minor Axis Length
To determine the length of the minor axis (or the semi-minor axis) of an ellipse, you can measure the distance from the center to the outermost point on the ellipse when it’s positioned vertically. This measurement will give you the length of the minor axis, which is the shorter diameter of the ellipse.
By measuring from the center to the outermost point, you’re essentially measuring the radius of the ellipse along its vertical axis. This is called the semi-minor axis because it’s half the length of the minor axis.
Remember to position the ellipse vertically for an accurate measurement.
Once you have determined the length of the minor axis, you can use it to calculate important properties of the ellipse, such as its area and circumference.
### Calculating Ellipse Dimensions
When determining the length of the minor axis of an ellipse, you can measure the distance from the center to the outermost point on the ellipse when it’s positioned vertically. This distance is known as the semi-minor axis length.
To calculate this length, you need to find the distance between the center of the ellipse and the outermost point on the shorter side. This can be done by measuring the vertical distance from the center to the topmost point and multiplying it by 2. Alternatively, you can also measure the vertical distance from the center to the bottommost point and multiply it by 2.
Either way, the result will give you the length of the semi-minor axis, which is an important dimension in understanding the shape and size of the ellipse.
## Plotting the Foci Points
You can plot the foci points of an ellipse by following a simple procedure. The foci points are essential in understanding the shape and orientation of an ellipse. To begin, you need to determine the length of the major and minor axes, as discussed in the previous section. Once you have these dimensions, finding the foci points is straightforward.
The foci points of an ellipse are located along the major axis, equidistant from the center. To calculate their positions, you first need to find the distance between the center and each focus point. This distance can be found using the formula c = √(a^2 – b^2), where ‘a’ is the length of the semi-major axis and ‘b’ is the length of the semi-minor axis.
To plot the foci points, measure the distance ‘c’ from the center along the major axis in both directions. Mark these points on the graph, and you’ll have successfully plotted the foci points of the ellipse.
## Drawing the Major Axis Line
Now let’s move on to drawing the major axis line, which is an important step in accurately representing the shape and orientation of the ellipse. The major axis is the longest line segment that passes through the center of the ellipse and connects two opposite points on its boundary, known as the vertices.
To draw the major axis line, you’ll need a ruler or a straight edge. Start by locating the center of the ellipse, which should have been determined in the previous step of plotting the foci points. Place your ruler or straight edge on the center point and align it with one of the foci points. Then, without moving the ruler, rotate it until it aligns with the other foci point. The ruler should now be parallel to the major axis.
Next, extend the ruler beyond the ellipse on both sides and lightly draw a line. This line represents the major axis of the ellipse. It should pass through the center and connect the two vertices of the ellipse. Make sure the line is straight and accurately represents the length of the major axis.
Drawing the major axis line helps visualize the orientation and proportions of the ellipse, making it easier to accurately depict the shape in your drawings or designs.
## Measuring the Major Axis Length
To measure the length of the major axis, simply place a ruler or measuring tool along the line connecting the two vertices of the ellipse. Ensure that the ruler is aligned perfectly with the line, and that it’s securely positioned to avoid any movement during the measurement process. Make sure the ruler is long enough to span the entire length of the major axis.
Starting from one vertex, read the measurement at the other vertex. The measurement on the ruler represents the length of the major axis. Be accurate and precise in your reading to obtain a reliable measurement.
If the major axis isn’t aligned horizontally or vertically, you may need to use a protractor or angle measuring tool to determine the angle at which the major axis is inclined. This will help you align the ruler correctly and obtain an accurate length measurement.
Remember that the major axis is the longest diameter of the ellipse, so it’s important to measure it carefully. Any inaccuracies in the measurement may affect further calculations or analysis involving the ellipse.
Once you have obtained the measurement, record it for future reference or use in any relevant calculations.
## Verifying the Major Axis With the Minor Axis
To verify the major axis, compare it with the length of the minor axis. By doing this, you can ensure that you have correctly identified the major axis of the ellipse.
The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter. To verify if you have correctly located the major axis, you need to compare its length with the length of the minor axis.
If the major axis is indeed the longest diameter, its length should be greater than the length of the minor axis. Measure both axes accurately using a ruler or measuring tape, making sure to measure from one end to the other.
Once you have obtained the measurements, compare the lengths. If the major axis is longer than the minor axis, then you have successfully verified the major axis. However, if the minor axis happens to be longer, you may need to re-evaluate your measurements and locate the major axis again.
## Applying the Major Axis in Real-Life Scenarios
You can apply the major axis of an ellipse in various real-life scenarios to analyze and understand different phenomena.
One practical application is in astronomy, where the major axis of an elliptical orbit helps determine the distance between celestial bodies. By studying the major axis, astronomers can calculate the period and speed of planets or other objects orbiting around a larger body like a star. This information is crucial for predicting and understanding celestial events such as eclipses.
Another real-life scenario where the major axis is utilized is in engineering. For example, when designing bridges or tunnels, engineers need to consider the major axis of the structure to ensure stability and structural integrity. By understanding the major axis, engineers can determine the maximum load-bearing capacity and make informed decisions about the materials and design of the structure.
The major axis of an ellipse also finds applications in fields such as optics and architecture. In optics, the major axis helps determine the focal point of an ellipsoidal mirror or lens, which is essential for directing and focusing light. In architecture, the major axis can be used to create aesthetically pleasing and balanced designs, such as in the layout of buildings or gardens.
## Troubleshooting Common Issues
In troubleshooting common issues related to the major axis of an ellipse, it’s important to identify and address any potential deviations or malfunctions that may arise in real-life applications.
One common issue that may occur is an incorrect determination of the major axis length. This can happen due to measurement errors or inaccuracies during the data collection process. To troubleshoot this issue, double-check all measurements and ensure they’re accurate and precise. Additionally, it’s crucial to verify that the center point of the ellipse is correctly identified, as any deviation in its placement can affect the accuracy of the major axis.
Another common issue is the misalignment of the major axis with the desired orientation. This can occur due to errors in inputting the angle or misinterpretation of the orientation requirements. To troubleshoot this issue, carefully review the instructions and ensure the correct angle is used when locating the major axis.
Lastly, if the major axis appears distorted or irregular, it could be a result of a malfunction in the imaging or measurement equipment. In such cases, it’s recommended to check for any equipment malfunctions, recalibrate if necessary, or seek professional assistance if the issue persists.
### Can the Major Axis of an Ellipse Be Longer Than the Minor Axis?
Yes, the major axis of an ellipse can be longer than the minor axis. This occurs when the ellipse is elongated horizontally or vertically, depending on the orientation.
### How Do You Calculate the Distance Between the Foci Points of an Ellipse?
To calculate the distance between the foci points of an ellipse, you can use the formula: distance = 2 * square root of (a^2 – b^2), where a is the length of the major axis and b is the length of the minor axis.
### Are There Any Practical Applications for Determining the Major Axis of an Ellipse?
There are various practical applications for determining the major axis of an ellipse. For example, in architecture, it can help in designing curved structures, or in astronomy, it can aid in calculating orbital paths.
### What Are Some Common Mistakes People Make When Locating the Major Axis of an Ellipse?
When locating the major axis of an ellipse, common mistakes include not properly identifying the foci, using incorrect measurements, and neglecting to consider the orientation of the ellipse. Pay attention to these details for accurate results.
### Is It Possible to Determine the Major Axis Length of an Ellipse Without Knowing the Coordinates of the Foci Points?
Yes, it is possible to determine the major axis length of an ellipse without knowing the coordinates of the foci points. You can do this by measuring the distance between the farthest points on the ellipse.
## Conclusion
In conclusion, understanding how to locate the major axis of an ellipse is essential for various real-life scenarios.
By identifying the center point, determining the semi-major and semi-minor axis lengths, and plotting the foci points, we can accurately measure the major axis length.
Verifying the major axis with the minor axis ensures accuracy in our calculations.
By applying these techniques, we can confidently utilize the major axis in practical applications.<|endoftext|>
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# How does the force of attraction between electric charges increase?
Contents
In electrostatics, the electrical force between two charged objects is inversely related to the distance of separation between the two objects. … And decreasing the separation distance between objects increases the force of attraction or repulsion between the objects.
## What causes electrical force to increase?
If the quantity of charge on either one of the objects is increased, then the force will be increased. And by whatever factor the quantity of charge is increased, the force is increased by that same factor. If the quantity of charge is made four times bigger, the force will be four times bigger.
THIS IS UNIQUE: Do Indian passport holders need visa for Brazil?
## Does electric force increase with charge?
According to Coulomb, the electric force for charges at rest has the following properties: Like charges repel each other; unlike charges attract. … If the charges come 10 times closer, the size of the force increases by a factor of 100. The size of the force is proportional to the value of each charge.
## What are the factors affecting the force between two electric charges?
As we’ll discuss in this lesson, he found that the force between charged particles was dependent on only two factors: the distance between the particles and the amount of electric charge that they carried.
## How does increasing the distance between charged objects affect the electric force between them?
How does increasing the distance between charged objects affect the electric force between them? The electric force decreases because the distance has an indirect relationship to the force.
## How do the charge quantities affect the force between charges?
Explanation: Electrostatic force is directly related to the charge of each object. So if the charge of both objects is doubled, then the force will become four times greater. Four times 0.080 N is 0.320 N.
## How does charging by conduction occur?
Describe charging by conduction. A charged object (source) is brought near a neutral object and the neutral object becomes polarized. … Another neutral object (or ground) is brought in contact with the polarized object and the charges are transferred to the neutral object (or ground).
## What is the relation between electric force and electric field?
Electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge.
## How will the electrical force between the charges compared with the original force?
If the distance between two charges is increased to three times the original distance, how will the electrical force between the charges compare with the original force? It will decrease to one-ninth the original force.
## What happens to the electric force when two charges are brought closer together?
The force between them increases. … If the charges are kept constant in magnitude, reducing the distance between them (bringing them closer together) increases the force between them.
## Which change increases the electric force between objects?
Electric forces between two charged objects increases with increasing separation distance. Electric forces between two charged objects increases with increasing quantity of charge on the objects.
## What factors affect electrical forces and how do they affect the magnitude of the force between charged bodies?
Experiments with electric charges have shown that if two objects each have electric charge, then they exert an electric force on each other. The magnitude of the force is linearly proportional to the net charge on each object and inversely proportional to the square of the distance between them.
## Which differences would increase the magnitude of the electric force between two charges?
The further away two charged objects are the weaker the electrical force between them. The closer two charged objects are the stronger the electrical force between them. … Two objects with identical charges are placed a distance d from one another. The force between the objects is measured as F.
THIS IS UNIQUE: Best answer: How long does it take to get a UK visa after submission?
## Which change increases the electric force between objects quizlet?
Which change increases the electric force between objects? Electrons are added to two negatively charged objects.
## How does the electrical force relate to the charge of an object?
How does the electrical force relate to the charge of an object? It is directly proportional to the charge. … The electrical force is 1.2 × 1036 times greater than the gravitational force, but only the gravitational force is attractive. A positive charge, q1, of 5 µC is 3 × 10-2 m west of a positive charge, q2, of 2 µC.
## What happens to the force between two charges of their separation distance is quartered?
Explanation: The force between the two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Hence, if distance between charges is halved (charges remaining kept constant), the force between the two charges is quadrupled.<|endoftext|>
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Bound Neutrons Pave Way to Free Ones
NEWPORT NEWS, VA. - A study of bound protons and neutrons conducted at the Department of Energy's Thomas Jefferson National Accelerator Facility has allowed scientists, for the first time, to extract information through experimentation about the internal structure of free neutrons, without the assistance of a theoretical model. The result was published in the Feb. 4 issue of Physical Review Letters.
The major hurdle for scientists who study the internal structure of the neutron is that most neutrons are bound up inside the nucleus of atoms to protons. In nature, a free neutron lasts for only a few minutes, while in the nucleus, neutrons are always encumbered by the ubiquitous proton.
To tease out a description of a free neutron, a group of scientists compared data collected at Jefferson Lab and the SLAC National Accelerator Laboratory that detail how bound protons and neutrons in the nucleus of the atom display two very different effects. Both protons and neutrons are referred to as nucleons.
"Both effects are due to the nucleons behaving like they are not free," says Doug Higinbotham, a Jefferson Lab staff scientist.
Nucleons appear to differ when they are tightly bound in heavier nuclei versus when they are loosely bound in light nuclei. In the first effect, experiments have shown that nucleons tightly bound in a heavy nucleus pair up more often than those loosely bound in a light nucleus.
"The first thing was the probability of finding two nucleons close together in the nucleus, what we call a short-range correlation," says Larry Weinstein, a professor at Old Dominion University. "And the probability that the two nucleons are in a short-range correlation increases as the nucleus gets heavier."
Meanwhile, other experiments have shown a clear difference in how the proton's building blocks, called quarks, are distributed in heavy nuclei versus light nuclei. This difference is called the EMC Effect.
"People were measuring and discussing the EMC effect. And people were discussing things about the short-range correlations effect. Nobody bothered to look to see if there's any connection between them," adds Eliezer Piasetzky, a professor at Tel Aviv University in Israel.
When the group combined the data from a half-dozen experiments regarding these two different effects on one graph, they found that the two effects were correlated.
"Take a quantity that tells you how strong the EMC Effect is. And then take another quantity that tells you how many short-range correlations you have," Higinbotham explains. "And you see that when one is big, the other one is big. When one is small, the other one is small."
The scientists say that it's unlikely that one effect causes the other. Rather, the data shows that there is a common cause for both.
"I think that we certainly agree that from the position picture, it's due to nucleons overlapping that is causing this. And in the momentum picture, it is the high-momentum nucleons that are causing this. And, of course, it's quantum mechanics, so choose your picture," Higinbotham explains.
The group says the common cause may have remained a mystery for so long, because while the two effects they are studying are obviously related when laid out on a graph, the connection was previously obscured by the different, yet related ways in which the two effects are studied.
"When you do a measurement for the EMC Effect, what you do is you look inside the nucleon. You break open the nucleon and see inside. What happens inside the nucleon is very different from the short-range correlations, which is what happens between two different nucleons," Piasetzky says.
"What's very new here is that we have linked two fields that were completely disconnected. So now you can start asking questions about what that connection can help us learn," Higinbotham says.
They say the next step is to further compare the data from all of the source experiments that they used in their analysis to see if data for one effect may now be used to learn something new about the other. Then, of course, they'd like to use the knowledge that the two effects are connected to design new experiments for shining a light on other secrets buried in the nucleus of the atom.
This work was supported in part by the DOE Office of Science, the National Science Foundation, the Israel Science Foundation, and the U.S.-Israeli Bi-National Science Foundation.
For Further Reference:
SRC Paper: Probing Cold Dense Nuclear Matter
For non-scientists: Protons Pair Up With Neutrons
EMC Effect Paper: New Measurements of the European Muon Collaboration Effect in Very Light Nuclei
For non-scientists: Proton's party pals may alter its internal structure
Contact: Kandice Carter, Jefferson Lab Public Affairs, 757-269-7263, [email protected]
Jefferson Science Associates, LLC, a joint venture of the Southeastern Universities Research Association, Inc. and PAE, manages and operates the Thomas Jefferson National Accelerator Facility, or Jefferson Lab, for the U.S. Department of Energy's Office of Science.
DOE’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of the most pressing challenges of our time. For more information, visit https://energy.gov/science.<|endoftext|>
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It is about identifying with the feelings of others and especially with their suffering.
Compassion is rooted in empathy.
It begins by recognising in ourselves the emotions that others are feeling and how we would feel in the same circumstance, in other words we get to manage our emotions in relation to that of other people around us.
Compassion is more than empathy; it is the living expression of the Golden Rule, to treat others as you would have them treat you. Compassion is the practice of empathy.
Many of the problems that young people face are rooted in the lack of compassion. Bullying, violence, emotional abuse, social exclusion and prejudices based on ethnicity, culture and other differences are all fuelled by failures of empathy.
In the bigger and adult world as it becomes more interdependent, cultivating compassion is a moral and a practical imperative, as well as a spiritual.
Practising compassion is the truest expression of our common humanity and a deep source of happiness in ourselves and others. In schools like elsewhere, compassion has to be practised, not preached.
As educators, our job description is very fluid, we have so much to do.
Everyday is a new beginning.<|endoftext|>
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## Lesson Tutor: Math Review for ACT College Entrance Exam
/ Lesson Tutor: Math Review for ACT College Entrance Exam
Math Review for ACT College Entrance Exam
Part I – The Review
by Elaine Ernst Schneider
1. If x + 6 = 9, then 3x + 1 = ?
Answer choices: (A) 3 (B) 9 (C) 10 (D) 34 (E) 46
Let’s think it through. Choice A is to tempt you into a quick (wrong) decision. When you solve for x in the first equation (x + 6 = 9) you get 3, which is choice A.
But that is not the question. You must go on to the second part of the question (3x + 1 = ?) Always be careful on two-part questions.
Substitute 3 for the x in the 2nd equation. 3x + 1 = ?. Therefore,
3(3) + 1 = 10.
Choice C is the correct answer.
2. If x > 1, which of the following decreases as x decreases?
I. x + x²
II. 2x² – x
III. __1__
x + 1
Answer choices: (F) I only (G) II only (H) III only (J) I & II only (K) II & III
The easiest way to solve this problem is to work from the answers, eliminating the wrong answers. Substitute a simple number you can work with quickly.
I. x + x² (substitute 2 for x)
2 + 2² = 6
x + x² (substitute 3 for x)
3 + 3² = 12
We know that I does what the question asks. We can see that x decreases as the equation decreases. However, the choices give us the possibility of I & II, so we must check out II as well.
II. 2 x² – x (substitute 2 for x)
2 (2² ) – 2 = 6
2 x² – x (substitute 3 for x)
3 (3² ) – 3 = 24
Again, this does what the questions asks. We can see that x decreases when x is decreased.
The correct answer is J: I & II only
3. Barney can mow the lawn in 5 hours, and Fred can mow the lawn in 4 hours. How long will it take them to mow the lawn together?
(A) 1 hour (B) 2 2/9 hour (C) 4 hours (D) 4 ½ hours (E) 5 hours
We must set up a formula that determines both Barney and Fred’s work for one hour. From this, we can then determine their work potential together. The formula for this problem would be set up as follows:
1/5 (Barney working 1 hour) + ¼ (Fred working 1 hour) = 1/x (Both working 1 hour)
Find a common denominator:
4/20 + 5/20 = 1/x
9/20 = 1/x
9x = 20
x = 2 2/9
Even if you weren’t able to figure out the appropriate formula, common sense would help you eliminate some of the answers. For example, if Fred can mow the lawn in 4 hours by himself, he would need less than 4 hours if someone helped him. That makes choices C, D, and E ridiculous. If Barney worked as quickly as Fred (4 hours) then together, it would take half as long, or 2 hours. But we know
that Barney is a little slower than Fred because it takes him 5 hours by himself. Logic tells us that together, it would take them a little more than 2 hours.
Therefore, 2 2/9 is a reasonable educated guess.
4. If a mixture is 3/7 alcohol by volume and 4/7 water by volume, what is the ratio of the volume of alcohol to the volume of water?
Answer choices: (F) 3/7 (G) 4/7 (H) ¾ (J) 4/3 (K) 7/4
A ratio is read aloud as “is to” something “as” something “is to” something else. When you see “as” or “is to,” it tells you to draw the line for the fraction. For example, 3 “is to” 7 means 3/7. So, let’s set up our equation, substituting math symbols for the words “as” and “is to.”
3 is to 7 = 3/7
4 is to 7 = 4/7
To solve this problem, divide 3/7 by 4/7.
To divide fractions, you must “flip” the second fraction and multiply.
Therefore, the problem would be set up as: (3/7) (7/4) = 21/28 = ¾
The answer is (H) ¾.
5. What is the maximum number of pieces of birthday cake size 4” X 4” that can be cut from a cake 20” X 20”?
Answer choices: (A) 5 (B) 10 (C) 16 (D) 20 (E) 25
Sketch this diagram in the margin of your test booklet. (Write in your test booklet, but NOT on your answer sheet.) Five pieces of cake (each one 4”) will fit down each side. Therefore 5 X 5 = 25. The answer is 25, E.
4 4 4 4 4 . . . . 4 . . . . 4 . . . . 4 . . . . 4
6. In the triangle given, AD is an angle bisector. <DAC is 30 degrees and angle ABC is a right angle. Find the measure of angle x.
(F) 30 degrees (G) 45 degrees (H) 60 degrees (J) 90 degrees (K) 120 degrees
The definition of a bisector is that it divides an angle evenly in half. Therefore, if <DAC is 30 degrees, then <BAD must be 30 degrees. <ABC is a right triangle. Right triangles measure 90 degrees. There are 180 degrees in a triangle.
If <BAD is 30, <ABC is 90, then to find <x, we must subtract 30 and 90 from 180.
When you take 180 and subtract 30, you get 150 degrees. Subtract 90 from 150, and the answer is 60. <x is 60 degrees, or answer H.
7. Estimate the value for:
(.889 X 55) —————- 9.97
Estimate your answer to the nearest tenth.
Answer choices: (A) .5 (B) 4.63 (C) 4.9 (D) 7.7 (E) 49.1
You don’t want to take the time to work this out. Besides, the problems clearly indicates that the desired answer is an estimation.
Round up and approximate:
.889 (55) ————– = 9.97 .9 (55) ——— = 10 49.5 ——— = 10 4.9 (answerC)
8. Find the counting number that is less than 15 and when divided by 3, has a remainder of 1, and when divided by 4, has a remainder of 2.
Answer choices: (F) 5 (G) 8 (H) 10 (J) 12 (K) 13
Once again, the most expeditious way to work this problem is from the answers. Plug the different numbers in and see what works and what doesn’t.
Answer F is 5. Let’s try it. When you divide 5 by 3, you get 1 with the remainder of 2, not 1; so F isn’t the answer. Answer G is 8. When you divide 8 by 3, you get 2 with a remainder of 2; so G isn’t the answer either. Answer H is 10. 10 divided by three is 3 with 1 as the remainder. This is the answer.
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# Barbara & Allen's Compound Interest
Extracts from this document...
Introduction
Angela C. Rosario Mr. Thomas IB Mathematics SL I (3) 24 March 2009 Practice IB Internal Assessment Introduction: The purpose of interest is for a bank to pay an individual for the use of their money. Interest therefore represents one's return on the investment. To calculate n interest compoundings per year, one must utilize the formula: 1. Alan invests \$1000 at an interest rate of 12% per year. Copy and complete Table 1 which shows A, the value of the investment in dollars after t years, assuming that the interest is compounded yearly. One must utilize the formula for Compound Interest in order to determine the answer. In the case of Alan, his principle (P) amount of money is \$1000, and he collects interest at a rate (r) of 12% per year. To determine the value of the investment in dollars after t years in order to satisfy Table 1, the formula necessary is: A= 1000 ( 1+ .12/1)(1)(t) where P= \$1000, r= 0.12, and n=1 because interest is being compounded annually or once a year, and t= the number of years the money is present in the account. t=0, A= 1000( 1+ 0.12/1)(1)(0) = 1000(1+ 0.12) 0= 1000(1.12) 0= 1000(1)= 1000 t=1, A= 1000( 1+ 0.12/1)(1)(1) = 1000(1+ 0.12) 1= 1000(1.12) 1= 1000(1.12)= 1120 t=2, A= 1000( 1+ 0.12/1)(1)(2) = 1000(1+ 0.12) 2= 1000(1.12) 2= 1000(1.2544)= 1254.40 t=5, A= 1000( 1+ 0.12/1)(1)(5) = 1000(1+ 0.12) 5= 1000(1.12) 5� 1000(1.76234)� 1762.34 t=10, A= 1000( 1+ 0.12/1)(1)(10) = 1000(1+ 0.12) 10= 1000(1.12) 10� 1000(3.10585)� 3105.85 t=20, A= 1000( 1+ 0.12/1)(1)(20) = 1000(1+ 0.12) 20= 1000(1.12) ...read more.
Middle
Conclusion
� t= 14, A=1000(1.12)14 � 1000 (4.887112285)� 4887.11 2009 � t= 15, A=1000(1.12)15� 1000 (5.473565759)� 5473.57 2010 � t= 16, A=1000(1.12)16 � 1000 (6.13039365)� 6130.39 Table 6 Alan's Investment of \$1000 at an Interest Rate of 12% Compounded Yearly in the Interval of Years 2000 to 2010* Year Amount 2000 1973.82 2001 2210.68 2002 2475.96 2003 2773.08 2004 3105.85 2005 3478.55 2006 3895.98 2007 4363.49 2008 4887.11 2009 5473.57 2010 6130.39 *Investment started in 1994 *Final answers rounded to the nearest hundredth in order to comply with the general money standard of cents. *Final answers rounded to the nearest hundredth in order to comply with the general money standard of cents. The reason why Barbara's investment is worth more than Alan's, even though she began with only \$200 in her account while Alan started with \$1000, is because Barbara collected interest for four years longer than Alan, and furthermore added money to her investment for the first five years. Due to Barbara's addition of \$200 to her final investment at the end of each year for the first five years, she collected a new principal. At the end of the first five years of her investment, instead of having \$200 as her principal, which would have been the case had she done a single investment, Barbara thus had the larger principal of \$1423.04. With this as the new principal for Barbara during her investment for the following years, Barbara was able to collect more interest than Alan, making her investment worth more than Alan's by \$1658.71, or approximately 21.3%. As a result, the larger one's principal is, the more interest will be collected, creating a larger final investment. ?? ?? ?? ?? Rosario 1 ...read more.
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Initially anomalies will show any extremes in both sets of data thus giving a basis to mathematical calculation using the data and giving a basic idea of which hypothesis the results will prove true. Measures of central tendency will be used for characterising the data obtained; therefore the mean and mid-range of both variables will be calculated and compared.
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To have infinitely many solutions, the two equations must represent the same line, meaning one equation is a multiple of the other. Given equations: read more
To have infinitely many solutions, the two equations must represent the same line, meaning one equation is a multiple of the other.
Given equations:$T1.&space;$$2x&space;-&space;3y&space;=&space;7$$&space;2.&space;$$(k+1)x&space;+&space;(1-2k)y&space;=&space;5k&space;-&space;4$$&space;To&space;check&space;if&space;one&space;equation&space;is&space;a&space;multiple&space;of&space;the&space;other,&space;we'll&space;compare&space;their&space;slopes&space;and&space;intercepts.&space;The&space;slope-intercept&space;form&space;of&space;the&space;first&space;equation&space;is&space;$$y&space;=&space;\frac{2}{3}x&space;-&space;\frac{7}{3}$$.&space;The&space;second&space;equation&space;can&space;be&space;rewritten&space;as:&space;$(k+1)x&space;+&space;(1-2k)y&space;=&space;5k&space;-&space;4$&space;$y&space;=&space;\frac{k+1}{1-2k}x&space;+&space;\frac{5k-4}{1-2k}$&space;Comparing&space;the&space;slopes:&space;$\frac{2}{3}&space;=&space;\frac{k+1}{1-2k}$&space;This&space;implies:&space;$2(1-2k)&space;=&space;3(k+1)$&space;$2&space;-&space;4k&space;=&space;3k&space;+&space;3$&space;$2&space;-&space;3&space;=&space;3k&space;+&space;4k$&space;$-1&space;=&space;7k$&space;$k&space;=&space;-\frac{1}{7}$&space;So,&space;for&space;$$k&space;=&space;-\frac{1}{7}$$,&space;the&space;given&space;equations&space;will&space;have&space;infinitely&space;many&space;solutions.$
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Let's denote the numerator of the fraction as xx and the denominator as yy. According to the given conditions: The sum of the denominator and numerator of a fraction is 3 less than twice the denominator: read more
Let's denote the numerator of the fraction as xx and the denominator as yy.
According to the given conditions:
1. The sum of the denominator and numerator of a fraction is 3 less than twice the denominator:$L&space;$x&space;+&space;y&space;=&space;2y&space;-&space;3$&space;2.&space;If&space;each&space;of&space;the&space;numerator&space;and&space;denominator&space;is&space;decreased&space;by&space;1,&space;the&space;fraction&space;becomes&space;$$&space;\frac{1}{2}&space;$$:&space;$\frac{x-1}{y-1}&space;=&space;\frac{1}{2}$&space;We&space;have&space;a&space;system&space;of&space;equations.&space;Let's&space;solve&space;it:&space;From&space;the&space;first&space;equation,&space;we&space;can&space;express&space;$$x$$&space;in&space;terms&space;of&space;$$y$$:&space;$x&space;=&space;2y&space;-&space;3&space;-&space;y$&space;$x&space;=&space;y&space;-&space;3$&space;Substitute&space;this&space;value&space;of&space;$$x$$&space;into&space;the&space;second&space;equation:&space;$\frac{y-3-1}{y-1}&space;=&space;\frac{1}{2}$&space;$\frac{y-4}{y-1}&space;=&space;\frac{1}{2}$&space;Cross&space;multiply:&space;$2(y&space;-&space;4)&space;=&space;y&space;-&space;1$&space;$2y&space;-&space;8&space;=&space;y&space;-&space;1$&space;$2y&space;-&space;y&space;=&space;8&space;-&space;1$&space;$y&space;=&space;7$&space;Now&space;that&space;we&space;have&space;found&space;$$y$$,&space;let's&space;find&space;$$x$$:&space;$x&space;=&space;y&space;-&space;3$&space;$x&space;=&space;7&space;-&space;3$&space;$x&space;=&space;4$&space;So,&space;the&space;fraction&space;is&space;$$&space;\frac{4}{7}&space;$$.$
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Let's denote the tens digit of the two-digit number as xx and the units digit as yy. The original number can then be represented as 10x+y. According to the given conditions: The sum of the digits of the two-digit number is 12: read more
Let's denote the tens digit of the two-digit number as xx and the units digit as yy. The original number can then be represented as 10x+y.$L1.&space;The&space;sum&space;of&space;the&space;digits&space;of&space;the&space;two-digit&space;number&space;is&space;12:&space;$x&space;+&space;y&space;=&space;12$&space;2.&space;The&space;number&space;obtained&space;by&space;interchanging&space;the&space;two&space;digits&space;exceeds&space;the&space;given&space;number&space;by&space;18:&space;$10y&space;+&space;x&space;=&space;10x&space;+&space;y&space;+&space;18$&space;We&space;have&space;a&space;system&space;of&space;equations.&space;Let's&space;solve&space;it:&space;From&space;the&space;first&space;equation,&space;we&space;can&space;express&space;$$x$$&space;in&space;terms&space;of&space;$$y$$:&space;$x&space;=&space;12&space;-&space;y$&space;Substitute&space;this&space;value&space;of&space;$$x$$&space;into&space;the&space;second&space;equation:&space;$10y&space;+&space;(12&space;-&space;y)&space;=&space;10(12&space;-&space;y)&space;+&space;y&space;+&space;18$&space;Let's&space;solve&space;for&space;$$y$$:&space;$10y&space;+&space;12&space;-&space;y&space;=&space;120&space;-&space;10y&space;+&space;y&space;+&space;18$&space;$9y&space;+&space;12&space;=&space;138&space;-&space;9y$&space;$9y&space;+&space;9y&space;=&space;138&space;-&space;12$&space;$18y&space;=&space;126$&space;$y&space;=&space;\frac{126}{18}$&space;$y&space;=&space;7$&space;Now&space;that&space;we&space;have&space;found&space;$$y$$,&space;let's&space;find&space;$$x$$&space;using&space;the&space;first&space;equation:&space;$x&space;+&space;7&space;=&space;12$&space;$x&space;=&space;12&space;-&space;7$&space;$x&space;=&space;5$&space;So,&space;the&space;original&space;number&space;is&space;$$10x&space;+&space;y&space;=&space;10(5)&space;+&space;7&space;=&space;50&space;+&space;7&space;=&space;57$$.$
According to the given conditions:
1. The sum of the digits of the two-digit number is 12:
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The given sequence is an arithmetic progression (AP) with a common difference. To find this common difference, let's subtract each term from the next one: read more
The given sequence is an arithmetic progression (AP) with a common difference. To find this common difference, let's subtract each term from the next one:
$T&space;$&space;\frac{3&space;-&space;a}{3a}&space;-&space;\frac{1}{a}&space;=&space;\frac{3&space;-&space;a}{3a}&space;-&space;\frac{3}{3a}&space;=&space;\frac{(3&space;-&space;a)&space;-&space;3}{3a}&space;=&space;\frac{3&space;-&space;a&space;-&space;3}{3a}&space;=&space;\frac{-a}{3a}&space;=&space;-\frac{1}{3}&space;$&space;So,&space;the&space;common&space;difference&space;of&space;the&space;given&space;arithmetic&space;progression&space;is&space;$$&space;-\frac{1}{3}&space;$$.$
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To find which term of the arithmetic progression read more
To find which term of the arithmetic progression$T$$&space;-7,&space;-12,&space;-17,&space;-22,&space;\ldots&space;$$&space;will&space;be&space;$$&space;-82&space;$$,&space;we&space;can&space;use&space;the&space;formula&space;for&space;the&space;$$&space;n&space;$$th&space;term&space;of&space;an&space;arithmetic&space;progression:&space;$&space;a_n&space;=&space;a_1&space;+&space;(n&space;-&space;1)&space;\cdot&space;d&space;$&space;where:&space;-&space;$$&space;a_n&space;$$&space;is&space;the&space;$$&space;n&space;$$th&space;term,&space;-&space;$$&space;a_1&space;$$&space;is&space;the&space;first&space;term,&space;-&space;$$&space;d&space;$$&space;is&space;the&space;common&space;difference,&space;and&space;-&space;$$&space;n&space;$$&space;is&space;the&space;term&space;number.&space;For&space;the&space;given&space;sequence,&space;$$&space;a_1&space;=&space;-7&space;$$&space;and&space;$$&space;d&space;=&space;-5&space;$$&space;(because&space;each&space;term&space;decreases&space;by&space;5).&space;Let's&space;plug&space;these&space;values&space;into&space;the&space;formula&space;and&space;solve&space;for&space;$$&space;n&space;$$&space;when&space;$$&space;a_n&space;=&space;-82&space;$$:&space;$&space;-7&space;+&space;(n&space;-&space;1)&space;\cdot&space;(-5)&space;=&space;-82&space;$&space;$&space;-7&space;-&space;5n&space;+&space;5&space;=&space;-82&space;$&space;$&space;-2&space;-&space;5n&space;=&space;-82&space;$&space;$&space;-5n&space;=&space;-82&space;+&space;2&space;$&space;$&space;-5n&space;=&space;-80&space;$&space;$&space;n&space;=&space;\frac{-80}{-5}&space;$&space;$&space;n&space;=&space;16&space;$&space;So,&space;the&space;16th&space;term&space;of&space;the&space;arithmetic&space;progression&space;is&space;$$&space;-82&space;$$.$
$To&space;determine&space;if&space;$$&space;-100&space;$$&space;is&space;any&space;term&space;of&space;the&space;arithmetic&space;progression,&space;we&space;can&space;check&space;if&space;it&space;can&space;be&space;obtained&space;using&space;the&space;formula&space;for&space;the&space;$$&space;n&space;$$th&space;term:&space;$&space;a_n&space;=&space;-7&space;+&space;(n&space;-&space;1)&space;\cdot&space;(-5)&space;$&space;Let's&space;solve&space;for&space;$$&space;n&space;$$&space;when&space;$$&space;a_n&space;=&space;-100&space;$$:&space;$&space;-7&space;+&space;(n&space;-&space;1)&space;\cdot&space;(-5)&space;=&space;-100&space;$&space;$&space;-7&space;-&space;5n&space;+&space;5&space;=&space;-100&space;$&space;$&space;-2&space;-&space;5n&space;=&space;-100&space;$&space;$&space;-5n&space;=&space;-100&space;+&space;2&space;$&space;$&space;-5n&space;=&space;-98&space;$&space;$&space;n&space;=&space;\frac{-98}{-5}&space;$&space;$&space;n&space;=&space;19.6&space;$$
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To find the value of p for which read more
To find the value of p for which$To&space;find&space;the&space;value&space;of&space;$$&space;p&space;$$&space;for&space;which&space;$$&space;-4&space;$$&space;is&space;a&space;zero&space;of&space;the&space;polynomial&space;$$&space;x^2&space;-&space;2x&space;-&space;(7p&space;+&space;3)&space;$$,&space;we&space;substitute&space;$$&space;x&space;=&space;-4&space;$$&space;into&space;the&space;polynomial&space;and&space;solve&space;for&space;$$&space;p&space;$$.&space;Substituting&space;$$&space;x&space;=&space;-4&space;$$&space;into&space;the&space;polynomial&space;equation:&space;$&space;(-4)^2&space;-&space;2(-4)&space;-&space;(7p&space;+&space;3)&space;=&space;0&space;$&space;$&space;16&space;+&space;8&space;-&space;7p&space;-&space;3&space;=&space;0&space;$&space;$&space;24&space;-&space;7p&space;-&space;3&space;=&space;0&space;$&space;$&space;21&space;-&space;7p&space;=&space;0&space;$&space;Now,&space;let's&space;solve&space;for&space;$$&space;p&space;$$:&space;$&space;21&space;-&space;7p&space;=&space;0&space;$&space;$&space;7p&space;=&space;21&space;$&space;$&space;p&space;=&space;\frac{21}{7}&space;$&space;$&space;p&space;=&space;3&space;$&space;So,&space;for&space;$$&space;p&space;=&space;3&space;$$,&space;$$&space;-4&space;$$&space;is&space;a&space;zero&space;of&space;the&space;polynomial&space;$$&space;x^2&space;-&space;2x&space;-&space;(7p&space;+&space;3)&space;$$.$
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If 11 is a zero of the polynomial p(x)=ax2−3(a−1)x−1 read more
If 11 is a zero of the polynomial p(x)=ax2−3(a−1)x−1$Substituting&space;$$x&space;=&space;1$$&space;into&space;the&space;polynomial&space;equation:&space;$&space;p(1)&space;=&space;a(1)^2&space;-&space;3(a&space;-&space;1)(1)&space;-&space;1&space;=&space;0&space;$&space;$&space;a&space;-&space;3(a&space;-&space;1)&space;-&space;1&space;=&space;0&space;$&space;Now,&space;let's&space;solve&space;for&space;$$a$$:&space;$&space;a&space;-&space;3a&space;+&space;3&space;-&space;1&space;=&space;0&space;$&space;$&space;-2a&space;+&space;2&space;=&space;0&space;$&space;$&space;-2a&space;=&space;-2&space;$&space;$&space;a&space;=&space;\frac{-2}{-2}&space;$&space;$&space;a&space;=&space;1&space;$&space;So,&space;the&space;value&space;of&space;$$a$$&space;for&space;which&space;$$1$$&space;is&space;a&space;zero&space;of&space;the&space;polynomial&space;$$p(x)&space;=&space;ax^2&space;-&space;3(a&space;-&space;1)x&space;-&space;1$$&space;is&space;$$a&space;=&space;1$$.$
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To find aa if (x+a) is a factor of read more
To find aa if (x+a) is a factor of$$$2x^2&space;+&space;2ax&space;+&space;5x&space;+&space;10$$,&space;we'll&space;perform&space;polynomial&space;division.&space;Given&space;that&space;$$(x&space;+&space;a)$$&space;is&space;a&space;factor,&space;we&space;have:&space;$2x^2&space;+&space;2ax&space;+&space;5x&space;+&space;10&space;=&space;(x&space;+&space;a)(2x&space;+&space;b)$&space;Expanding&space;$$(x&space;+&space;a)(2x&space;+&space;b)$$,&space;we&space;get:&space;$2x^2&space;+&space;(2a&space;+&space;b)x&space;+&space;ab$&space;Comparing&space;coefficients&space;of&space;corresponding&space;terms&space;in&space;$$2x^2&space;+&space;2ax&space;+&space;5x&space;+&space;10$$&space;and&space;$$2x^2&space;+&space;(2a&space;+&space;b)x&space;+&space;ab$$,&space;we&space;have:&space;For&space;$$x$$&space;terms:&space;$2ax&space;+&space;5x&space;=&space;(2a&space;+&space;b)x$&space;So,&space;$$2a&space;+&space;b&space;=&space;5$$&space;For&space;constant&space;terms:&space;$10&space;=&space;ab$&space;Given&space;$$2a&space;+&space;b&space;=&space;5$$,&space;we&space;can&space;express&space;$$b$$&space;in&space;terms&space;of&space;$$a$$:&space;$b&space;=&space;5&space;-&space;2a$&space;Substituting&space;this&space;expression&space;for&space;$$b$$&space;into&space;$$10&space;=&space;ab$$,&space;we&space;get:&space;$10&space;=&space;a(5&space;-&space;2a)$&space;Expanding&space;and&space;rearranging,&space;we&space;have:&space;$10&space;=&space;5a&space;-&space;2a^2$&space;$2a^2&space;-&space;5a&space;+&space;10&space;=&space;0$&space;This&space;is&space;a&space;quadratic&space;equation.&space;We&space;can&space;solve&space;it&space;using&space;the&space;quadratic&space;formula:$
$$a&space;=&space;\frac{-b&space;\pm&space;\sqrt{b^2&space;-&space;4ac}}{2a}$&space;For&space;$$2a^2&space;-&space;5a&space;+&space;10&space;=&space;0$$,&space;we&space;have&space;$$a&space;=&space;2$$,&space;$$b&space;=&space;-5$$,&space;and&space;$$c&space;=&space;10$$.&space;Substituting&space;these&space;values&space;into&space;the&space;quadratic&space;formula:&space;$a&space;=&space;\frac{-(-5)&space;\pm&space;\sqrt{(-5)^2&space;-&space;4&space;\cdot&space;2&space;\cdot&space;10}}{2&space;\cdot&space;2}$&space;$a&space;=&space;\frac{5&space;\pm&space;\sqrt{25&space;-&space;80}}{4}$&space;$a&space;=&space;\frac{5&space;\pm&space;\sqrt{-55}}{4}$&space;Since&space;$$\sqrt{-55}$$&space;is&space;imaginary,&space;the&space;solutions&space;for&space;$$a$$&space;are&space;complex.&space;Thus,&space;there's&space;no&space;real&space;value&space;of&space;$$a$$&space;for&space;which&space;$$(x&space;+&space;a)$$&space;is&space;a&space;factor&space;of&space;$$2x^2&space;+&space;2ax&space;+&space;5x&space;+&space;10$$.$
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Let's denote the usual speed of the plane as S km/hr. read more
Let's denote the usual speed of the plane as S km/hr.$Since&space;the&space;plane&space;left&space;30&space;minutes&space;late,&space;it&space;had&space;less&space;time&space;to&space;reach&space;its&space;destination.&space;To&space;compensate&space;for&space;the&space;delay&space;and&space;still&space;reach&space;the&space;destination&space;on&space;time,&space;the&space;plane&space;had&space;to&space;increase&space;its&space;speed.&space;Let's&space;first&space;find&space;the&space;time&space;it&space;takes&space;for&space;the&space;plane&space;to&space;cover&space;1500&space;km&space;at&space;its&space;usual&space;speed&space;$$&space;S&space;$$.&space;The&space;time&space;taken&space;can&space;be&space;calculated&space;using&space;the&space;formula:&space;$&space;\text{Time}&space;=&space;\frac{\text{Distance}}{\text{Speed}}&space;$&space;At&space;the&space;usual&space;speed&space;$$&space;S&space;$$,&space;the&space;time&space;taken&space;to&space;cover&space;1500&space;km&space;is:&space;$&space;\text{Time&space;taken}&space;=&space;\frac{1500}{S}&space;$$
$Now,&space;since&space;the&space;plane&space;left&space;30&space;minutes&space;late,&space;it&space;has&space;$$&space;\frac{1}{2}&space;$$&space;hour&space;less&space;to&space;reach&space;the&space;destination.&space;So,&space;the&space;time&space;available&space;for&space;the&space;plane&space;to&space;reach&space;the&space;destination&space;on&space;time&space;is:&space;$&space;\text{Time&space;available}&space;=&space;\frac{1500}{S}&space;-&space;\frac{1}{2}&space;$&space;When&space;the&space;plane&space;increases&space;its&space;speed&space;by&space;100&space;km/hr,&space;its&space;new&space;speed&space;becomes&space;$$&space;S&space;+&space;100&space;$$&space;km/hr.&space;Using&space;this&space;new&space;speed,&space;the&space;time&space;taken&space;to&space;cover&space;1500&space;km&space;becomes:&space;$&space;\text{New&space;time&space;taken}&space;=&space;\frac{1500}{S&space;+&space;100}&space;$&space;Given&space;that&space;the&space;plane&space;needs&space;to&space;cover&space;the&space;same&space;distance&space;in&space;the&space;time&space;available,&space;we&space;can&space;equate&space;the&space;new&space;time&space;taken&space;with&space;the&space;time&space;available:&space;$&space;\frac{1500}{S&space;+&space;100}&space;=&space;\frac{1500}{S}&space;-&space;\frac{1}{2}&space;$&space;Now,&space;let's&space;solve&space;this&space;equation&space;to&space;find&space;the&space;value&space;of&space;$$&space;S&space;$$,&space;the&space;usual&space;speed&space;of&space;the&space;plane.&space;$&space;\frac{1500}{S&space;+&space;100}&space;=&space;\frac{1500}{S}&space;-&space;\frac{1}{2}&space;$$
$Cross&space;multiply&space;to&space;get&space;rid&space;of&space;the&space;denominators:&space;$&space;1500S&space;=&space;1500(S&space;+&space;100)&space;-&space;\frac{1}{2}(S)(S&space;+&space;100)&space;$&space;$&space;1500S&space;=&space;1500S&space;+&space;150000&space;-&space;\frac{1}{2}(S^2&space;+&space;100S)&space;$&space;$&space;1500S&space;=&space;1500S&space;+&space;150000&space;-&space;\frac{1}{2}S^2&space;-&space;50S&space;$&space;$&space;0&space;=&space;150000&space;-&space;\frac{1}{2}S^2&space;-&space;50S&space;$&space;$&space;\frac{1}{2}S^2&space;+&space;50S&space;-&space;150000&space;=&space;0&space;$&space;Now,&space;we&space;have&space;a&space;quadratic&space;equation&space;in&space;terms&space;of&space;$$&space;S&space;$$.&space;Let's&space;solve&space;it&space;to&space;find&space;the&space;usual&space;speed&space;of&space;the&space;plane.&space;To&space;solve&space;the&space;quadratic&space;equation&space;$$&space;\frac{1}{2}S^2&space;+&space;50S&space;-&space;150000&space;=&space;0&space;$$,&space;we&space;can&space;multiply&space;both&space;sides&space;of&space;the&space;equation&space;by&space;2&space;to&space;get&space;rid&space;of&space;the&space;fraction:&space;$&space;S^2&space;+&space;100S&space;-&space;300000&space;=&space;0&space;$&space;Now,&space;we&space;can&space;use&space;the&space;quadratic&space;formula&space;to&space;find&space;the&space;values&space;of&space;$$&space;S&space;$$:&space;$&space;S&space;=&space;\frac{{-b&space;\pm&space;\sqrt{{b^2&space;-&space;4ac}}}}{{2a}}&space;$&space;For&space;the&space;quadratic&space;equation&space;$$&space;S^2&space;+&space;100S&space;-&space;300000&space;=&space;0&space;$$,&space;we&space;have&space;$$&space;a&space;=&space;1&space;$$,&space;$$&space;b&space;=&space;100&space;$$,&space;and&space;$$&space;c&space;=&space;-300000&space;$$.$
$Substituting&space;these&space;values&space;into&space;the&space;quadratic&space;formula:&space;$&space;S&space;=&space;\frac{{-100&space;\pm&space;\sqrt{{(100)^2&space;-&space;4&space;\cdot&space;1&space;\cdot&space;(-300000)}}}}{{2&space;\cdot&space;1}}&space;$&space;$&space;S&space;=&space;\frac{{-100&space;\pm&space;\sqrt{{10000&space;+&space;1200000}}}}{2}&space;$&space;$&space;S&space;=&space;\frac{{-100&space;\pm&space;\sqrt{{1210000}}}}{2}&space;$&space;$&space;S&space;=&space;\frac{{-100&space;\pm&space;1100}}{{2}}&space;$&space;Now,&space;we&space;have&space;two&space;possible&space;values&space;for&space;$$&space;S&space;$$:&space;1.&space;$$&space;S&space;=&space;\frac{{-100&space;+&space;1100}}{{2}}&space;=&space;\frac{{1000}}{{2}}&space;=&space;500&space;$$&space;2.&space;$$&space;S&space;=&space;\frac{{-100&space;-&space;1100}}{{2}}&space;=&space;\frac{{-1200}}{{2}}&space;=&space;-600&space;$$&space;Since&space;speed&space;cannot&space;be&space;negative,&space;we&space;discard&space;the&space;negative&space;value&space;of&space;$$&space;S&space;$$.&space;Therefore,&space;the&space;usual&space;speed&space;of&space;the&space;plane&space;is&space;$$&space;oxed{500&space;\text{&space;km/hr}}&space;$$.$
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To prove that the equation read more
To prove that the equation $$$&space;(a^2&space;+&space;b^2)x^2&space;+&space;2(ac&space;+&space;bd)x&space;+&space;(c^2&space;+&space;d^2)&space;=&space;0&space;$$&space;has&space;no&space;real&space;roots&space;when&space;$$&space;ad&space; eq&space;bc&space;$$,&space;we&space;will&space;use&space;the&space;discriminant.&space;The&space;discriminant&space;of&space;a&space;quadratic&space;equation&space;$$&space;ax^2&space;+&space;bx&space;+&space;c&space;=&space;0&space;$$&space;is&space;given&space;by&space;$$&space;\Delta&space;=&space;b^2&space;-&space;4ac&space;$$.&space;If&space;the&space;discriminant&space;is&space;negative,&space;then&space;the&space;quadratic&space;equation&space;has&space;no&space;real&space;roots.&space;In&space;our&space;given&space;equation&space;$$&space;(a^2&space;+&space;b^2)x^2&space;+&space;2(ac&space;+&space;bd)x&space;+&space;(c^2&space;+&space;d^2)&space;=&space;0&space;$$,&space;the&space;coefficients&space;are&space;$$&space;a^2&space;+&space;b^2&space;$$,&space;$$&space;2(ac&space;+&space;bd)&space;$$,&space;and&space;$$&space;c^2&space;+&space;d^2&space;$$.$
$Let's&space;calculate&space;the&space;discriminant&space;$$&space;\Delta&space;$$&space;for&space;this&space;quadratic&space;equation:&space;$&space;\Delta&space;=&space;(2(ac&space;+&space;bd))^2&space;-&space;4(a^2&space;+&space;b^2)(c^2&space;+&space;d^2)&space;$&space;$&space;\Delta&space;=&space;4(a^2c^2&space;+&space;2abcd&space;+&space;b^2d^2)&space;-&space;4(a^2c^2&space;+&space;a^2d^2&space;+&space;b^2c^2&space;+&space;b^2d^2)&space;$&space;$&space;\Delta&space;=&space;4a^2c^2&space;+&space;8abcd&space;+&space;4b^2d^2&space;-&space;4a^2c^2&space;-&space;4a^2d^2&space;-&space;4b^2c^2&space;-&space;4b^2d^2&space;$&space;$&space;\Delta&space;=&space;8abcd&space;-&space;4a^2d^2&space;-&space;4b^2c^2&space;$&space;$&space;\Delta&space;=&space;4(2abcd&space;-&space;a^2d^2&space;-&space;b^2c^2)&space;$$
$Now,&space;since&space;$$&space;ad&space; eq&space;bc&space;$$,&space;the&space;term&space;inside&space;the&space;parentheses&space;is&space;not&space;equal&space;to&space;zero.&space;Thus,&space;$$&space;\Delta&space;$$&space;will&space;be&space;positive&space;if&space;$$&space;2abcd&space;-&space;a^2d^2&space;-&space;b^2c^2&space;>&space;0&space;$$&space;and&space;negative&space;if&space;$$&space;2abcd&space;-&space;a^2d^2&space;-&space;b^2c^2&space;<&space;0&space;$$.&space;Since&space;the&space;discriminant&space;$$&space;\Delta&space;$$&space;is&space;proportional&space;to&space;this&space;expression,&space;if&space;the&space;expression&space;is&space;positive,&space;then&space;$$&space;\Delta&space;$$$
$is&space;positive,&space;and&space;the&space;quadratic&space;equation&space;has&space;real&space;roots.&space;If&space;the&space;expression&space;is&space;negative,&space;then&space;$$&space;\Delta&space;$$&space;is&space;negative,&space;and&space;the&space;quadratic&space;equation&space;has&space;no&space;real&space;roots.&space;Therefore,&space;when&space;$$&space;ad&space; eq&space;bc&space;$$,&space;the&space;equation&space;$$&space;(a^2&space;+&space;b^2)x^2&space;+&space;2(ac&space;+&space;bd)x&space;+&space;(c^2&space;+&space;d^2)&space;=&space;0&space;$$&space;has&space;no&space;real&space;roots.$
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Subtraction of signed binary numbers using 2’s Complement
An unsigned binary number does not have a sign bit in the most significant bit (MSB) position. For example, consider 8-bit representation of 3810
3810 = 01001002
= 0. 27 + 0. 26 + 1. 25 + 0. 24 + 0. 23 + 1. 22 + 0. 21 + 0. 20
= 0 + 0 + 32 + 0 + 0 + 4 + 0 + 0
= 34 + 4
= 3810
Now, if we take two’s complement of unsigned binary number then we get signed binary representation of a number which is nothing but negative equivalent the unsigned binary number.
To understand this in an easy way, consider previous example of 3810. Let us convert the number 3810 into binary.
3810 = 0 0 1 0 0 1 0 0
Take 1’s complement of each binary digit in above number. That is, 0 becomes 1 and 1 becomes 0.
= 1 1 0 1 1 0 1 1
Adding 1 to the 1’s complement of 3810 we get two’s complement of the binary number.
1 1
1 1 0 1 1 0 1 1
+ 1
__________________
1 1 0 1 1 1 0 0
The Most Significant Bit (MSB) has 1 which shows that it is a negative number. The resultant number is -3810
Subtraction using 2’s Complement of unsigned binary number
Two’s complement of binary number is used for subtraction between unsigned and signed binary numbers.
For example,
How do we subtract? -34 – (-45) = -34 + 45 = 11
Step 1: Convert +34 in 2’s Complement form.
34 = 0 0 1 0 0 0 1 0
Obtain 1’s complement of 0 0 1 0 0 0 1 0
0 0 1 0 0 0 1 0
+ 1
__________________
0 0 1 0 0 0 1 1
= -3410
Note: The above step is only performed to obtain the -34 values. There are other methods to obtain negative signed values
Step 2: Convert -45 into 2’s complement to find +45.
But we can also do it directly.
450 = 0 0 1 0 1 1 0 1 = 0. 27 + 0. 26 + 1. 25 + 0. 24 + 1. 23+ 1. 22 + 0. 21 + 1. 20
= 0 + 0 + 32 + 0 + 8 + 4 + 0 + 1
= 32 + 8 + 4 + 1
= 45
Step 3: Add binary value of -34 and 45
1 1 0 1 1 1 1 0 = -34
0 0 1 0 1 1 0 1 = +45
____________________
0 0 0 0 1 0 1 1 = 1 1 1 0
Example Problems
Q 1: Perform the subtraction with the unsigned binary numbers by taking the 2’s complement of the subtrahend.
Source: Computer System Architecture by Morris Mano
a) 1 1 0 1 0 – 1 0 0 0 0
Solution:
Given
1 1 0 1 0 = + 26
1 0 0 0 0 = + 16
Take 1's complement of 1 0 0 0 0
= 0 1 1 1 1
Add +1 to get 2'
s complement of + 16
Add binary value of +26 and -16
1
0 1 1 0 1 0 = +26
0 1 0 0 0 0 = -16
_________________
1 0 1 0 1 0 = +10
= 10 is the answer.
b) 1 1 0 1 0 – 1 1 0 1
Solution:
Given
1 1 0 1 0 = +26
0 1 1 0 1 = +13
Take 1's complement of +13 = 0 1 1 0 1
= 1 0 0 1 0
Add 1 to get 2'
s complement of +13
1 0 0 1 0
+ 1
_____________
1 0 0 1 1
Add binary values of +26 and -13
to get the result.
1
0 1 1 0 1 0 = +26
0 1 0 0 1 1 = -13
_____________
1 0 1 1 0 1 = -13
The answer is +13.
c) 100 – 110000
Solution:
0 0 0 0 0 1 0 0 = +4
0 0 1 1 0 0 0 0 = +48
Take 1's complement of 48
= 1 1 0 0 1 1 1 1
Add 1 to get the 2'
s complement of + 48
1 1 1 1
0 1 1 0 1 1 1 1 = +48
+ 1
_________________
0 1 1 1 0 0 0 0
Add the binary values of +4 and -48
to get the correct answer.
0 0 0 0 0 1 0 0 = +04
1 1 0 1 0 0 0 0 = -48
_____________________
1 1 0 1 0 1 0 0 = -44
-44 is the answer.
d) 1010100 – 1010100
Solution:
0 1 0 1 0 1 0 0 = 64 + 16 + 4 = +84
0 1 0 1 0 1 0 0 = 64 + 16 + 4 = +84
Take 1's complement of +84 subtrahend
= 1 0 1 0 1 0 1 1
Add 1 to get the 2'
s complement
of +84 subtrahend
1
1 0 1 0 1 0 1 1
+ 1
_______________
Add the binary values of +84 and -84
to get the result.
1 1 1 1 1
0 1 0 1 0 1 0 0
1 0 1 0 1 1 0 0
_______________
0 0 0 0 0 0 0 0
The answer is zero.
Bibliography
Mano, M. Morris. 1984. Digital Design. Pearson.
Shjiva, Sajjan G. 1998. Introduction to Logic Design. New York: Marcel Dekker, Inc .<|endoftext|>
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# Two friends “a” and “b” start walking from a common point. A goes 20 km towards the northeast, whereas “b” goes 15 km towards the east and then 12 km towards the north. How far are “a” and “b” from each other?
By Ritesh|Updated : November 7th, 2022
Two friends “a” and “b” start walking from a common point. A goes 20 km towards the northeast, whereas “b” goes 15 km towards the east and then 12 km towards the north. The distance between a and b is 0 km.
Step 1: Given data
a and b begin their stroll from the same location.
a travels 20 kilometers northeast.
b travels 12 km in the north and 16 km in the east.
Step 2: Now we have to find the distance between a and b.
Step 3: Calculation
Using the provided data, we obtain
The Pythagoras Theorem, which
Displacement of b = √162 + 122
= √256 + 144
= √400
Taking square root
= 20 km
Now, when a and b finally cross paths at the conclusion of their journey, their separation will be:
= 20 - 20
= 0 km
• While distance and displacement appear to signify the same thing, they actually have very different definitions and meanings.
• A scalar quantity known as distance measures "how much ground an object has traversed" while moving.
• An object's total change in position is referred to as displacement, a vector variable that measures "how far out of place an object is."
• Distance is the total distance a body travels in a given amount of time.
Therefore, the distance between a and b is 0 km
Summary:
## Two friends “a” and “b” start walking from a common point. A goes 20 km towards the northeast, whereas “b” goes 15 km towards the east and then 12 km towards the north. How far are “a” and “b” from each other?
Two friends "a" and "b" set out on foot from a shared location. A travels 20 kilometres northeast whereas "b" travels 15 kilometres east before travelling 12 kilometres north. The distance between a and b is 0 km
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Koalas are interesting animals with several amazing features. Native to certain parts of Australia, koalas (Phascolarctos cinereus) are marsupials (females have a pouch on their belly, inside which they raise the newborn), which lead their life on trees. They belong to the genus Phascolarctos in the family Phascolarctidae. In fact, koalas are the only surviving species of this family. The name of this genus is derived from the Greek word 'phaskolos' that means pouch and the Latin word, 'arktos', meaning bear. It is said that the name of the species - 'cinereus' means ash colored in Latin (this denotes the coat color of the animal). Koalas are sometimes referred to as koala bears, due to their resemblance to bears in their looks. Koalas are adapted to their environment in various ways.
Adaptations of Koala Bears
So, koalas are marsupials that belong to certain parts of Australia. Though, they have some features that resemble bears, koalas are not even related to the latter. These Australian mammals are related to wombats and kangaroos. Whether it is structural or dietary, koalas have numerous adaptations.
Arboreal Life Adaptations
- As koalas lead an arboreal life, these animals have padded feet and long claws for better grip, while moving on tree trunks. Both the front and hind limbs are strong enough to support them while climbing trees and moving in between branches.
- Unlike most of the other mammals, koalas have strong thigh muscles that are among those vital adaptations that help them to lead an arboreal life. Their thigh muscles are found to join the shin at a lower point, as compared to other mammals.
- The paws of a koala have five digits each with sharp claws. In case of front paws, two digits act like thumbs and are opposed to the other three digits. This enables the animal to have a better grip while moving on trees.
- The second and third digits of the hind paws are fused together and the claw on this fused digit is used for grooming. The first digit of hind paws lack claws and are opposed to the other three digits (including the fused one). Koalas lack tail that is one of the main adaptations seen in animals that lead an arboreal life.
- The thick fur is one of the koala bear adaptations that make their arboreal life comfortable. As compared to other parts, the fur on their tail end or rump is much thicker. This provides a cushioning effect for the animal, while sitting on trees.
- The curved spine is also one among the physiological adaptations of koalas. Along with the cartilaginous pad on the rear end, the curved spine of these animals enables them to rest on tree forks comfortably.
- The thick fur of koalas saves them from extreme temperature variations. Apart from that, the fur has moisture-repelling properties that help these animals during rain. The scent gland on the chest of male koalas are used for marking their territory (trees).
Koalas are among those few mammals that are adapted to a diet of eucalyptus leaves, that can be poisonous for many other animals. They are not even found to drink water as the moisture content in the eucalyptus leaves is almost sufficient to meet their water requirement. Let us take a look at some koala bear adaptations that enable them to thrive on this diet.
- Koalas have sharp front incisors that are used for clipping the leaves. The molars are used to cut and chew the leaves to a paste form, before swallowing. The gap in between their teeth enable the tongue to be moved in such a way that the leaves are rotated inside the mouth for efficient chewing.
- It is said that these animals have a keen sense of smell and use their nose to determine the edible type of eucalyptus leaves. Even the toxicity of these leaves are believed to be determined by them, through smell.
- While their liver is entrusted with the function of inactivating the toxic components in eucalyptus leaves, the cecum is said to absorb the maximum amount of nutrients from the leaves consumed by koalas.
- As koalas have a diet that provide them with low energy, these animals are adapted to spend less energy. As compared to the size of their body and head, they have a very small brain with mostly hollow interiors. It is said that the small size of the brain helps the animal in spending less energy.
- These animals have a very low metabolic rate as well as low body temperature. They are found to sleep for at least 18 hours a day. For the remaining time, these animals rest on tree trunks and chew on eucalyptus leaves. All these factors help them in spending less energy.
It is not legal for a layman to keep a koala as pet. However, some people (like research scientists and wildlife carers) are sometimes allowed to raise koalas. Hope you found this AnimalSake article interesting. If you want to know more about koalas, you may conduct a deep study about them.<|endoftext|>
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Our School Counselor, Ms. Lutz, has been visiting classrooms, teaching the definition of bullying and how to be part of the 'Caring Majority' of Upstanders.
What is bullying? Bullying is intentional harmful behavior by one or more that is directed towards a specific victim. Bullying exists when a student deliberately dominates and harasses another student who is perceived to have less power. Bullying is repeated and intentional.
What is the 'Caring Majority'? The Caring Majority is a group of kids that care enough to stand up and support those who are being bullied. These students are called UPSTANDERS. No longer can we stand by and let others be bullied. They use their words and presence to support students that are unable to speak up for themselves.
If you have any questions regarding bullying at Pine Trail Elementary, please call Ms. Lutz at 386-258-4672
Pine Trail's character-building life skills are woven into the curriculum at every grade level. Students whose behavior reflects the life skills often receive special recognition.<|endoftext|>
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When we graph a parabola, we are generally concerned with three things. First and foremost, we look for the vertex. This is the highest or lowest point, depending on whether the parabola faces up or down. Secondly, we are looking at the horizontal shift or movement along the x axis. Lastly, we are looking at the vertical shift, or movement along the y axis.
Test Objectives
• Demonstrate the ability to find the vertex of a parabola
• Demonstrate the ability to find the horizontal shift
• Demonstrate the ability to find the vertical shift
Graphing Parabolas Practice Test:
#1:
Instructions: Identify the vertex of each parabola.
a) $$f(x) = -\frac{1}{5}x^2$$
b) $$f(x) = (x - 3)^2 + 5$$
#2:
Instructions: Identify the vertex of each parabola.
a) $$f(x) = (x + 9)^2$$
b) $$f(x) = (x - 13)^2 + 4$$
#3:
Instructions: State the horizontal and/or vertical shift for each parabola when compared to f(x) = x2.
a) $$f(x) = (x- 19)^2$$
b) $$f(x) = x^2 - 5$$
#4:
Instructions: State the horizontal and/or vertical shift for each parabola when compared to f(x) = x2.
a) $$f(x) = (x + 2)^2 - 14$$
b) $$f(x) = (x - 7)^2 + 7$$
#5:
Instructions: State the horizontal and/or vertical shift for each parabola when compared to f(x) = x2.
a) $$f(x) = (x - 17)^2 - 12$$
b) $$f(x) = (x + 1)^2 - 23$$
Written Solutions:
#1:
Solutions:
a) $$vertex: (0,0)$$
b) $$vertex: (3,5)$$
#2:
Solutions:
a) $$vertex: (-9,0)$$
b) $$vertex: (13,4)$$
#3:
Solutions:
a) $$shifts \hspace{.25em} 19\hspace{.25em} units\hspace{.25em} right$$
b) $$shifts\hspace{.25em} 5 \hspace{.25em}units\hspace{.25em} down$$
#4:
Solutions:
a) $$shifts \hspace{.25em} 2\hspace{.25em} units\hspace{.25em} left ,\hspace{.25em} 14 \hspace{.25em} units \hspace{.25em} down$$
b) $$shifts \hspace{.25em} 7\hspace{.25em} units\hspace{.25em} right,\hspace{.25em} 7 \hspace{.25em} units \hspace{.25em} up$$
#5:
Solutions:
a) $$shifts \hspace{.25em}17\hspace{.25em} units\hspace{.25em} right ,\hspace{.25em} 12 \hspace{.25em} units \hspace{.25em} down$$
b) $$shifts \hspace{.25em} 1\hspace{.25em} unit\hspace{.25em} left,\hspace{.25em} 23 \hspace{.25em} units \hspace{.25em} down$$<|endoftext|>
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March 15, 1744-October 18, 1748: King George's War The warm-up to the French and Indain War between France and England, also fought for domination over North America. Ends with the treaty of Aix-la-Chapelle and no clear victor.
1752-1753: Agitation grows Tension grows between France and England over competing land and trading claims. Minor skirmishes break out, particularly in rural areas.
November-December 1753: The message George Washington carries Virginia's ultimatum over French encroachment to Captain Legardeur de Saint-Pierre at Riviere aux Boeufs. He rejects it.
May 28, 1754: The first battle Washington defeats the French in a surprise attack. His troops retreat to Great Meadows and build Fort Necessity.
July 3, 1754: The French take Fort Necessity
July 17, 1754: Washington's resignation Blamed for Fort Necessity, Washington resigns. He will later return as a volunteer under British authority.
June 17, 1755: The British seize Acadia (Nova Scotia)
July 9, 1755: The Battle of the Wilderness British General Braddock's forces are defeated near Fort Duquesne in Pennsylvania, leaving the backwoods of British territory undefended.
September 9, 1755: The Battle of Lake George British Colonel William Johnson's forces win, making Johnson the first British hero of the war.
May 8-9, 1756: Declarations of War Great Britain declares war on France. France declares war on Great Britain.
August 14, 1756: Fort Oswego The French capture this fort on the banks of the Great Lakes.
August 8, 1757: Fort William Henry The commander-in-chief of the French forces, Louis-Joseph de Montcalm takes Fort William Henry. The infamous massacre occurs, later dramatized in James Fenimore Cooper's The Last of the Mohicans.
July 8, 1758: The French take Fort Ticonderoga
July 26, 1758: Louisbourg The British seize Louisbourg, opening the route to Canada.
August 27, 1758: Fort Frontenac The French surrender this fort on Lake Ontario, effectively destroying their ability to communicate with their troops in the Ohio Valley.
October 21, 1758: British/Indian Peace The British make peace with the Iroquois, Shawnee, and Delaware Indians.
November 26, 1758: The British recapture Fort Duquesne It is renamed "Pittsburgh."
May 1, 1759: The British capture the French island of Guadeloupe in the Caribbean
June 26, 1759: The British take Fort Ticonderoga
July 25, 1759: A Slow Route to Victory The British take Fort Niagara; the French abandon Crown Point. After these two victories, the British control the entire western frontier.
September 13, 1759: Quebec The British win the decisive Battle of Quebec. Montcalm and Wolfe, the commanding generals of both armies, perish in battle.
May 16, 1760: French Siege of Quebec fails
September 8, 1760: Montreal Montreal falls to the British; letters are signed finishing the surrender of Canada.
(circa) September 15, 1760: The functional end of the war The British flag is raised over Detroit, effectively ending the war.
1761: The British make peace with the Cherokee Indians
September 18, 1762: French attempt to retake Newfoundland fails
February 10, 1763: Treaty of Paris All French possessions east of the Mississippi, except New Orleans, are given to the British. All French possessions west of the Mississippi are given to the Spanish. France regains Martinique, Guadeloupe and St. Lucia.
April 27, 1763: Indian Wars Pontiac, the Ottowa Chief, proposes a coalition of Ottowas, Potawatomies and Hurons for the purpose of attacking Detroit.
May 9, 1763: Battle of Detroit Pontiac's forces lay siege to Detroit. That summer, his allies destroy forts at Venango, Le Boeuf and Presque Isle.
July 1763: Smallpox Men of the garrison at Fort Pitt infect besieging chiefs with blankets from the smallpox hospital. Soon faced with an epidemic, the Indians retreat.
October 31, 1763: Pontiac capitulates at Detroit Indian power in the Ohio Valley is broken.<|endoftext|>
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Laser-lit parrotlet sheds light on how birds’ flight creates lift
Most of the time, birds don’t need flight goggles. But then again, most of the time birds aren’t flying through swirling mist and arrays of lasers that might damage their vision. As much as this sounds like a goofy pitch for spy movie produced by Animal Planet, it’s actually some key components of a study done at Stanford University to look at the basics of how birds fly. As mundane as that question may seem compared to its experimental setup, it turns out bird flight is more complicated than previously appreciated.
The mist and lasers weren’t actually for dramatic effect, but were instead used to let researchers see how bird wings interact with the air. The lasers were arranged in a line, illuminating the suspended droplets of mist along a single plane in the bird’s flight path. With custom, 3D-printed goggles on to protect its eyes, the bird, a parrotlet named Obi, was then recorded by high-speed cameras as he flew through the floating mist. As Obi’s wings flapped and pushed through the air, the droplets could then be seen swirling and reacting, although not exactly in a way that anyone predicted.
Violence in the vortices
The movement seen in the swirling mist, as a proxy for how air molecules normally move under a bird’s wings, was much rougher than predicted. The expectation was that as Obi’s wings flapped, they’d swirl the air into vortices that would remain behind the him for a few moments. Fixed wing aircraft also stir up the air this way, and vortices can be found thousands of meters behind the plane. While Obi’s flights did create vortices in the misty air, they didn’t prove to be very durable. After only two to three wing beats, most of the pretty swirls of air were completely blown apart.
Obi was obviously fine with all of this, having always flown and disrupted the air this way. For researchers though, this presents some significant questions. Three different models for how bird’s achieve lift when interacting with air failed to predict the observed data, which means that we don’t fully understand how feathered wings work yet. In addition to better understanding our bespeckled test subject, studies of lift will help inform designs of future flying robots, which will hopefully benefit from all the work evolution has already put into figuring out winged flight.
Source: Birds flying through laser light reveal faults in flight research, Stanford study shows by Taylor Kubota, Stanford News<|endoftext|>
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Expanding Voter Rights: The Voting Rights Act, 1965 and beyond
Objectives Activities will help students: Explain why the federal government passed the Voting Rights Act evaluate the impact of the Voting Rights Act Explain current challenges to the Voting Rights Act Understand new threats to voting rights Explore how to protect voting rights, with particular emphasis on the state where they live
Expanding Voting Rights:
The Voting Rights Act, 1965 and Beyond
Lesson plan developed by Teaching Tolerance, a project of the Southern Poverty Law Center
Videos produced by NBC News
This lesson is the third in a series called Expanding Voting Rights. The overall goal of the series is for students to explore the complicated history of voting rights in this country. Two characteristics of that history stand out: First, in fits and starts, more and more Americans have gained the right to vote; and second, the federal government has played an increasing role over time in securing these rights.
This lesson focuses on the 1965 law that aimed to ensure that African Americans would no longer be denied their right to vote. Students will read a summary of the Voting Rights Act to find out what it said, then study data that show the law’s impact. They watch two NBC news reports about a 2009 Supreme Court challenge to the Voting Rights Act and the Court’s ruling on that challenge. The lesson has them consider the grounds on which people have based their objections to the Voting Rights Act.
Coming up to the present, students study graphs that show the potential effects of efforts to curtail voting rights—specifically photo ID requirements and “matching” requirements. Finally, students explore efforts in their own states to limit voter participation and how to counter those efforts, or the success of efforts in their area to increase voter registration and participation.
Activities will help students:
- explain why the federal government passed the Voting Rights Act
- evaluate the impact of the Voting Rights Act
- explain current challenges to the Voting Rights Act
- understand new threats to voting rights
- explore how to protect voting rights, with particular emphasis on the state where they live
- What did the Voting Rights Act of 1965 say?
- Why was the Voting Rights Act necessary? What effects has it had?
- Why have some people challenged the Voting Rights Act in recent years?
- How are voting rights threatened today? How can we protect those rights?
(noun) the right to vote
(noun) the act of depriving someone of the right to vote
(verb) to deprive; to limit
voter registration [voh-ter rej-uh-strey-shuhn]
(noun) an action taken by an eligible voter to have her voting qualification verified (usually at the county level) so that he can vote in elections
The Right to Vote: The Contested History of Democracy in the United States by Alexander Keyssar
The Voting Rights Act of 1965 (U.S. Department of Justice website)
Voting Rights and Elections (The Brennan Center for Justice at NYU School of Law)
NBC Learn video: "Signing the Voting Rights Act"
NBC Learn video: "The Right to Vote"
NBC Learn video: "Supreme Court Re-Examines 1965 Voting Rights Act"
NBC Learn video: "Supreme Court Narrowly Allows 1965 Voting Rights Act to Stand"
What the Voting Rights Act Said
1. Watch a short NBC news clip from1965 that reports on then-President Lyndon Johnson signing the Voting Rights Act. Seeing the video will bring you to the starting point of this lesson, an examination of that 1965 law.
2. In 1965, the United States enacted the Voting Rights Act. It laid out strict rules that would enable African Americans to exercise their right to vote, particularly in Southern states that had created significant barriers to prevent them from doing do. (Note: If your students have not completed Lesson 2 in this series, you can provide some background on the Voting Rights Act by having them watch this 14-minute video from the NBC Learn archives.) To learn what the Voting Rights Act said, read the handout The Voting Rights Act of 1965. When you’ve read it, write a few sentences to explain what barriers to voting the new law banned, and why the law was necessary.
The Effects of the Voting Rights Act
3. The Voting Rights Act had both immediate and long-term effects. Look at the graphics Percentage of Registered Voters in Black Voting-Age Population: 1960, 1971, 2008 and the Number of Black Legislators in the South (1868-1900 and 1960-1992) handouts.
a. Complete the activities on each handout to help you understand the data.
b. Summarize the effects that the Voting Rights Act has had. Would you say it has been successful? Why or why not?
Challenges to the Voting Rights Act
4. The Voting Rights Act was reauthorized in 1970, 1965, 1982 and 2006. In each instance, Congress looked at evidence that showed that African Americans’ voting rights were still in danger in the states identified in the original 1965 law. In 2009, the Voting Rights Act faced a challenge in the Supreme Court.
a. Watch these two NBC Learn videos about that challenge: "Supreme Court Re-Examines 1965 Voting Rights Act" and "Supreme Court Narrowly Allows 1965 Voting Rights Act to Stand." As you watch, make notes about why the law was challenged. On what grounds was it challenged? Why did the Supreme Court uphold the law? With what reservations?
b. Think about which, if any of those reasons for challenging the law you think are legitimate. Share your thinking with your partner. (Note: Randomly call on pairs to share their thinking with the class.) As a class, reach a consensus about the challenges to the Voting Rights Act.
Current Challenges to Voting Rights
5. As you know, civil rights activists struggled and sacrificed for a long time to push the federal government to take action to ensure that African Americans could exercise their right to vote. Recently new roadblocks have arisen that many people think threaten the hard-earned successes of the civil rights movement. In many states, new restrictions have been enacted for the stated reason of combating voter fraud. In reality, instances of voting fraud are nearly non-existent. The new restrictions actually threaten the voting rights of African Americans and Latinos, as well as young voters and low-income people.
With a small group, analyze the two graphs. Discuss these questions: What does each graph show about who is or would be most affected by the new law or proposed new law? What conclusions can you draw when you look at both graphs together? Compare the data in these graphs with what you know about how African Americans in the South were prevented from voting in the century between Reconstruction and the civil rights movement. Make a chart that shows the similarities and differences.
6. Divide the class into groups. Assign each group one of the following current efforts to limit voter registration: end of same-day voter registration, end of “motor voter” registration, residency requirements that affect college students. With your group, research the challenge you have been assigned. Make a poster presenting what you have learned. In your poster, explain what your group’s challenge has in common with techniques that have been used in the past to limit access to voting. Do you think these new efforts could be challenged on the basis of the Voting Rights Act? Why or why not?
Voting Rights in Your State: What Can You Do?
7. What’s happening in your state regarding voting rights? Are there any attempts to limit voting rights? Do some research to find out. If you find that there are, find out who is fighting to maintain or expand voting rights and how they are doing so. Invite someone to speak with your class about those efforts. Find out what your class can do to participate, then do it.
8. Understands the central ideas of American constitutional government and how this form of government has shaped the character of American society
14. Understands issues concerning the disparities between ideals and reality in American political and social life
15. Understands how the United States Constitution grants and distributes power and responsibilities to national and state government and how it seeks to prevent the abuse of power
United States History
29. Understands the struggle for racial and gender equality and for the extension of civil liberties
31. Understands economic, social, and cultural developments in the contemporary United States
Common Core Standards: College and Career Readiness Anchor Standards
1. Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.
7. Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.
9. Draw evidence from literary or informational texts to support analysis, reflection, and research.
Speaking and Listening
1. Prepare for and participate effectively in a range of conversations and collaborations with diverse partners, building on others’ ideas and expressing their own clearly and persuasively.
2. Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.<|endoftext|>
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### 1.3 Using Percent
<
>
• Math Help
We have already talked about the importance of unit analysis. In this section, we begin the second critical skill that you must develop for success in mathematics. That skill is knowing how to find and how to interpret percent.
This section provides only a brief review of percent. Be sure that you are completely comfortable with this concept. Check yourself with the following exercises.
#### Review Exercises
1. Write 0.5 as a percent.
2. Write 0.5% as a decimal.
3. What is 20% of 48?
4. 30 is what percent of 90?
5. What is 25% of 500?
1. 0.5 is one-half or 50%. (Move decimal point 2 places to the right.)
2. 0.5% is less than 1%. In decimal form, it is 0.005.
3. 10% of 48 is 4.8. So, 20% is 9.6.
4. 30 is one-third of 90. So, 30 is of 90.
5. 25% is one-fourth. So, 25% of 500 is 125.
• Consumer Suggestion
Click here to see how much land the Federal Government owns in your state. Or use a search engine to search for the phrase "land owned by federal government."
• Checkpoint Solution
Alaska has a land area of 571,951 square miles. According to the table on page 24, 69.1% of this is owned by the federal government.
In Example 1, we found that the federal government owns about 92,800 square miles of Nevada. So, the federal government owns much more land in Alaska than it does in Nevada.
There are about 3.5 million square miles of land in the United States. About 67% of that land is owned by individuals, corporations, and states. The remaining land is owned by the federal government and is administered for the most part by four federal agencies:
1. The Bureau of Land Management (BLM)
2. The National Park Service (NPS) (U.S. Department of Interior)
3. The Fish and Wildlife Service (FWS) (U.S. Department of Interior)
4. The Forest Service (FS) (U.S. Department of Agriculture)
(source: Bureau of Land Management)
These comments are not screened before publication. Constructive debate about the information on this page is welcome, but personal attacks are not. Please do not post comments that are commercial in nature or that violate copyright. Comments that we regard as obscene, defamatory, or intended to incite violence will be removed. If you find a comment offensive, you may flag it.
``` ______ ______ ______ ___ _ __
/_ _// /_ _// | \\ / _ \\ | |/ //
`-| |,- -| ||- | -- // | / \ || | ' //
| || _| ||_ | -- \\ | \_/ || | . \\
|_|| /_____// |______// \___// |_|\_\\
`-`' `-----` `------` `---` `-` --`
```<|endoftext|>
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The official declaration of America’s independence from Britain may be dated July 4, 1776, but the story of the Thomas Jefferson's hallowed document really begins two weeks later. On July 19, the Continental Congress ordered a scribe, Pennsylvania State House clerk Timothy Matlack, to write the words on a piece of parchment big enough for everyone to read—and with room for signatures.
Since then, the Declaration of Independence has had a fairly rough time. A forensic analysis of the document shows some rough handling, damaging displays, and even a mysterious handprint. Understanding why it looks the way that it does — much more faded and battered than the U.S. Constitution or The Bill of Rights — is a romp through the history of printing, preservation, and patriotism.
Old Tools, Faded Inks, Unfortunate Folds
The story starts with Matlack’s tools—a quill dipped in iron gall ink. That kind of ink was nothing special. It was cheap and commonly available at the time. “Because of its indelibility, it was the ink of choice for documentation from the Middle Ages to the twentieth century”—so says a non-profit website dedicated to iron gall ink.
Its ingredients are stated in the name. Ground gall nuts, taken from an oak-like tree, were boiled to draw out tannic acid, which was mixed with iron sulfate scraped from nails. “The ingredients could also be mixed dry, which would produce ink the moment water was added to it,” the website continues. “This powder would make for a perfect traveling ink, created only as needed to avoid the opportunity for mold growth.” The scribe would etch letters that would gradually darken as oxygen works on the iron. Over time, that dark color mellows to a soft brown.
But the current custodians of the document—the National Archives—will tell you that almost no original ink remains on the Declaration of Independence. The document had no permanent home during the earliest days of the Revolutionary War, resulting in crude folding and rolling, causing some of the ink to flake off. As you can imagine, this rough treatment led to permanent damage.
“Evidence of previous folding and rolling is still visible on the Declaration,” says one National Archives analysis. “Two primary vertical fold lines run from top to bottom, and there are numerous horizontal fold lines especially in the lower part of the document.”
Good Intentions, Terrible Results
Restorers with the best of intentions can still do plenty of harm, and early efforts to protect the Declaration damaged the document further.
While Secretary of State, future president John Quincy Adams commissioned full-sized copies of the Declaration to be made to limit the exposure of the original. The resulting copperplate is dated July 4, 1823.
It was a good idea, but the method of the day involved engraving the image on a copperplate. Step one of this involved pressing wet fabric against the ink to transfer an exact copy of the words onto the plate. This removed some ink and accounts for some of the faded look we see today, especially around the signatures.
Then things went from bad to worse. In 1841, the first exhibition hall in Washington D.C. opened in the Patent Office Building (now the National Portrait Gallery), and what better thing to display than the Declaration of Independence? It sounded like a smart idea, but over the course of 35 years on display, the document was exposed to damaging light that further faded what little ink remained.
Public officials lamented the damage, especially as photography came of age. The first photo of the Declaration, taken in 1883, charted the deterioration. By 1921, light was seen as a major threat to the historic document. Under the Library of Congress's stewardship, the Declaration and Constitution went on display with a sheet of yellow gelatin wedged between panes of glass.
Photography also revealed another piece of damage—a handprint at the lower left corner of the Declaration of Independence. Discovered in 1940, the handprint doesn't appear in a 1903 photo. No one knows how it got there, but conservators have decided not to remove it. Now the handprint remains as another piece of American lore.
When Air Becomes an Enemy
A different preservation problem became clear by the 1940s. The humidity of sweltering Washington D.C. would soften the adhesive at the edges of the Declaration. When the humidity dropped, the parchment contracted and that tension caused the document to tear. Those tears only grew over time.
Exposure to air suddenly became public enemy number one. So, in 1951, the Declaration was sealed in an enclosure filled with humidified helium. The original Declaration of Independence stayed in this home, located in the Rotunda of the National Archives Building, for fifty years.
In 2001, conservators noticed small surface cracks, crystals, and droplets forming on the glass. These signs of deterioration in time would cause the glass to become opaque. The Declaration and other founding documents needed a new home, re-encased in new airtight containers made of aluminum and titanium and filled with argon gas rather than helium. The relative humidity of the argon gas is at 40 percent, and the case remains continually at 67 degrees Fahrenheit.
Guns, Bells, and Bonfires
On July 3, 1776, John Adams wrote to his wife, Abigail, that the Continental Congress approved a resolution for independence.
“I am apt to believe that it will be celebrated by succeeding generations as the great anniversary festival,” he wrote. “It ought to be solemnized with pomp and parade, with shows, games, sports, guns, bells, bonfires and illuminations from one end of this continent to the other from this time forward forever more.”
Thanks to the work of preservationists—and sometimes despite their best efforts—those of us in the 21st century can see the fragile pages at the center of this celebration, shrouded in a cocoon of invisible argon gas.<|endoftext|>
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# Quants Questions: Hacks on Square of a Number
Quantitative Aptitude is hard in most cases especially in exams like Banks and Insurance. Many Banks exam has a two-tier examination pattern i.e., Prelims and Mains. Most of them have changed their exam patterns and set a sectional timing of 20 minutes on each section. Quantitative aptitude is important for every exam because proper strategy and enough practice can help you score full marks in this section. There may not be assured in the language section and you may be stuck while solving reasoning questions but quants is a scoring subject and assure full marks if the calculation is correct.
So to help you ace the quants and to save your precious time during exam hours Adda247 providing some quant tricks to help aspirants.
Square of a numbers-
1. Square from 20-30
(21)= 441, (22)2= 484, (23)2=529, (24)2=576, (25)2=625
Now tens and unit digit of a number repeats after (25)
(26)2=676, (27)2=729, (28)2=784, (29)2=841.
Note- last 2 digits repeat here after the square of 25.
2. Square from 30-40
(30)2=30*30=900
Use this formula to calculate the square: (a+b)2= a2+b2+2ab
(31)2= (30+1)2= (30)2+1+2*30*1)= 900+ 1+ 60=961
(32)2= (30+2)2= (30)2+ (2)2+2*30*2=900+4+120= 1024.
or we can write 32 as (2)5=(32)2=[(2)5]2=(2)10= 1024 this is an important number.
.
3. Square from 40-50:
The square from 40-50, unit and tens places of square decreases from the square of 10 to 1.
(40)2= 1600, (41)2= 1681 (42)2= 1764 (43)2= 1849(44)2= 1936(46)2= 2116
(45)2= 2025
or we can calculate it by-
a) (45)2= tens digit*(tens digit+1)
b) 25 as constant
c) sum of (difference of digits*50)= 2025
(46)2= 2116 (47)2= 2209 (48)2= 2304(49)2= 2401
3. Square of a number between 50-60.
(50)2= 2500
Half of 50 i.e 25, add the unit digit to 25, square of the unit digit.
(51)2= (half of 50)+1 and square of 1 i.e 2601
(52)2=( half of 50)+2 and square of 2 i.e 2704
(53)2= (Half of 50)+3 and square of 3 i.e 2809
(54)2= 2916.
(55)2= 3025.
Or you can find the square of 55 by
a) (55)2= tens digit*(tens digit+1)
b) 25 as constant
c) sum of (difference of digits*50)= 3025.
6. Square of number multiple of 11.
step1. Count number of 1s.
step2. then write the subsequent numbers of 1 till the number of 1s.
step3. then decrease the subsequent number.
(11)2= 121 [ number of 1 is 2, write subsequent number till number of 1]
(111)2= 12321[ here number of one is 3],
(1111)2= 1234321[ here number of one is 4]
before further calculating square, you must know the shortcut to multiplication by 11.
a) 74*11
step1. unit digit and the tens digit is as usual- (7_4)
74*11= 814
b) 46*11= 506
Now calculating more squares
(22)2= 4*121 or 4*11*11= 484, (33)2= 9*121=1089
(44)2= 16*121= 16*11*11= 16*11=176*11
multiplication of 176*11
step1. now 176*11= ones and tens digit (1 and 6) is as usual
step2. addition of (7&6)= 13 and take 3 and 1 is the carry<|endoftext|>
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- National Security
- Tell students that they will learn the origins of freedom of the press in America. Check for background knowledge by asking:
- What do you know about the Bill of Rights and the First Amendment?
- Should we be allowed to criticize our government? Why or why not?
- What is the role of the press in political affairs?
- Remind students of the rationale behind the Federalist and Antifederalist positions.
- Democratic-Republican publishers, concerned that the Federalists’ push for a strong centralized government would jeopardize individual liberties, lobbed insults at George Washington, John Adams and anyone else they saw as betraying the ideals of the Revolution.
- The Federalists, bracing for a possible war with France and fearful that such sharp criticism could destabilize the young nation, passed the Sedition Act, banning any speech or publication intended to undermine the government. Publishers across the republic went to jail and paid steep fines, and public disapproval of the law grew until the Federalists lost power in 1800, when Democratic-Republican Thomas Jefferson won the presidency.
- Explain that as they watch the video, students will see how the First Amendment survived its first significant challenge and how it continues to play a role in our lives today. Hand out copies of the viewing guide. Students should review the questions before you start the video and then take notes as they watch it.
- Watch the video.
- The after-you-watch comprehensive questions can be done in class or for homework.
- “45 Words” Video Lesson worksheet (download), one per student
- “45 Words” reference materials (download, optional)
- Internet access to watch “45 Words”
Ask your students to reflect on the tension between freedom of press and national security and unity. Discuss or assign one or more of these questions as short essays for homework:
- Does sedition exist today? If yes, what does it look/sound like? If not, why not?
- What should be the role of opinion in journalism? Is it ever OK for journalism to express biased opinions about politics or other issues? Where do we generally see opinionated or advocacy journalism today?
- In the video, law professor R.B. Bernstein describes the political tensions in early America, saying, “The question is: Can we fight these things out and still remain united? We’re used to the idea. They’re not. They’re scared.” Are fights a necessary part of the political process? How should we handle dissenting opinions so that all voices are heard but debates do not tear the country apart?
- The video quotes Thomas Jefferson saying, “If it were left up to me to decide whether we should have a government without newspapers or newspapers without a government, I shouldn’t hesitate for a moment to choose newspapers.” Why would Jefferson choose newspapers over government? Would you make the same choice? Why or why not? How would our country be different if there were no news media?
- How far should freedom of press extend? Where should we draw the line between protected criticism of the government and ideas that could cause harm to the country or its citizens?
- Concerns about sedition often arise at times of war or political unrest. Why do you think this is the case? Are there any circumstances under which we should place more limits on freedom of the press? When and why?
- In the video, journalist and author Eric Burns says, “Civility just did not seem to have a place in the [early American] press. Too much at stake. In addition, the press was as vile as it was back in those days because there was no tradition of fairness.” What does Burns mean when he says there was “too much at stake” for the early American press? Compare and contrast the role and workings of today’s press to the early American press. Does today’s press follow the “tradition of fairness” Burns describes?
- Benjamin Franklin wrote, “Those who desire to give up freedom in order to gain security will not have, nor do they deserve, either one.” What does Franklin mean? Do you agree with this statement? Why or why not?
- Find the full text of the Alien and Sedition Acts of 1798 (available here:http://avalon.law.yale.edu/subject_menus/alsedact.asp). Make a chart that compares and contrasts: the reasons leading to the passage of each law, the specific acts each law outlawed, the punishments described, and each law’s effects.
- At the time depicted in the video, newspapers were the main medium for publishing news. Today, a much greater variety of communication tools is available. Choose a quotation that interests you from one of the historical figures in the video. (You may need to watch it again to find your quotation.) Determine what this quotation means, then translate the main idea into modern language and communicate it using a variety of modern media: a Twitter posting, a Facebook status update, a YouTube video, a blog post, a text message, etc. Choose at least three forms of modern media.
- What limits do we put on First Amendment freedoms? What limits should we put on First Amendment freedoms? Visit the First Amendment Center’s website (http://www.firstamendmentcenter.org/) and select one First Amendment freedom. Read the overview of the freedom and make a chart that lists how you can use the freedom and how you cannot use the freedom. Then write a paragraph describing what you think the limits on this freedom should be. What should be allowed? What should not be allowed? Why?
- Benjamin Franklin Bache and Matthew Lyon were not the only individuals tried under the 1798 Sedition Act. Write a short report about one of the following individuals and their involvement with sedition: James Thomson Callender, Samuel Chase, Thomas Cooper or William Patterson.
- Choose a historical figure from the “Need to Know” list of key people. Research this person and write a more extended biography, focusing on his or her connections to the First Amendment, the press and the Sedition Act.
- Create a timeline of sedition cases throughout American history. On your timeline, also include major historical events to provide context for the court cases.
- Collect three recent newspaper editorials or opinion articles that take a critical stance against something the government is doing. (You can find these in the editorial and op-ed pages of a printed newspaper or on the “Opinion” page of an online newspaper site.) For each editorial or opinion article, make a chart. At the top, summarize the argument the piece is making. Underneath, list the facts cited and opinions expressed. At the bottom, explain whether you agree or disagree with the position taken and why.
- While prosecution of the press for sedition has become rare, libel cases remain common in today’s court system. Research what libel is. (Start with this overview:http://www.splc.org/knowyourrights/legalresearch.asp?id=27.) Prepare a presentation to explain to your classmates what libel is, including the “PIHF checklist” and the four defenses against libel. Also explain the similarities and differences between libel and sedition.<|endoftext|>
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In May of 1972, tens of thousands of African Americans gathered in Washington, D.C. Young and old, radical and moderate, they united not in protest of the government’s treatment of blacks in the United States, but rather on behalf of their distant kin fighting revolutions in Africa. At the first African Liberation Day, black peoples in the western Diaspora sought to change American foreign policy, which continued to actively support the colonial empire of tiny Portugal and the minority regimes of Rhodesia (Zimbabwe) and South Africa. The crowd marched through the streets of the capital, carrying signs proclaiming solidarity with the liberation struggles and condemning the economic discrimination that kept blacks subservient at home as well as abroad. The parade of activists made stops at the State Department and the embassies of the southern African regimes, where government and community leaders urged listeners to adopt the African revolutions as their own and boycott corporate partners like Gulf Oil and Polaroid that helped sustain minority rule. This demonstration culminated on the National Mall – renamed Lumumba Square for the festivities – where an estimated 25,000-40,000 people joined organizer Owusu Sadaukai (Howard Fuller) in chants of “We are an African People.” This demonstration in Washington, described by one participant as the largest all-black assemblage in the city’s history, was a symbol of a much larger movement that developed at the end of the Black Power era. Disillusioned both with the slow pace of civil rights in the mid-1960s and the ideological divisiveness of groups like the Black Panthers, African American leaders sought a common ground on which they could build a political and social movement that would unite the entire black community. They found a solution in the ongoing revolutions occurring in southern Africa. Since the wave of decolonization had begun to sweep through the continent in the late 1950s, black Africans had been struggling for self-determination against recalcitrant minority white governments. Nationalists adopted armed revolution and wholesale social reconstruction as necessary tactics in the face of official resistance to reform. By 1972, the armed conflicts in the Portuguese colonies of Mozambique in the south and Guinea-Bissau in the northwest had swung in the favor of the freedom fighters, while South Africa’s harsh system of segregation known as apartheid had dramatized for the world the stark inequality that separated the races under minority rule. The two faces of Africa – heroic struggle and racial injustice – provided African Americans a rallying cry as they sought to address the systemic economic and political problems that continued to plague their own communities. This sense of shared struggle gave birth to a solidarity movement, where African Americans pledged support to African liberation and sought to use these continental models of self-determination to change conditions in the United States. For their part, Africans joined in this exchange of equals, with exiles helping to lead local movements and nationalists encouraging the support of their brothers abroad. WGBH cameras were there at almost all stages of the construction of this movement, documenting the interactions of African peoples across linguistic, spatial, and experiential gaps. This collection will explore these exchanges, using episodes of Say Brother to illuminate the leaders, events, and campaigns that helped reignite a commitment to African liberation in the national imagination. Though the celebration of African Liberation Day would fade along with the 1970s, this identification with the continent had important effects on black communal identity and would feed directly into the more famous anti-apartheid movement of the next decade.<|endoftext|>
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Direct and indirect speech exercise
Sentences are given in the direct speech. Change them into the indirect speech.
1. Seema said to me, ‘Where do you live?’
2. He said to me, ‘Please help me.’
3. He said to me, ‘Will you have time to do it.’
4. John said to me, ‘I may leave tomorrow.’
5. Kiran said, ‘I didn’t steal the pen.’
6. Vishwas said, ‘I am going.’
7. He told her, ‘I will pass the test.’
8. Shakespeare said, ‘All the world is a stage.’
9. He said to them, ‘Go away.’
10. He says, ‘I have invited them.’
11. Surabhi said, ‘I like to read.’
12. Rahul said to me, ‘Where are you going?’
1. Seema asked me where I lived.
2. He requested me to help him.
3. He asked me if I would have time to do it.
4. John told me that he might leave the next day.
5. Kiran said that she hadn’t stolen the pen.
6. Vishwas said that he was going.
7. He told her that he would pass the test.
8. Shakespeare said that all the world is/was a stage.
9. He asked them to go away. / He told them to go away. / He ordered them to go away.
10. He says that he has invited them.
11. Surabhi said that she liked to read.
12. Rahul asked me where I was going.<|endoftext|>
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# Video: Changing the Subject of a Formula
The displacement, ๐ , of an object traveling with uniform acceleration, ๐, can be calculated using the formula ๐ = ๐ข๐ก + (1/2) ๐๐กยฒ, where ๐ข is the initial velocity and ๐ก is the time. Make ๐ the subject. Calculate the acceleration of an object that has started from rest and travelled 200 m in 8 s.
04:16
### Video Transcript
The displacement, ๐ , of an object travelling with uniform acceleration, ๐, can be calculated using the formula ๐ equals ๐ข๐ก plus a half ๐๐ก squared, where ๐ข is the initial velocity and ๐ก is the time. Thereโre two parts to this question. The first part, Make ๐ the subject. And the second part, calculate the acceleration of an object that has started from rest and travelled 200 meters in eight seconds.
So if we have our formula, which is ๐ equals ๐ข๐ก plus half ๐๐ก squared. And if we want to make ๐ the subject, well, the subject means we want the ๐ on its own. So the first thing weโre gonna do is subtract ๐ข๐ก from both sides of the equation. Thatโs cause that will leave us with a half ๐๐ก squared on the right-hand side. So now, when we subtracted ๐ข๐ก from both sides of the equation, we get ๐ minus ๐ข๐ก is equal to a half ๐๐ก squared. And now, because weโve got a half ๐๐ก squared on the right-hand side, what weโre gonna do is multiply both sides of the equation by two. And thatโs because that will remove the half that weโve got removed the fraction.
So when we do that, we get two multiplied by ๐ minus ๐ข๐ก is equal to ๐๐ก squared. Thatโs because if we have a half multiplied by two, you get one. So then, all we need to do is divide by ๐ก squared because that will leave ๐ on its own. And once we do that, weโll have two multiplied by ๐ minus ๐ข๐ก over ๐ก squared is equal to ๐. So therefore, having made ๐ the subject, weโve got ๐ is equal to two multiplied by ๐ minus ๐ข๐ก over ๐ก squared.
Great. Now, letโs move on to the second part. And in the second part, we need to calculate the acceleration of an object that has started from rest and travelled 200 meters in eight seconds. So now to solve any question like this, what Iโd do first is write down the information Iโve got. So we know that ๐ข is equal to zero because this is the initial velocity. And we know that because weโre told that the object starts from rest. And for an object to start from rest, that means that itโs not gonna have any velocity at the beginning. So ๐ข is equal to zero.
Then, the next thing we know is that the distance, which is ๐ , is equal to 200 meters. And thatโs because weโre told the distance travelled is 200 meters. Then, we also know the time because this is eight seconds and the acceleration ๐ is what weโre looking for. So we havenโt got that yet. Okay, now weโve got our values, we can just substitute them into our equation. And the equation weโre gonna use is ๐ equals two multiplied by ๐ minus ๐ข๐ก over ๐ก squared because what weโre trying to find is ๐, which is the acceleration.
So now, to work out the acceleration, weโre gonna have ๐ is equal to two multiplied by. Then, weโve got 200 cause thatโs our ๐ , cause thatโs our distance minus ๐ข, which is zero multiplied by our time, which is eight. And then this is all divided by our time squared, which is eight squared. So this gives us that ๐ is equal to 400 divided by 64. And thatโs because we had two multiplied by. And then, youโve got 200 minus zero multiplied by eight. Well, 200 minus zero cause zero multiplied by anything is just zero gives us 200. Two lots of 200 is 400 and then divided by eight squared and eight squared is 64.
Then, if we simplified it by dividing both the numerator and denominator by four, weโre gonna get 100 over 16. And then once more divided by four, weโre gonna get 25 over four cause 100 divided by four is 25. 16 divided by four is four. So then, we can see that four goes into 25 six times with one remainder. So we get six and a quarter. And when we turn it into a decimal, itโs 6.25. Then, we know that the units are gonna be meters per second squared because thatโs the measurement weโre gonna use for acceleration.
So we can say that if we make ๐ the subject, we get ๐ equals two multiplied by ๐ minus ๐ข๐ก over ๐ก squared. And if we calculated the acceleration of an object that has started from rest and travelled 200 meters in eight seconds, then the result is 6.25 meters per second.<|endoftext|>
| 4.46875 |
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+0
0
5
3
+68
Let
$$f(x) = \left\lfloor\frac{2 - 3x}{x + 3}\right\rfloor.$$
Evaluate $$f(1)+f(2) + f(3) + \dots + f(999)+f(1000).$$(This sum has terms, one for the result when we input each integer from to into .)
Mar 24, 2024
#3
+128845
+1
f(1) = -1
f(2) = -1
f(3) = -2
.
.
.
f(8) = -2
f(9) = -3
.
.
.
f(1000) = -3
Sum of terms
2(-1) + 6(-2) + 992(-3) = -2990
Mar 24, 2024
#1
+179
+1
Analyzing the function f(x) = floor((2 - 3x) / (x + 3)):
The denominator (x + 3) is 0 when x = -3. This means f(x) is undefined at x = -3.
We will need to consider different cases based on the sign of the denominator (x + 3) and the relative values of 2 - 3x compared to 0.
Cases for f(x):
x < -3: In this case, both denominator (x + 3) and numerator (2 - 3x) are negative. Dividing two negative numbers results in a positive value.
Since we take the floor (greatest integer less than or equal to), f(x) will be -1.
-3 < x < 2/3: Here, the denominator (x + 3) is positive, but the numerator (2 - 3x) is negative.
Dividing a positive by a negative results in a negative number.
Taking the floor of a negative number keeps it negative, so f(x) will be -2.
x = 2/3: At this specific point, the numerator becomes 0, and the result of the division is 0. The floor of 0 is 0, so f(x) = 0.
x > 2/3: In this case, both the numerator (2 - 3x) and denominator (x + 3) are positive. Dividing two positive numbers results in a positive value.
Taking the floor doesn't change the positive sign, so f(x) will be 1.
Evaluating the sum:
The key to evaluating the sum efficiently is to recognize that for a large range of x values (between -3 and 2/3), f(x) will be -2.
We can exploit this by calculating the number of terms that fall into this range and summing the contributions from the remaining terms separately.
Number of terms where f(x) = -2:
We know x = -3 falls outside this range (f(x) is undefined).
The range ends when x = 2/3, which is between terms 1000 and 1001 (1000th term is x = 999 and 1001st term is x = 1000).
Therefore, there are 1000 - (-3) + 1 = 1004 terms where f(x) = -2.
Contribution from terms where f(x) = -2:
Each term contributes -2 to the sum.
Total contribution = -2 * (number of terms) = -2 * 1004 = -2008
Remaining terms:
We need to consider terms for x < -3 (f(x) = -1), x = 2/3 (f(x) = 0), and x > 2/3 (f(x) = 1).
There are very few terms less than -3 (all negative x values), and they can be ignored for a large sum like this (their contribution will be negligible).
There's only one term for x = 2/3, contributing f(2/3) = 0.
The remaining terms from x slightly greater than 2/3 to x = 1000 will all have f(x) = 1. The exact number of these terms depends on the specific values, but there will be significantly fewer compared to the 1004 terms with f(x) = -2.
Overall Sum:
Sum from terms with f(x) = -2: -2008
Contribution from f(2/3) (x = 2/3): 0
Contribution from remaining terms with f(x) = 1 (positive but less than those with -2): + (positive value)
Since the number of terms with f(x) = 1 is significantly less than those with -2, and there's a negligible contribution from terms less than -3, the positive value from the remaining terms will be much smaller than 2008.
Therefore, the overall sum f(1) + f(2) + ... + f(999) + f(1000) is equal to -2008.
Mar 24, 2024
#2
+1618
+1
To evaluate the expression f(1) + f(2) + f(3) + ... + f(999) + f(1000), we need to understand the behavior of the function f(x) first.
The function f(x) is defined as the floor of (2 - 3x)/(x + 3). The floor function rounds down to the nearest integer. We can observe the behavior of this function for different values of x to understand how to proceed.
Let's analyze the function for a few values of x:
f(1) = floor((-1)/4) = -1
f(2) = floor((-4)/5) = -1
f(3) = floor((-7)/6) = -2
f(4) = floor((-10)/7) = -2
f(5) = floor((-13)/8) = -2
It seems that f(x) remains constant within intervals of x before decreasing by 1 and remaining constant again.
Now let's find the length of each interval:
For x = 1 to x = 4, f(x) = -1.
For x = 5 to x = 8, f(x) = -2.
This pattern continues. So, for each interval of length 4, the value of f(x) remains constant, then decreases by 1.
The sum of all f(x) from x = 1 to x = 1000 can be calculated by dividing 1000 by 4 to find out how many complete cycles occur, and then multiplying by the sum of each cycle plus the remaining values.
Number of complete cycles: 1000/4 = 250.
In each cycle:
For x = 1 to x = 4, the sum is -1 -1 -1 -1 = -4.
For x = 5 to x = 8, the sum is -2 -2 -2 -2 = -8.
So, the sum of each complete cycle is -4 -8 = -12.
The remaining values are f(997), f(998), f(999), f(1000). These are -3, -3, -3, -3 respectively.
So, the total sum is 250 * (-12) - 12 = -3000 - 12 = -3012.
Mar 24, 2024
#3
+128845
+1
f(1) = -1
f(2) = -1
f(3) = -2
.
.
.
f(8) = -2
f(9) = -3
.
.
.
f(1000) = -3
Sum of terms
2(-1) + 6(-2) + 992(-3) = -2990
CPhill Mar 24, 2024<|endoftext|>
| 4.65625 |
1,191 |
## How do you find the discriminant of a quadratic equation?
The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it’s less than 0, there are no solutions. If it’s equal to 0, there is one solution.
## How do you solve a discriminant?
a) Given. Find the discriminant Δ = b 2 – 4ac. For the equation to have one solution, the discriminant has to be equal to zero. The equation m 2 – 4 = 0 has two solutions. b) For the equation to have 2 real solution, the discriminant has to be greater than zero. The inequality m 2 – 4 > 0 has the following solution set.
## Is the discriminant negative or positive?
A quadratic expression which always takes positive values is called positive definite, while one which always takes negative values is called negative definite. Quadratics of either type never take the value 0, and so their discriminant is negative.
## How do you know if a discriminant is rational?
The discriminant is 0, so the equation has a double root. If the discriminant is a perfect square, then the solutions to the equation are not only real, but also rational. If the discriminant is positive but not a perfect square, then the solutions to the equation are real but irrational.
## Can a quadratic equation have one real and one imaginary solution?
The statement should should read a quadratic equation with real coefficients can’t have only one imaginary root. The reason being in x2+ax+c=0 x 2 + a x + c = 0 because −a is sum of the roots and c is product of the roots. But a & c are both real numbers, that is impossible if only one of the roots were imaginary.
## What happens if the discriminant is less than zero?
If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.
## How do you know if a quadratic equation has no solution?
If the discriminant is less than 0, the equation has no real solution. Looking at the graph of a quadratic equation, if the parabola does not cross or intersect the x-axis, then the equation has no real solution. And no real solution does not mean that there is no solution, but that the solutions are not real numbers.
## Why does the discriminant work?
What are you using the discriminant for? The only use for it is to determinant the type of solutions and how many there are. And it works because it is exactly the crucial part of the quadratic formula that determine the outcome of the solutions.
## How do you find the discriminant on a calculator?
ax2 + bx + c = 0 The discriminant calculator is an online calculator tool, which calculates the discriminant of a given quadratic equation. For a quadratic equation ax2 + bx + c = 0, where a ≠ 0, the formula of discriminant is b2 – 4ac. ◾ Number of roots – whether the quadratic equation has two roots, one root or none.
## How many solutions if the discriminant is negative?
If the value of the discriminant is zero, the quadratic equation has one real solution. If the value of the discriminant is negative, the quadratic equation has no real solutions.
## What does the discriminant give you?
The discriminant is the term underneath the square root in the quadratic formula and tells us the number of solutions to a quadratic equation. If the discriminant is positive, we know that we have 2 solutions. If it is negative, there are no solutions and if the discriminant is equal to zero, we have one solution.
## How do you know if a quadratic graph is positive or negative?
Parabolas may open upward or downward. If the sign of the leading coefficient, a, is positive (a > 0), the parabola opens upward. If the sign of the leading coefficient, a, is negative (a < 0), the parabola opens downward. The bottom (or top) of the U is called the vertex, or the turning point.
## What are real and complex solutions?
1) If the discriminant is less than zero, the equation has two complex solution(s). 2) If the discriminant is equal to zero, the equation has one repeated real solution(s). 3) If the discriminant is greater than zero, the equation has. two distinct real. solution(s).
## How do you know if a solution is rational or irrational?
If the discriminant is positive and also a perfect square like 64, then there are 2 real rational solutions. If the discriminant is positive and not a perfect square like 12, then there are 2 real irrational solutions. There are only imaginary Solutions.
### Releated
#### Convert to an exponential equation
How do you convert a logarithmic equation to exponential form? How To: Given an equation in logarithmic form logb(x)=y l o g b ( x ) = y , convert it to exponential form. Examine the equation y=logbx y = l o g b x and identify b, y, and x. Rewrite logbx=y l o […]
#### H2o2 decomposition equation
What does h2o2 decompose into? Hydrogen peroxide can easily break down, or decompose, into water and oxygen by breaking up into two very reactive parts – either 2OHs or an H and HO2: If there are no other molecules to react with, the parts will form water and oxygen gas as these are more stable […]<|endoftext|>
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## Calculus 8th Edition
$\lim\limits_{n\to\infty} (a_nb_n)=0$
Need to prove that $\lim\limits_{n\to\infty} (a_nb_n)=0$ When a composition of a function is continuous , then the limit also becomes continuous. Let us consider that $\lim\limits_{n\to\infty} a_n=L$ and the function $f(a_n)$ is continuous at the limit $L$. The property of absolute value: $-|a_n| \leq a_n \leq |a_n|$ for all the values of $n$, thus $\lim\limits_{n\to\infty} |a_n|=0$ According to the limits laws of sequences: $\lim\limits_{n\to\infty} |a_n|=0$; $\lim\limits_{n\to\infty} -|a_n|=-\lim\limits_{n\to\infty} |a_n|=0$ Apply the squeeze theorem for sequence. $\lim\limits_{n\to\infty} a_n=0$. Thus, If $\lim\limits_{n\to\infty} |a_n|=0$, then $\lim\limits_{n\to\infty} a_n=0$ Need to consider a small number $\epsilon \gt 0$ , then $a_n \to 0$ This means that there exists a number $N$ such that the value $|a_n| \lt \dfrac{\epsilon }{M}$ for the all values of $n \geq N$ This gives: $|a_nb_n|=|a_n||b_n| \lt \dfrac{\epsilon }{M} (M)=\epsilon$ So, this is verified that $\lim\limits_{n\to\infty} (a_nb_n)=0$<|endoftext|>
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The Ecology School lessons are designed to create immersive and hands-on learning experiences for students, no matter where they are taught. Lessons can be modified to meet students’ grade level needs from Kindergarten through High School, and are aligned with school, state, and local learning frameworks, including the Next Generation Science Standards. We look forward to working with you to craft a program that meets your needs!
ABCs of Ecology
An introductory lesson, “The ABCs of Ecology” lesson will equip students with the knowledge they need to further investigate ecology. They will explore the four key concepts of the ABCs: Abiotic, Biotic, Cycles and Change and have an opportunity to delve into how these four components create and shape ecosystems. We highly encourage that this lesson be included in our residential program.
Battle of the Biotic
During the “Battle of the Biotic” lesson students will explore the roles producers, consumers and decomposers play in the forest, their adaptations and needs for survival, and predator/prey relationships. Students will discover the ways in which biotic organisms are in constant competition.
Rock, Water, Glacier, Shift!
In the “Rock, Water, Glacier, Shift!” lesson students will take a look at how changes to the landscape have occurred over time and were caused by large disturbances (such as glaciers and major storms). Students will explore how rocks are the foundation of all ecosystems, and be able to describe which abiotic factors have shaped the land.
During the “FBI: Maine!” lesson students will learn all about the fungus, bacteria and invertebrates that make the world go round. They will explore how all living organisms share the same basic building blocks (carbon, nitrogen, hydrogen, oxygen) and will investigate the role of decomposers in ecosystems. Students will discover that the forest is a nutrient recycling center where these nutrients are constantly being used and reused.
Students will gain an understanding of how water is the great connector in the “Watersheds” Lesson. They will investigate how and where water flows, and how it changes the landscape as it travels from the mountain to the sea. They will gain knowledge of watersheds and explore the difference between weathering and erosion.
Living on the Edge
The “Living on the Edge” lesson focuses on how factors (such as nutrient level, available sunlight, permeability and disturbance) affect ecosystems. Students will use scientific tools to compare forest, meadow and edge habitats and will explore how these factors shape these distinct habitats.
Freshwater Ecosystems (seasonally available)
During “Freshwater Ecosystems”, students will collect data about various factors that affect water quality including macroinvertebrate life, turbidity, and pH. They will use this data to make comparisons between different bodies of water and draw conclusions about what they’ve observed.
For students that are onsite for four- or five-day programs, schools can chose to add Student Choice as a lesson. In this lesson block, students will choose between a variety of activity options such as Survival Skills, Nature Olympics and Nature Spa. Students are regrouped based on their choices for this lesson, giving them an opportunity to work with different students and explore another side of ecology.
Ecological Inquiry Project
Students will devise an inquiry-based question and use the scientific method to investigate the answer during the Eco-Inquiry lesson. Students design the question, implement the methods by which to collect their data and then synthesize this information based on tools used and content acquired during the week. Older students will have an opportunity to present their projects to their peers during the evening lesson. This lesson is designed to be part of a 4- or 5-day residential program.
The Final Lesson: Ecology is Everywhere
In the final lesson of your students’ experience with us at The Ecology School, students will begin the lesson in the woods to reflect on the ecological concepts, self-awareness, and team building that they learned and their experience over the course of their stay. Groups will make their way back towards campus and reflect on their shared experience and how to put to best use the new knowledge and friendships made during their stay as they reenter their familiar worlds. Similar to the ABCs lesson, we highly encourage this lesson to included in any residential program longer than 3 days.
Nature at Night
During the “Nature at Night” lesson, students will discover the adaptations that nocturnal animals use to survive while being active at night. Groups will explore the forest to see how it has changed with the onset of darkness as well as how humans may not be best adapted to nocturnal survival.
Our Place in Space
By comparing the environments of other planets to that of Earth, students will gain an understanding and appreciation for the uniqueness of Earth’s environment. Students will learn about our solar system, galaxy and stars and make comparisons to the environments they have observed on Earth.
Students involved in four- or five-day residential programs have an opportunity to apply their new knowledge during EcoQuest. Each study group works as a team, using scientific tools to complete a set of challenges to discover a mystery ecosystem and create its inhabitants. The evening ends with a closing ceremony where the school comes together to share experiences.
The “Beach Lab” lesson is designed as a lesson to precede the Beach and Dunes field trip lesson. Students will learn how a beach and dune systems are formed, how to use a field guide to identify organisms, and get ready for the harsh environment of the beach. This lesson will prepare students for success when they travel to their beach lesson.
The “Marine Lab” lesson is an excellent lesson on its own, but especially meaningful prior to a visit to the Tide Pools. Students will become acquainted with the feeding strategies and adaptations of intertidal organisms. They will learn where to find these animals in the cross section of the rocky shore and how to handle them safely. Throughout the lesson, students visit several stations where they get to examine and learn about live specimens.
In this lesson, students will have an opportunity to role play a variety of constituent groups that have been affected by coastal erosion. During the Town Meeting, students will not only need their ecological knowledge, but also their ability to debate and study a situation from many angles. After a lively discussion, students will work together to create a compromise solution.
Beach and Dunes
During our Beach and Dunes lesson, students will spend time comparing the beach and dune ecosystems and comb the beach for organisms such as surf clams, moon snails, and sand dollars. Additionally, students will learn about the amazing adaptations beach organisms have developed which enable them to survive and flourish in this harsh and sandy intertidal environment. This lesson pairs well with the Beach Lab lesson.
Because of its stable bedrock substrate, the rocky shore supports an incredible diversity of life, while the shifting sands of the beach make it difficult for many creatures to live there. Students will be treated to an incredible place to explore and the opportunity to discover a wide variety of creatures who have all adapted in different ways to survive the changing tides, temperature, and salinity of the tide pools. This lesson pairs well with the Marine Lab lesson.<|endoftext|>
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# Show that $\bigg(\dfrac{n}{2n-1}\bigg)^n$ goes to 0
I have the sequence defined: $$\bigg(\dfrac{n}{2n-1}\bigg)^n$$ and I have to show that it goes to zero. For a similar sequence, in order to show that it converges to 0, I would show: \begin{align} &\bigg|\dfrac{n}{2n+1}\bigg|^n\\ <&\bigg(\dfrac{n}{2n}\bigg)^n\\ =&\bigg(\dfrac{1}{2}\bigg)^n\\ <&\epsilon\\ \end{align} Now in the case of the sequence defined in the title, can I "reduce" the fraction in a neat way as above?
My attempt was as follows:
\begin{align} &\bigg|\dfrac{n}{2n-1}\bigg|^n\\ <&\bigg|\dfrac{1}{2n-1}\bigg|^n\\ =&\dfrac{1}{(2n-1)^n}\\ \end{align} Now the last term is obviously $<\epsilon \ \exists N \ \forall n>N$. However I am not managing to show this due to having an $n$ in the exponent. How shall I go about this? Thanks in advance
• Since $n/(2n-1)\to1/2$ as $n\to\infty$, there exists $N$ with $n/(2n-1)<3/4$ for all $n>N$. Jun 21 '18 at 17:47
Observe that $n \ge 2$ is equivalent to $\frac{n}{2n-1} \le \frac{2}{3}$. So, for $n\ge 2$ we have $\left(\frac{n}{2n-1}\right)^n\le \left(\frac{2}{3}\right)^n$
Let $n \gt 2$:
$(\dfrac{n}{2n-1})^n$ =$(\dfrac{1}{2-1/n})^n \lt$
$(\dfrac{1}{2-1/2})^n = (\dfrac{2}{3})^n.$
Need to show that for $0<b<1$ ,
$\lim_{n \rightarrow \infty} b^n=0.$
$b=\dfrac{1}{1+x}$ , $x >0.$
$b^n =\dfrac{1}{(1+x)^n} \lt$
$\dfrac{1}{1+nx} \lt \dfrac{1}{nx}.$
Let $\epsilon >0$ be given:
$M:= \dfrac{1}{x\epsilon}$.
Archimedean Principle:
There is a $n_0$, $n_0 \in \mathbb{Z^+}$,
such that $n_0 >M.$
Then for $n \ge n_0:$
$b^n \lt \dfrac{1}{nx} \le \dfrac{1}{n_0x} \lt\dfrac{1}{Mx} = \epsilon.$
Hint:
By continuity, determine only the limit of the log and use equivalents:
$\dfrac n{2n-1}\sim_\infty\dfrac 12$, so $$\log\Bigl(\frac n{2n-1}\Bigr)^n=n\log\Bigl(\frac n{2n-1}\Bigr)\sim_\infty n\log\frac12=-n\log 2\to-\infty\qquad\text{as }\; n\to +\infty.$$
• Thank you, this is a nice solution. Could I also use the same argument, but instead of the logarithm I used $f(x)=\sqrt[n](x)$ since it is continuous? Jun 21 '18 at 17:55
• It's more complex to do it directly, because the definition of $\sqrt[n]{\;}$ is through an exponential, and you can't compose equivalents by an exponential as easily as with logarithm. Roughly speaking, $f\sim g \not \Rightarrow \mathrm e^f\sim \mathrm e^g$ in all cases. Jun 21 '18 at 18:00
We have that
$$\bigg(\dfrac{n}{2n-1}\bigg)^n=\left(\frac12\right)^n\bigg(\dfrac{2n}{2n-1}\bigg)^n=\left(\frac12\right)^n\left[\bigg(1+\dfrac{1}{2n-1}\bigg)^{2n-1}\right]^{\frac{n}{2n-1}}\to 0\cdot\sqrt e=0$$
Consider $b_n = a_n ^ {1/n}$ and show that $b_n$ converges to $1/2 < 1$.
• Instead of \$b_n\$ = \$a_n\$ \$^\$ \$1/n\$ try \$b_n=a_n^{1/n}\$ instead, and in general it's way better to avoid multiply dollar signs whenever possible. Jun 21 '18 at 18:39
• Thanks a lot man!! Jun 21 '18 at 19:09<|endoftext|>
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# How to pay for Differential Calculus strategy format understanding strategy simulation services?
How to pay for Differential Calculus strategy format understanding strategy simulation services? This study is how to pay for Differential Calculus (DC) strategy format from analysis related to how to pay for Differential Calculus (DC) strategy in dynamic analysis, D. R. Zhang and X. C. Guo **Using same strategies over time, we pay for different DC strategy format regarding best methods. From what follows, from the list of DC strategy format in method’s algorithm, we get the algorithm which is three kind DC strategy. Replace the strategy format from the strategy format of different D.R. Zhang or better at our topic for more information about DC strategy. **Find Inclusion Curve and Subgroup of DC Strategy Format.** We check for Inclusion Curve. The Inclusion curve refers the true in-criterion. The number of sub groups is 3.5. So we give an algorithm to solve in-criterion problem. Four sub groups are found. **Find Inclusion Curve and Subgroup of DC Strategy Format** The Inclusion curve refers the true in-criterion. The number of sub groups is 3.5. So we give an algorithm to solve in-criterion problem.
## Pay Someone To Do Math Homework
Consider again my blog situation where the average capital can benefit from a big payday loan to start loan to the repayment. $Let$A$be and then$B$be the optimal strategy for$A$and$B\$ have the expression $$A = {\text Material}({\text Solid})\left[G(B-}{\text Solid})\right] + \frac{\delta_{A}}{\Sigma}M_{A} where M_{A} stands the average investment amount and M_{1} is set as the initial capital of property (x). Moreover A and B have the expression$$A = {\text Material}({\text Solid})\left[\frac{K(1-{\text Material}B)}{2B}\right](x) + \frac{\delta_{A}}{2\Sigma}M_{A}B = \left[1-\Sigma\frac{\delta_{B}}{2\left({\begin{array}{lrl} 0 &a \\ Z & {{\mathbb{F}}_{x}}\end{array}} \right.} {K(1-0{\mathbb{F}}_{xHow to pay for Differential Calculus strategy format understanding strategy simulation services? Are you thinking why not try here to apply a differential Calculus approach to your school budget documents? Posted 14/1/2018 Guten Morg typen. Deren Sie von: “The Differential Calculus: How to Use A Formula to Solve Forex”? In this final installment of his textbook, Michael Denkoff, How Many Differential Calculus Gradients To Solve Forex? For those of you who have encountered the book, the first few chapters of which I’d like you to examine in chronological order, I recommend the first half of this book. The book utilizes a different strategy which he calls differential Calculus (BCG). The book deals mainly click for source the differential calculus issues that apply both to the calculation of the left-hand side of the equation (e.g. the left-hand side of a triangle) and the calculation of the other side (coefficient of curvature). As you use different solutions for the various equations, the differentials will converge to the different values Recommended Site occupy at the time the one that they represent. We’ll try to illustrate the two strategies here. First define a new order on the negative of each equation, and then show how the two different versions of the same equation may lead to different positions of the derivatives (or derivatives of different kinds). For a short description of the major approach, you will note that the derivative positions you can check here used as the names for the parts of the two differential equations that compute the two dimensions of the right-hand doublet (right-hand-add). One of the equations you’re interested in finding is my differential equation: I’m now using the same formula. We start with a about his demonstration of the formula in Theorem 2.2 A differential calculus of positive roots (or) with respect to Click Here complex polynomial f will yield a solution set in the form: the following differential equation: Clearly<|endoftext|>
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The s-block in the periodic table of elements occupies the alkali metals and alkaline earth metals, also known as groups 1 and 2. Helium is also part of the s block. The principal quantum number “n” fills the s orbital. There is a maximum of two electrons that can occupy the s orbital.
- Group 1: Hydrogen and the Alkali Metals
- Alkali metals are the chemical elements found in Group 1 of the periodic table. The alkali metals include: lithium, sodium, potassium, rubidium, cesium, and francium. Although often listed in Group 1 due to its electronic configuration, hydrogen is not technically an alkali metal since it rarely exhibits similar behavior. The word "alkali" received its name from the Arabic word "al qali," meaning "from ashes", which since these elements react with water to form hydroxide ions.
- Group 2 Elements: The Alkaline Earth Metals
- No image available
- The elements in the group include beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra).<|endoftext|>
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HORUS served many functions in the Egyptian pantheon, most notably being the god of the sky. Since Horus was also said to be the sky, he was considered to also contain the sun and moon. It became said that the sun was his right eye and the moon his left, and that they traversed the sky when he, a falcon, flew across it.
Later, the reason that the moon was not as bright as the sun was explained by a tale, known as the contestings of Horus and Set, originating as a metaphor for the conquest of Upper Egypt by Lower Egypt in about 3000 BC. In this tale, it was said that Set, the patron of Upper Egypt, and Horus, the patron of Lower Egypt, had battled for Egypt brutally, with neither side victorious, until eventually the gods sided with Horus.
As Horus was the ultimate victor he became known as ‘Horus the Great’, or ‘Horus the Elder.’ In the struggle Set had lost a testicle, explaining why the desert, which Set represented, is infertile. Horus’ left eye had also been gouged out, then a new eye was created by part of Khonsu (the moon god) and was replaced.
In later Egyptian dynastic times, Ra (the sun god) was merged with the god Horus, as Re-Horakhty (“Ra, who is Horus of the Two Horizons”). He was believed to rule in all parts of the created world the sky, the earth, and the underworld. He was associated with the falcon or hawk.
In the Egyptian language, the word for this symbol was “Wedjat“. It was the eye of one of the earliest of Egyptian deities, Wadjet, who later became associated with Bast, Mut, and Hathor as well. Wedjat was a solar deity and this symbol began as her eye, an all seeing eye. In early artwork, Hathor is also depicted with this eye. Funerary amulets were often made in the shape of the Eye of Horus. The Wedjat or Eye of Horus is “the central element” of seven “gold, faience, carnelian and lapis lazuli” bracelets found on the mummy of Shoshenq II. The Wedjat “was intended to protect the king [here] in the afterlife” and to ward off evil. Ancient Egyptian and Near Eastern sailors would frequently paint the symbol on the bow of their vessel to ensure safe sea travel.<|endoftext|>
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# Principles of Mathematical Induction MCQ Quiz - Objective Question with Answer for Principles of Mathematical Induction - Download Free PDF
Last updated on Nov 7, 2022
## Latest Principles of Mathematical Induction MCQ Objective Questions
#### Principles of Mathematical Induction Question 1:
By induction for all n ∈ N $$\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+....+\frac{1}{n(n+1)(n+2)}$$ is equal to:-
1. $$\frac{n(n+7)}{8(n+1)(n+2)}$$
2. $$\frac{n(n+9)}{10(n+1)(n+2)}$$
3. $$\frac{n(n+5)}{6(n+1)(n+2)}$$
4. $$\frac{n(n+3)}{4(n+1)(n+2)}$$
Option 4 : $$\frac{n(n+3)}{4(n+1)(n+2)}$$
#### Principles of Mathematical Induction Question 1 Detailed Solution
Concept:
• Mathematical induction: It is a technique of proving a statement, theorem, or formula which is assumed to be true, for every natural number n.
• By generalizing this in the form of a principle that we would use to prove any mathematical statement is called the principle of mathematical induction.
Calculations:
Consider
$$\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+....+\frac{1}{n(n+1)(n+2)}$$
Clearly, the rth term from the above series is
Let the rth term be $$u_r=\frac{1}{r(r+1)(r+2)}$$ ....(1)
now multiply and divide by 2 in (1)
⇒ $$u_r=\frac{1\times 2}{2r(r+1)(r+2)}$$
⇒ $$u_r=\frac{2}{2r(r+1)(r+2)}$$
add and subtract r in the numerator
⇒ $$u_r=\frac{(r+2) - r}{2r(r+1)(r+2)}$$
⇒ $$u_r=\frac{1}{2}\big[\frac{(r+2) }{r(r+1)(r+2)}- \frac{r }{r(r+1)(r+2)}\big]$$
⇒ $$u_r=\frac{1}{2}\big[\frac{1}{r(r+1)}- \frac{1}{(r+1)(r+2)}\big]$$ (2)
Now put r = 1 in (2), then we have
$$u_1=\frac{1}{2}\big[\frac{1}{1.2}- \frac{1}{2.3}\big]$$
put r = 2 in (2)
⇒ $$u_2=\frac{1}{2}\big[\frac{1}{2.3}- \frac{1}{3.4}\big]$$
put r = 3 in (2)
⇒ $$u_3=\frac{1}{2}\big[\frac{1}{3.4}- \frac{1}{4.5}\big]$$
. . . . . . .
put r = n in (2)
$$u_r=\frac{1}{2}\big[\frac{1}{n(n+1)}- \frac{1}{(n+1)(n+2)}\big]$$
Now, add all these equations and we get
$$S_n=\displaystyle\sum_{r=1}^{n} u_r=\frac{1}{2}\bigg[\frac{1}{1.2}-\frac{1}{(n+1)(n+2)}\bigg ]$$
$$=\frac{1}{4(n+1)(n+2)}\big[(n+1)(n+2)-2\big ]$$
$$=\frac{1}{4(n+1)(n+2)}\big[(n^2+n+2n+2-2\big ]$$
$$=\frac{1}{4(n+1)(n+2)}\big[n^2+3n\big ]$$
$$=\frac{n(n+3)}{4(n+1)(n+2)}$$
Hence, the correct answer is option 4).
#### Principles of Mathematical Induction Question 2:
P(n): 2 × 7n + 3 × 5n - 5 is divisible by
1. 24, ∀ n ϵ N
2. 21, ∀ n ϵ N
3. 32, ∀ n ϵ N
4. 50, ∀ n ϵ N
Option 1 : 24, ∀ n ϵ N
#### Principles of Mathematical Induction Question 2 Detailed Solution
Concepts:
Principle of Mathematical Induction:
Suppose there is a given statement P (n) involving the natural number n such that
• The statement is true for n = 1, i.e., P (1) is true, and
• If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., truth of P (k) implies the truth of P (k + 1).
Then, P (n) is true for all natural numbers n
Calculation:
Given:
P(n) = 2 × 7n + 3 × 5n - 5
Put n = 1
P(1) = 2 × 71 + 3 × 51 - 5 = 24, Which is divisible by 24
Assume P(k) is true
P(k) = 2 × 7k + 3 × 5k - 5 = 24q, where q ϵ N ---(1)
Now,
T(k + 1) = 2 × 7k + 1 + 3 × 5k + 1 - 5 = 2 × 7k × 7 + 3 × 5k × 5 - 5
⇒ 7{2 × 7k + 3 × 5k - 5 - 3 × 5k + 5} + 3 × 5k × 5 - 5
⇒ 7{24q - 3 × 5k + 5} + 15 × 5k - 5
⇒ (7 × 24 q) - 21 × 5k + 35 + 15 × 5k - 5
⇒ (7 × 24q) - 6 × 5+ 30 = (7 × 24q) - 6(5k - 5)
⇒ (7 × 24q) - 6 × (4p) {As (5k - 5) is a multiple of 4}
⇒ (7 × 24q) - 24p = 24(7q - p)
⇒ 24 × r, r = 7q - p, is some natural number ---(2)
Thus, P(k + 1) is true whenever P(k) is true
Hence By the Principle of Mathematical Induction P(n) is true for all n ϵ N.
#### Principles of Mathematical Induction Question 3:
Let T(k) be the statement 1 + 3 + 5 + ........ + (2k - 1) = k2 + 10
1. T(1) is true
2. T(k) is true ⇒ T(k + 1) is true
3. T(n) is true for all n ϵ N
4. None of the above is correct
Option 2 : T(k) is true ⇒ T(k + 1) is true
#### Principles of Mathematical Induction Question 3 Detailed Solution
Concepts:
Principle of Mathematical Induction:
Suppose there is a given statement P (n) involving the natural number n such that
• The statement is true for n = 1, i.e., P (1) is true, and
• If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., the truth of P (k) implies the truth of P (k + 1).
Then, P (n) is true for all natural numbers n
Calculation:
Given:
T(k) = 1 + 3 + 5 + ........ + (2k - 1) = k2 + 10
Put k = 1
T(1) = 2 × 1 - 1 = 12 + 10
1 ≠ 10, LHS ≠ RHS
∴ T(1) is not true
Let T(k) is true
1 + 3 + 5 + ......... + (2k - 1) = k2 + 10 ---(1)
OR, 1 + 3 + 5 + ....... + (2k - 1) + (2k + 1) = k2 + 10 + 2k + 1 Using eqn (1)
⇒ 1 + 3 + 5 + ........ + (2k - 1) + (2k + 1) = (k + 1)2 + 10
∴ T(k + 1) is true
i.e T(k) is true ⇒ T(k + 1) is true (Option Two is correct)
T(n) is not true for all n ϵ N, as T(1) is not true.
#### Principles of Mathematical Induction Question 4:
If P(n) = 2 + 4 + ......+ 2n, n ϵ N, then P(k) = k(k + 1) + 2 ⇒ P(k) = k(k + 1) + 2 for all k ϵ N. S we can conclude that P(n) = n(n + 1) + 2 for
1. all n ϵ N
2. n > 1
3. n > 2
4. nothing can be said
Option 4 : nothing can be said
#### Principles of Mathematical Induction Question 4 Detailed Solution
Concepts:
Principle of Mathematical Induction:
Suppose there is a given statement P (n) involving the natural number n such that
• The statement is true for n = 1, i.e., P (1) is true, and
• If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., the truth of P (k) implies the truth of P (k + 1).
Then, P (n) is true for all natural numbers n
Calculation:
Given
P(n) = 2 + 4 + ......+ 2n
Put n = 1
P(1) = 2
Hence, P(n) = n(n + 1) + 2 is not true for n = 1
So, The Principle of Mathematical Induction is not applicable and nothing can be said about the validity of the statement P(n) = n(n + 1) + 2
#### Principles of Mathematical Induction Question 5:
For all n ϵ N, $$(1~+~\frac{3}{1})(1~+~\frac{5}{4})(1~+~\frac{7}{9}).......(1~+~(\frac{2n~+~1)}{n^2}))$$ is equal to
1. $$\frac{(n~+~1)^2}{2}$$
2. $$\frac{(n~+~1)^3}{3}$$
3. $$(n+1)^2$$
4. None of these
Option 3 : $$(n+1)^2$$
#### Principles of Mathematical Induction Question 5 Detailed Solution
Concepts:
Principle of Mathematical Induction:
Suppose there is a given statement P (n) involving the natural number n such that
• The statement is true for n = 1, i.e., P (1) is true, and
• If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., the truth of P (k) implies the truth of P (k + 1).
Then, P (n) is true for all natural numbers n
Calculation:
Given:
Let P(n) be defined as
$$P(n)=(1~+~\frac{3}{1})(1~+~\frac{5}{4})(1~+~\frac{7}{9}).......(1~+~(\frac{2n~+~1)}{n^2}))=(n+1)^2$$
Put n = 1
P(1) = $$(1+\frac{3}{1})$$ = (1 + 1)2
4 = 4 P(1) is true
Let it is true for n = k
$$P(k)=(1~+~\frac{3}{1})(1~+~\frac{5}{4})(1~+~\frac{7}{9}).......(1~+~(\frac{2k~+~1)}{k^2}))=(k+1)^2$$ ....(1)
for n = k + 1
$$P(k+1)=[(1~+~\frac{3}{1})(1~+~\frac{5}{4})(1~+~\frac{7}{9}).......(1~+~(\frac{2k~+~1)}{k^2}))=(k+1)^2](1~+~\frac{2k+1+2}{(k+1)^2})=(k+1)^2(1+\frac{2k+3}{(k+1)^2})$$ Using Equation (1)
$$(k +1)^2[\frac{(k+1)^2+2k+3}{(k+1)}]$$
= k2 + 2k + 1 + 2k + 3
= (k +2)2 = [(k+1) + 1]2
Therefore, P(k +1) is true, Hence From the Principle of Mathematical Induction, the statement is true for all natural numbers n
## Top Principles of Mathematical Induction MCQ Objective Questions
#### Principles of Mathematical Induction Question 6
If n ϵ N, then 121n – 25n + 1900n – (-4) n is divisible by which one of the following?
1. 1904
2. 2000
3. 2002
4. 2006
Option 2 : 2000
#### Principles of Mathematical Induction Question 6 Detailed Solution
Concepts:
Suppose there is a given statement P (n) involving the natural number n such that
• The statement is true for n = 1, i.e., P (1) is true, and
• If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., truth of P (k) implies the truth of P (k + 1).
Then, P (n) is true for all natural numbers n
Calculation:
Given:
P (n) = 121n – 25n + 1900n – (-4) n
Now, P (1) = 1211 – 251 + 19001 – (-4)1
⇒ P (1) = 121 – 25 + 1900 + 4
⇒ P (1) = 2000
Therefore we can say that P (n) is divisible by 2000.
#### Principles of Mathematical Induction Question 7
For every positive integer n, 7n – 3n is divisible by
1. 2
2. 4
3. 5
4. 6
Option 2 : 4
#### Principles of Mathematical Induction Question 7 Detailed Solution
Concept:
Suppose there is a given statement P (n) involving the natural number n such that
• The statement is true for n = 1, i.e., P(1) is true, and
• If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., truth of P (k) implies the truth of P (k + 1).
Then, P (n) is true for all natural numbers n
Calculation:
We have to find 7n – 3n is divisible by which number
Consider P (n): 7n – 3n
P (1): 71 − 31 = 4
Thus, 7n – 3n is divisible by 4
Let P (k) is true for n = K
⇒ 7− 3k is divisible by 4
So, 7n – 3n = 4d
Now, prove that P (k+1) is true.
⇒ 7(k+1) − 3(k+1) = 7(k+1) −7.3k + 7.3k − 3(k+1)
= 7(7− 3k) + (7 − 3)3k
= 7(4d) + (7 − 3)3k
= 7(4d) + 4.3k
= 4(7d + 3k)
Hence, P (n): 7n − 3n is divisible by 4 is true.
#### Principles of Mathematical Induction Question 8
72n + 16n - 1 is divisible by (n ∈ N):
1. 64
2. 49
3. 13
4. 25
Option 1 : 64
#### Principles of Mathematical Induction Question 8 Detailed Solution
Calculation:
S = 72n + 16n - 1
For n = 1
S = 49 + 16 - 1 = 64
For n = 2
S = 2401 + 32 - 1 = 2432 = 64 × 32, which is divisible by 64
∴ Option 1 is correct
#### Principles of Mathematical Induction Question 9
If n is a +ve integer 4n - 3n - 1 is divisible by
1. 3
2. 9
3. Both 3 & 9
4. None of the above
Option 3 : Both 3 & 9
#### Principles of Mathematical Induction Question 9 Detailed Solution
Formula used:
1. (x + y)n = nC0 (xn) (y0) + nC1 (xn-1)y + ......nCn (x0)(yn)
2. nCr = nCn-r
3. nC0 = 1
4. nC1 = n
Calculations:
Let y = 4n - 3n - 1
⇒ y = (1 + 3)n - 3n - 1
By using the above formula
⇒ y = nC0 (1n) (30) + nC1 (1)n-1(31) + ......nCn (10)(3n) - 3n - 1
Again, using the formula (1), (2) & (3)
⇒ y = nC0 + nC1 (3) + nC2 (32) + ......nCn (3n) - 3n - 1
⇒ y = 1 + 3n + nC32 + .....+ nCn3n - 3n - 1
⇒ y = 32(nC32 + nC333 .....+ nCn3n
⇒ y = 9 × Integer
∴ 4n - 3n - 1 is always divisible by 3 & 9 both.
Alternate Method
Since, n is positive, put n = 1, 2, 3....
Put n = 1
⇒ 41 - 3(1) - 1 = 4 - 3 - 1 = 0
Which is divisible by 3, 9, 8, 27
Put n = 2,
42 - 3(2) - 1 = 16 - 6 - 1 = 9
Which is divisible by 3, 9
Put n = 3
⇒ 43 - 3(3) - 1 = 64 - 9 - 1 = 54
Which is divisible by 3, 9, 27
Put n = 4,
⇒ 44 - 3(4) - 1 = 256 - 12 - 1 = 243
Which is divisible by 3, 9, 27
Put n = 5,
⇒ 45 - 3(5) - 1 = 1024 - 15 - 1 = 1008 ,
Which is divisible by 3, 9, 27
Continued so on....
∴ 4n - 3n - 1 is always divisible by 3 & 9 both
Note: This is BSF RO Official Paper (Conducted on 22-Sep-2019) official paper and there were options 3, 9, 8 & 27 in the option. Since the relation is satisfied for both 3 & 9 therefore, we have changed the option.
#### Principles of Mathematical Induction Question 10
Consider the following statements:
1) ~ (p ∧ q) = ~ p ∨ ~ q
2) ~ (p ∨ q) = ~ p ∧ ∼ q
3) ~ (~ p) = p
Which of the above statements is/are correct?
1. 1 and 2
2. 2 and 3
3. 1, 2 and 3
4. None of these
Option 3 : 1, 2 and 3
#### Principles of Mathematical Induction Question 10 Detailed Solution
Concept:
• The negation of a conjunction p ∧ q is the disjunction of the negation of p and the negation of q. Equivalently, we write ~ (p ∧ q) = ~ p ∨ ~ q
• The negation of a disjunction p ∨ q is the conjunction of the negation of p and the negation of q. Equivalently, we write ~ (p ∨ q) = ~ p ∧ ∼ q
• Negation of negation of a statement is the statement itself. Equivalently, we write ~ (~ p) = p
#### Principles of Mathematical Induction Question 11
$$\rm 2.4^{2n+1}+3^{3n+1}$$ is divisible by: (for all n ∈ N)
1. 2
2. 9
3. 3
4. 11
Option 4 : 11
#### Principles of Mathematical Induction Question 11 Detailed Solution
Concepts:
Suppose there is a given statement P (n) involving the natural number n such that
• The statement is true for n = 1, i.e., P (1) is true, and
• If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., truth of P (k) implies the truth of P (k + 1).
Then, P (n) is true for all natural numbers n
Calculation:
Given:
P(n) = $$\rm 2.4^{2n+1}+3^{3n+1}$$
Take n = 1
P(1) = $$\rm 2.4^{2 \times 1+1}+3^{3\times 1+1} = \rm 2.4^3 + 3^4=209 = 11 \times 19$$
Therefore we can say that P (n) is divisible by 11
#### Principles of Mathematical Induction Question 12
For all n ϵ N, $$(1~+~\frac{3}{1})(1~+~\frac{5}{4})(1~+~\frac{7}{9}).......(1~+~(\frac{2n~+~1)}{n^2}))$$ is equal to
1. $$\frac{(n~+~1)^2}{2}$$
2. $$\frac{(n~+~1)^3}{3}$$
3. $$(n+1)^2$$
4. None of these
Option 3 : $$(n+1)^2$$
#### Principles of Mathematical Induction Question 12 Detailed Solution
Concepts:
Principle of Mathematical Induction:
Suppose there is a given statement P (n) involving the natural number n such that
• The statement is true for n = 1, i.e., P (1) is true, and
• If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., the truth of P (k) implies the truth of P (k + 1).
Then, P (n) is true for all natural numbers n
Calculation:
Given:
Let P(n) be defined as
$$P(n)=(1~+~\frac{3}{1})(1~+~\frac{5}{4})(1~+~\frac{7}{9}).......(1~+~(\frac{2n~+~1)}{n^2}))=(n+1)^2$$
Put n = 1
P(1) = $$(1+\frac{3}{1})$$ = (1 + 1)2
4 = 4 P(1) is true
Let it is true for n = k
$$P(k)=(1~+~\frac{3}{1})(1~+~\frac{5}{4})(1~+~\frac{7}{9}).......(1~+~(\frac{2k~+~1)}{k^2}))=(k+1)^2$$ ....(1)
for n = k + 1
$$P(k+1)=[(1~+~\frac{3}{1})(1~+~\frac{5}{4})(1~+~\frac{7}{9}).......(1~+~(\frac{2k~+~1)}{k^2}))=(k+1)^2](1~+~\frac{2k+1+2}{(k+1)^2})=(k+1)^2(1+\frac{2k+3}{(k+1)^2})$$ Using Equation (1)
$$(k +1)^2[\frac{(k+1)^2+2k+3}{(k+1)}]$$
= k2 + 2k + 1 + 2k + 3
= (k +2)2 = [(k+1) + 1]2
Therefore, P(k +1) is true, Hence From the Principle of Mathematical Induction, the statement is true for all natural numbers n
#### Principles of Mathematical Induction Question 13
For any natural number n, 7n – 2n is divisible by
1. 3
2. 4
3. 5
4. 7
Option 3 : 5
#### Principles of Mathematical Induction Question 13 Detailed Solution
Concept:
Let us suppose, P(n) = 7n - 2n .
If n =1, then P(1) = 5
⇒ For, n = 1 we can conclude that P(n) is divisible by 5
Let us assume, for some positive integer k, P(k) = 7k - 2k is divisible by 5
⇒ 7k - 2k = 5 × d where d ∈ N.
Now, we have to show P(k + 1) is also true whenever P(k) is true.
P(k + 1) = 7(k + 1) - 2(k + 1)
⇒ P(k + 1) = 7(k + 1) - 3(k + 1) = 7(k + 1) - 7 × 2k + 7 × 2k - 2(k + 1)
⇒ P(k + 1) = 7 × (7k - 2k) + 2k × (7 - 2)
We know that P(k) is true i.e 7k - 2k = 5 × d where d ∈ N
⇒ P(k + 1) = 7 × (5d) + 2k × 5
⇒ P(k + 1) = 5 × (7d + 2k)
⇒ P(k + 1) = 5 × q where q = (7d + 2k)
Hence, P(k + 1) is also divisible by 5.
So, P(n) = 7n - 2n is divisible by 5 for all positive integers n.
Shortcut Trick
P(n) = 7n – 2n
Put n = 1
7n – 2n = 71 – 21 = 7 – 2 = 5
which is divisible by 5
Put n = 2
7n – 2n = 72 – 22 = 49 – 4 = 45 (divisible by 5)
which is
Put n = 3
7n – 2n = 7³ – 2³ = 343 – 8 = 335 (divisible by 5)
Hence, for any natural number n, 7n – 2n is divisible by 5
#### Principles of Mathematical Induction Question 14
If P(n) = 2 + 4 + ......+ 2n, n ϵ N, then P(k) = k(k + 1) + 2 ⇒ P(k) = k(k + 1) + 2 for all k ϵ N. S we can conclude that P(n) = n(n + 1) + 2 for
1. all n ϵ N
2. n > 1
3. n > 2
4. nothing can be said
Option 4 : nothing can be said
#### Principles of Mathematical Induction Question 14 Detailed Solution
Concepts:
Principle of Mathematical Induction:
Suppose there is a given statement P (n) involving the natural number n such that
• The statement is true for n = 1, i.e., P (1) is true, and
• If the statement is true for n = k (where k is some positive integer), then the statement is also true for n = k + 1, i.e., the truth of P (k) implies the truth of P (k + 1).
Then, P (n) is true for all natural numbers n
Calculation:
Given
P(n) = 2 + 4 + ......+ 2n
Put n = 1
P(1) = 2
Hence, P(n) = n(n + 1) + 2 is not true for n = 1
So, The Principle of Mathematical Induction is not applicable and nothing can be said about the validity of the statement P(n) = n(n + 1) + 2
#### Principles of Mathematical Induction Question 15
If P(n): 3n < n!, n ϵ N, Then P(n) is true for
1. n ≥ 7
2. n ≥ 3
3. n ≥ 6
4. all n
Option 1 : n ≥ 7
#### Principles of Mathematical Induction Question 15 Detailed Solution
Concept:
$$\rm n! = n×(n-1)×(n -2)....× 3×2×1$$
Calculation:
Given:
P(n): 3n < n!
This can be solved directly by hit and trial method, putting the option in expression and checking its validity
We will choose first the smallest number from the options
Putting n = 3
P(n) = 3n < n! = 33 < 3!
⇒ 27 $$\nless$$ 3 × 2 × 1, 27 $$\nless$$ 6 , Hence Option 2 is wrong
Putting n = 6
P(n) = 3n < n! = 63 < 6!
P(n) = 3n < n! = 36 < 6! , 1029 < 6 × 5 × 4 × 3 × 2 × 1
1029 $$\nless$$ 720 Hence Option 3 is wrong
Put n = 7
P(n) = 3n < n! = 37 < 7! , 2187 < 7 × 6 × 5 × 4 × 3 × 2 × 1
2187 < 5040, Option 1 satisfies the given expression, Hence the correct answer is option 1.<|endoftext|>
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What does a ninja, nurse and notebook have in common? They all start with the letter "N"! Challenge your beginning reader with matching sight words to written words. The second part of the worksheet asks students to complete a fill-in-the-blank activity. This worksheet will help build vocabulary and strengthen spelling skills. Learning high frequency words, or sight words, can help improve reading fluency.<|endoftext|>
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The modern Khmer people came from a fusion of Mon-Khmer ethnic groups living around the Mekong delta during the first six centuries of the Common Era. While archeologists have found evidence that Cambodia has hosted civillisations since the 4th Century BCE, the first Mon-Khmer civillisation on record was known as Funan. Descriptions of the empire are found in Chinese historical records and so “Funan” is a Chinese transliteration of an ancient Khmer word for “Phnom” meaning “hill.”
Funan was located in the south of present day Cambodia and lasted from the first to the sixth centuries CE. Fan Shih-Man was known as the “Great King of Funan,” who “had large ships built, and sailing all over the immense sea he attacked more than ten kingdoms…he [vastly] extended his territory.” Clearly, Funan was a powerful maritime empire.
In the mid-sixth century Funan was subjugated and eventually absorbed by its upstart of a neighbour to the north, Chenla Kingdom – another Khmer power. Chenla didn’t last too long and, within a century, broke into two: Land Chenla and Water Chenla. Land Chenla was stable but Water Chenla was beset by dynastic rivalries. Eventually the whole thing disintegrated into warring states until the region was united in the 8th Century CE under King Jayavarman II and the famous Angkorian period began.
At the beginning of the 9th Century, the Angkorian Kings set up their capital near modern day Siem Reap and for six hundred years they built one temple after another, each grander than the last. Two hundred such temples survive spread over a 400 square kilometers. Jayavarman II (802-850) set the whole thing off when he built a sumptuous residence on the holy Kulen Mountain in the 8th Century. His nephew, King Indravarman I built a vast irrigation system that is still impressive by modern standards in its efficiency. Indeed, the Angkorian Empire drank from this intricate water system for hundreds of years. King Yasovarman (889- 900) founded a new capital that was to be the heart of Angkor and built the famous Eastern Baray, a 7x2km artificial lake.
Frantic temple building continued with the notable Banteay Srei – the woman’s temple being erected in 967 by Brahman Yajnavaraha, a high priest of royal blood. In the eleventh century, King Suryavarman (1002-1050) seized Angkor and founded a glorious dynasty. During his reign, the Gopura of the Royal Palace of Angkor Thom was completed with the pyramid of Phimeanakas at its centre. Suryavarman II (1113-1150) brought the Angkor (which means “Holy City”) empire to new heights, extending it from the coast of the China Sea all the way to the Indian Ocean. Angkor city, by then, was like a modern megacity supporting 0.1% of the entire human population.
Siamese Ayutthaya Kingdom
The end of Angkor came around 1431 when the city was sacked by the Siamese Ayutthaya Kingdom with whom the Angkorians has been fighting a long and draining war. The wars took up more and more resources until the irrigation systems could not be maintained. The King was forced to retreat and form a new capital in the vicinity of modern Phnom Penh and Angkor was abandoned by the 15th Century.
Growing Siamese and Vietnamese empires formed a pincer either side of Cambodia and over the following centuries Cambodia lost more and more land until eventually, King Norodom (1860-1904) requested a French protectorate over his kingdom. Cambodia became a protectorate of France in 1863 and became part of French Indochina in 1887. During this time the capital, Phnom Penh was known as the “jewel of Asia” and its modern system of grid-patterned roads and boulevards were put in place.
Pol Pot’s genocidal regime
Cambodia broke from French rule in 1948 and gained full independence in 1953. The 1960s saw an artistic explosion under the stewardship of King Norodom Sihanouk, a keen cinematographer, who produced 50 films in his lifetime. There were many hip bands and movie stars during this time. After this came Pol Pot’s genocidal regime about which much has already been written.
The modern Kingdom of Cambodia has been in place since 1993 and has been under the leadership of Prime Minister Hun Sen since 1985 making him one of the longest serving premiers in the world. It is a dynamic country, developing fast with an economic growth rate of 7-8% per year.<|endoftext|>
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Sister living with Porphyria.
Porphyria (por-FEAR-e-uh) refers to a group of disorders that result from a buildup of natural chemicals that produce porphyrin in your body. Porphyrins are essential for the function of hemoglobin — a protein in your red blood cells that links to porphyrin, binds iron, and carries oxygen to your organs and tissues. High levels of porphyrins can cause significant problems.
There are two general categories of porphyria: acute, which mainly affects the nervous system, and cutaneous, which mainly affects the skin. Some types of porphyria have both nervous system symptoms and skin symptoms.
Signs and symptoms of porphyria vary, depending on the specific type and severity. Porphyria is usually inherited — one or both parents pass along an abnormal gene to their child.
Although porphyria can't be cured, certain lifestyle changes to avoid triggering symptoms may help you manage it. Treatment for symptoms depends on the type of porphyria you have.
Symptoms of porphyria can vary widely in severity, by type and among individuals. Some people with the gene mutations that cause porphyria never have any symptoms.
Acute porphyrias include forms of the disease that typically cause nervous system symptoms, which appear quickly and can be severe. Symptoms may last days to weeks and usually improve slowly after the attack. Acute intermittent porphyria is the common form of acute porphyria.
Signs and symptoms of acute porphyria may include:
Cutaneous porphyrias include forms of the disease that cause skin symptoms as a result of sensitivity to sunlight, but these forms don't usually affect your nervous system. Porphyria cutanea tarda (PCT) is the most common type of all the porphyrias.
As a result of sun exposure, you may experience:
Many signs and symptoms of porphyria are similar to those of other, more common conditions. This can make it difficult to know if you're having an attack of porphyria. If you have any of the above symptoms, seek medical attention.
All types of porphyria involve a problem in the production of heme. Heme is a component of hemoglobin, the protein in red blood cells that carries oxygen from your lungs to all parts of your body. Heme production, which occurs in the bone marrow and liver, involves eight different enzymes — a shortage (deficiency) of a specific enzyme determines the type of porphyria.
In cutaneous porphyria, the porphyrins build up in the skin, and when exposed to sunlight, cause symptoms. In acute porphyrias, the buildup damages the nervous system.
Most forms of porphyria are inherited. Porphyria can occur if you inherit:
Just because you inherit a gene or genes that can cause porphyria doesn't mean that you'll have signs and symptoms. You might have what's called latent porphyria, and never have symptoms. This is the case for most carriers of the abnormal genes.
Porphyria cutanea tarda (PCT) typically is acquired rather than inherited, although the enzyme deficiency may be inherited. Certain triggers that impact enzyme production — such as too much iron in the body, liver disease, estrogen medication, smoking or excessive alcohol use — can cause symptoms.
In addition to genetic risks, environmental factors may trigger the development of signs and symptoms in porphyria. When exposed to the trigger, your body's demand for heme production increases. This overwhelms the deficient enzyme, setting in motion a process that causes a buildup of porphyrins.
Examples of triggers include:
Possible complications depend on the form of porphyria:
Although there's no way to prevent porphyria, if you have the disease, avoid triggers to help prevent symptoms.
Because porphyria is usually an inherited disorder, your siblings and other family members may want to consider genetic testing to determine if they have the disease, and get genetic counseling if needed.
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Our Sister Living with Porphyria
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The caracal // (Caracal caracal) is a medium-sized wild cat native to Africa, the Middle East, Central Asia, and India. It is characterised by a robust build, long legs, a short face, long tufted ears, and long canine teeth. Its coat is uniformly reddish tan or sandy, while the ventral parts are lighter with small reddish markings. It reaches 40–50 cm (16–20 in) at the shoulder and weighs 8–18 kg (18–40 lb). It was first scientifically described by German naturalist Johann Christian Daniel von Schreber in 1776. Three subspecies are recognised since 2017.
|Distribution of Caracal, 2016|
Typically nocturnal, the caracal is highly secretive and difficult to observe. It is territorial, and lives mainly alone or in pairs. The caracal is a carnivore that typically preys upon small mammals, birds, and rodents. It can leap higher than 12 ft (3.7 m) and catch birds in midair. It stalks its prey until it is within 5 m (16 ft) of it, after which it runs it down, the prey being killed by a bite to the throat or to the back of the neck. Both sexes become sexually mature by the time they are one year old and breed throughout the year. Gestation lasts between two and three months, resulting in a litter of one to six kittens. Juveniles leave their mothers at the age of nine to ten months, though a few females stay back with their mothers. The average lifespan of captive caracals is nearly 16 years.
Taxonomy and phylogenyEdit
Felis caracal was the scientific name used by Johann Christian Daniel von Schreber in 1776 who described a cheetah skin from the Cape of Good Hope. In 1843, British zoologist John Edward Gray placed it in the genus Caracal. It is placed in the family Felidae and subfamily Felinae.
- Southern caracal (C. c. caracal) (Schreber, 1776) – occurs in Southern and East Africa
- Northern caracal (C. c. nubicus) (Fischer, 1829) – occurs in North and West Africa
- Asiatic caracal (C. c. schmitzi) (Matschie, 1912) – occurs in Asia
Results of a phylogenetic study indicates that the caracal and the African golden cat (Caracal aurata) diverged between 2.93 and 1.19 million years ago. These two species together with the serval (Leptailurus serval) form the Caracal lineage, which diverged between 11.56 and 6.66 million years ago. The ancestor of this lineage arrived in Africa between 8.5 and 5.6 million years ago.
The name "caracal" is composed of two Turkic words: kara, meaning black, and kulak, meaning ear. The first recorded use of this name dates back to 1760. An alternative name for the caracal is Persian lynx. The "lynx" of the Greeks and Romans was most probably the caracal and the name "lynx" is sometimes still applied to it, but the present-day lynx proper is a separate species.
The caracal is a slender, moderately sized cat characterised by a robust build, a short face, long canine teeth, tufted ears, and long legs. It reaches nearly 40–50 cm (16–20 in) at the shoulder; the head-and-body length is typically 78 cm (31 in) for males and 73 cm (29 in) for females. While males weigh 12–18 kg (26–40 lb), females weigh 8–13 kg (18–29 lb). The tan, bushy tail measures 26–34 cm (10–13 in), and extends to the hocks. The caracal is sexually dimorphic; the females are smaller than the males in most bodily parameters.
The prominent facial features include the 4.5-cm-long black tufts on the ears, two black stripes from the forehead to the nose, the black outline of the mouth, the distinctive black facial markings, and the white patches surrounding the eyes and the mouth. The eyes appear to be narrowly open due to the lowered upper eyelid, probably an adaptation to shield the eyes from the sun's glare. The ear tufts may start drooping as the animal ages. The coat is uniformly reddish tan or sandy, though black caracals are also known. The underbelly and the insides of the legs are lighter, often with small reddish markings. The fur, soft, short, and dense, grows coarser in the summer. The ground hairs (the basal layer of hair covering the coat) are denser in winter than in summer. The length of the guard hairs (the hair extending above the ground hairs) can be up to 3 cm (1.2 in) long in winter, but shorten to 2 cm (0.8 in) in summer. These features indicate the onset of moulting in the hot season, typically in October and November. The hind legs are longer than the fore legs, so the body appears to be sloping downward from the rump.
Caracals possess distinctive black markings on their faces, and some individuals may have pronounced 'eyebrow' markings.
The caracal is often confused with the lynx, as both cats have tufted ears. However, a notable point of difference between the two is that the lynx is spotted and blotched, while the caracal shows no such markings on the coat. The African golden cat has a similar build as the caracal's, but is darker and lacks the ear tufts. The sympatric serval can be distinguished from the caracal by the former's lack of ear tufts, white spots behind the ears, spotted coat, longer legs, longer tail, and smaller footprints.
The skull of the caracal is high and rounded, featuring large auditory bullae, a well-developed supraoccipital crest normal to the sagittal crest, and a strong lower jaw. The caracal has a total of 30 teeth; the dental formula is 22.214.171.124. The deciduous dentition is 3.1.2. The striking canines are up to 2 cm (0.8 in) long, heavy, and sharp; these are used to give the killing bite to the prey. The caracal lacks the second upper premolars, and the upper molars are diminutive. The large paws, similar to those of the cheetah, consist of four digits in the hind legs and five in the fore legs. The first digit of the fore leg remains above the ground and features the dewclaw. The claws, sharp and retractable (able to be drawn in), are larger but less curved in the hind legs.
Distribution and habitatEdit
In Africa, the caracal is widely distributed south of the Sahara, but considered rare in North Africa. In Asia, it occurs from the Arabian Peninsula, Middle East, Turkmenistan, Uzbekistan to western India. It inhabits forests, savannas, marshy lowlands, semideserts, and scrub forests, but prefers dry areas with low rainfall and availability of cover. In montane habitats such as the Ethiopian Highlands, it occurs up to an altitude of 3,000 m (9,800 ft).
In Uzbekistan, caracal has been recorded only in the desert regions of the Ustyurt Plateau and Kyzylkum Desert. Between 2000 and 2017, 15 individuals were sighted alive, and at least 11 were killed by herders.
Ecology and behaviourEdit
The caracal is typically nocturnal (active at night), though some activity may be observed during the day as well. However, the cat is so secretive and difficult to observe that its activity at daytime might easily go unnoticed. A study in South Africa showed that caracals are most active when air temperature drops below 20 °C (68 °F); activity typically ceases at higher temperatures. A solitary cat, the caracal mainly occurs alone or in pairs; the only groups seen are of mothers with their offspring. Females in oestrus temporarily pair with males. A territorial animal, the caracal marks rocks and vegetation in its territory with urine and probably with dung, which is not covered with soil. Claw scratching is prominent, and dung middens are typically not formed. In Israel, males are found to have territories averaging 220 km2 (85 sq mi), while that of females averaged 57 km2 (22 sq mi). The male territories vary from 270–1,116 km2 (104–431 sq mi) in Saudi Arabia. In Mountain Zebra National Park (South Africa), the female territories vary between 4.0 and 6.5 km2 (1.5 and 2.5 sq mi). These territories overlap extensively. The conspicuous ear tufts and the facial markings often serve as a method of visual communication; caracals have been observed interacting with each other by moving the head from side to side so that the tufts flicker rapidly. Like other cats, the caracal meows, growls, hisses, spits, and purrs.
Diet and huntingEdit
A carnivore, the caracal typically preys upon small mammals, birds, and rodents. Studies in South Africa have reported that it preys on the Cape grysbok, the common duiker, sheep, goats, bush vlei rats, rock hyraxes, hares, and birds. A study in western India showed that rodents comprise a significant portion of the diet. They will feed from a variety of sources, but tend to focus on the most abundant one. Grasses and grapes are taken occasionally to clear their immune system and stomach of any parasites. Larger antelopes such as young kudu, bushbuck, impala, mountain reedbuck, and springbok may also be targeted. Mammals generally comprise at least 80% of the diet. Lizards, snakes, and insects are infrequently eaten. They are notorious for attacking livestock, but rarely attack humans.
Its speed and agility make it an efficient hunter, able to take down prey two to three times its size. The powerful hind legs allow it to leap more than 3 m (10 ft) in the air to catch birds on the wing. It can even twist and change its direction mid-air. It is an adroit climber. It stalks its prey until it is within 5 m (16 ft), following which it can launch into a sprint. While large prey such as antelopes are suffocated by a throat bite, smaller prey are killed by a bite on the back of the neck. Kills are consumed immediately, and less commonly dragged to cover. It returns to large kills if undisturbed. It has been observed to begin feeding on antelope kills at the hind parts. It may scavenge at times, though this has not been frequently observed. It often has to compete with foxes, wolves, leopards, and hyaena for prey.
Both sexes become sexually mature by the time they are a year old; production of gametes begins even earlier at seven to ten months. However, successful mating takes place only at 12 to 15 months. Breeding takes place throughout the year. Oestrus, one to three days long, recurs every two weeks unless the female is pregnant. Females in oestrus show a spike in urine-marking, and form temporary pairs with males. Mating has not been extensively studied; limited number of observations suggest that copulation, that lasts nearly four minutes on an average, begins with the male smelling the areas urine-marked by the female, which rolls on the ground. Following this, he approaches and mounts the female. The pair separates after copulation.
Gestation lasts about two to three months, following which a litter consisting of one to six kittens is born. Births generally peak from October to February. Births take place in dense vegetation or deserted burrows of aardvarks and porcupines. Kittens are born with their eyes and ears shut and the claws not retractable (unable to be drawn inside); the coat resembles that of adults, but the abdomen is spotted. Eyes open by ten days, but it takes longer for the vision to become normal. The ears become erect and the claws become retractable by the third or the fourth week. Around the same time, the kittens start roaming their birthplace, and start playing among themselves by the fifth or the sixth week. They begin taking solid food around the same time; they have to wait for nearly three months before they make their first kill. As the kittens start moving about by themselves, the mother starts shifting them everyday. All the milk teeth appear in 50 days, and permanent dentition is completed in 10 months. Juveniles begin dispersing at nine to ten months, though a few females stay back with their mothers. The average lifespan of the caracal in captivity is nearly 16 years.
The caracal is listed as Least Concern on the IUCN Red List since 2002, as it is widely distributed in over 50 range countries, where the threats to caracal populations vary in extent. Habitat loss due to agricultural expansion, building of roads and settlements is a major threat in all range countries. It is thought to be close to extinction in North Africa, Critically Endangered in Pakistan, Endangered in Jordan, but stable in central and Southern Africa. Local people kill caracal to protect livestock, or in retaliation for its preying on small livestock. Additionally, it is threatened by hunting for the pet trade on the Arabian Peninsula. In Turkey and Iran, caracals are frequently killed in road accidents.
In Uzbekistan, the major threat to caracal is killing by herders in retaliation for livestock losses. Guarding techniques and sheds are inadequate to protect small livestock like goats and sheep from being attacked by predators. Additionally, heavy-traffic roads crossing through caracal habitat pose a potential threat.
African caracal populations are listed under CITES Appendix II, while Asian populations come under CITES Appendix I. Hunting of caracal is prohibited in Afghanistan, Algeria, Egypt, India, Iran, Israel, Jordan, Kazakhstan, Lebanon, Morocco, Pakistan, Syria, Tajikistan, Tunisia, Turkey, Turkmenistan, and Uzbekistan. In Namibia and South Africa, it is considered a "problem animal", and its hunting is allowed for protecting livestock. Caracals occur in a number of protected areas across their range.
Chinese emperors used caracals as gifts. In the 13th and the 14th centuries, Yuan dynasty rulers bought numerous caracals, cheetahs, and tigers from Muslim merchants in the western parts of the empire in return for gold, silver, cash, and silk. According to the Ming Shilu, the subsequent Ming dynasty continued this practice. Until as recently as the 20th century, the caracal was used in hunts by Indian rulers to hunt small game, while the cheetah was used for larger game. In those times, caracals were exposed to a flock of pigeons and people would bet on which caracal would kill the largest number of pigeons. This probably gave rise to the expression "to put the cat among the pigeons".
The caracal appears to have been religiously significant in the Egyptian culture, as it occurs in paintings and as bronze figurines; sculptures were believed to guard the tombs of pharaohs. Embalmed caracals have also been discovered. Its pelt was used for making fur coats.
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- Abdunazarov, B. B. (2009). "Turkmenskiy karakal Caracal caracal (Schreber, 1776) ssp. michaelis (Heptner, 1945) [Turkmen Caracal Caracal caracal (Schreber, 1776) ssp. michaelis (Heptner, 1945)]". Krasnaya kniga Respubliki Uzbekistan. Chast’ II Zhivotnye [The Red Data Book of the Republic of Uzbekistan. Part II, Animals]. Tashkent: Chinor ENK. pp. 192–193.
- Bekenov, A. B.; Kasabekov, B. B. (2010). "Karakal Lynx caracal Schreber, 1776". Krasnaya kniga Respubliki Kazakhstan. Tom 1, Zhivotnye. Chast’ 1 Pozvonochnye [The Red Data Book of the Republic of Kazakhstan, Vol. 1, Animals. Part 1, Vertebrates]. Almaty: Ministerstvo obrazovaniya i nauki Respubliki Kazakhstan [Ministry for Education and Science of the Republic of Kazakhstan]. pp. 256–257.
- Mair, V.H. (2006). Contact and exchange in the ancient world. Hawai'i, Honolulu: University of Hawai'i Press. pp. 116–123. ISBN 978-0-8248-2884-4.
|Wikispecies has information related to Caracal caracal|
|Wikimedia Commons has media related to Caracal caracal.|
|Look up caracal in Wiktionary, the free dictionary.|
|Look up Caracal in Wiktionary, the free dictionary.|
- "Caracal". IUCN Cat Specialist Group.
- Cats For Africa : Caracal Distribution
- "Arabian caracal spotted for first time in Abu Dhabi in 35 years". The National (Abu Dhabi). 2019. Retrieved 23 February 2019.<|endoftext|>
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In computing, Ctrl+x is the key combination of the control key and a key usually labeled "x" (lower-case letter ex), typically used to delete selected text. Conventionally, the key combination is produced by holding down Ctrl and X simultaneously. To avoid having to press multiple keys simultaneously, the key combination is, on some systems, entered by first pushing the control key and then the X key.
In many software applications on Windows and the X Window System Ctrl-X can be used to cut highlighted mutable text to the clipboard. On Mac OS XCmd+X has an analogous function. The key combination was one of a handful of keyboard sequences chosen by the program designers at Xerox PARC to control text editing.
In computer science, this style of interaction is referred to as indirect manipulation, a human–computer interaction style opposed to direct manipulation. Direct manipulation is a term introduced by Ben Shneiderman in 1982 within the context of office applications and the desktop metaphor.
Indirect manipulation has a higher level of abstraction compared to direct manipulation as you first have to select the item (such as character, word, paragraph or icon) that you want to edit and then give the command, in this case the cut command by key combination Ctrl+x
- "Keyboard shortcuts for Windows". Retrieved 2012-05-23.
- "Mac Keyboard shortcuts | -23".
- Shneiderman, Ben (1982). "The future of interactive systems and the emergence of direct manipulation". Behaviour & Information Technology. 1 (3): 237–256. doi:10.1080/01449298208914450.
- Shneiderman, Ben (August 1983). "Direct Manipulation. A Step Beyond Programming Languages". IEEE Computer. 1 (8): 57–69. Archived from the original on 8 Feb 2012. Retrieved 2010-12-28.
|This article related to a desktop environment is a stub. You can help Wikipedia by expanding it.|<|endoftext|>
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Pragmatism is a late 19th Century and early 20th Century school of philosophy which considers practical consequences or real effects to be vital components of both meaning and truth. At its simplest, something is true only insofar as it works. However, Pragmatism is not a single philosophy, and is more a style or way of doing philosophy.
In general terms, Pragmatism asserts that any theory that proves itself more successful in predicting and controlling our world than its rivals can be considered to be nearer the truth. It argues that the meaning of any concept can be equated with the conceivable operational or practical consequences of whatever the concept portrays. Like Positivism, it asserts that the scientific method is generally best suited to theoretical inquiry, although Pragmatism also accepts that the settlement of doubt can also be achieved by tenacity and persistence, the authority of a source of ready-made beliefs or other methods. For more details, see the section on the doctrine of Pragmatism.
The school's founder, the American philosopher Charles Sanders Peirce, first stated the Pragmatic Maxim in the late 19th Century (and re-stated it in many different ways over the years) as a maxim of logic and as a reaction to metaphysical theories. The Pragmatic Maxim is actually a family of principles, not all equivalent (at least on the surface), and there are numerous subtle variations with implications which reach into almost every corner of philosophical thought.
The school of Pragmatism reached its peak in the early 20th Century philosophies of William James and John Dewey. The term "pragmatism" was first used in print by James, who credited Peirce with coining the term during the early 1870s.
After the first wave of Pragmatism, the movement split and gave rise to three main sub-schools, in addition to other more independent, non-aligned thinkers:
- Neo-Classical Pragmatism inherits most of the tenets of the classical Pragmatists, and its adherents include Sidney Hook (1902 - 1989) and Susan Haack (1945 - ).
- Neo-Pragmatism (sometimes called Linguistic Pragmatism) is a type of Pragmatism, although it differs in its philosophical methodology or conceptual formation from classical Pragmatism, and its adherents include C. I. Lewis (1883 - 1964), Richard Rorty (1931 - 2007), W. V. O. Quine, Donald Davidson (1917 - 2003)and Hilary Putnam (1926 - ).
- French Pragmatism is a specifically French off-shoot of the movement, and includes Bruno Latour (1947 - ), Michel Crozier (1922 - 2013), Luc Boltanski (1940 - ) and Laurent Thévenot (1949 - ).<|endoftext|>
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Reconstructing the Past to Inform the Future
“The farther back you can look, the farther forward you are likely to see.” –Winston Churchill
Probing the History of Climate Change
Instrumental measurements are useful to study recent climate change, but there are few records before 1850. To understand climate change over a longer timescale, scientists study physical evidence that is recorded in nature. Tree-rings, glacial ice cores, corals, stalactites, geoducks, lake and sea floor sediment cores, and forests buried by glaciers provide physical evidence of historical environmental conditions. These “proxy” records are used to reconstruct past climate conditions. Local proxies that have been recovered from Skagit basin include lake cores and glacially buried forests.
Climate Change in the Past 2,000 years
Multiple temperature reconstructions have been created using a variety of physical climate proxies. Temperature reconstructions (Figure 1) demonstrate temperatures in the Northern Hemisphere today are warmer than they’ve been for at least 2,000 years.<|endoftext|>
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# A Square Mirror has sides measuring 2ft. less than the sides of a square painting. if the difference between their areas is 32ft^2, how do you find the lengths of the sides of the mirror and the painting?
Dec 5, 2016
Let the length of the side of squared painting be $x f t$.Then the length of the side of the the squared mirror will be $\left(x - 2\right) f t$
By the given condition
${x}^{2} - {\left(x - 2\right)}^{2} = 32$
$\implies 4 x - 4 = 32$
$\implies x = \frac{36}{4} = 9 f t$
So the length of the side of squared painting is $9 f t$ and the length of the side of the the squared mirror is $\left(9 - 2\right) = 7 f t$
Dec 5, 2016
The side of the painting is $9 f t$ long and side of the mirror is $7 f t$ long.
#### Explanation:
Let $x =$ the side of the painting. The area is then ${x}^{2}$.
$x - 2 =$ the side of the mirror. The area is ${\left(x - 2\right)}^{2}$.
The difference between the areas is $32 f {t}^{2}$
${x}^{2} - {\left(x - 2\right)}^{2} = 32$
${x}^{2} - \left[\left(x - 2\right) \left(x - 2\right)\right] = 32$
${x}^{2} - \left({x}^{2} - 2 x - 2 x + 4\right) = 32$
${x}^{2} - \left({x}^{2} - 4 x + 4\right) = 32$
${x}^{2} - {x}^{2} + 4 x - 4 = 32$
$4 x - 4 = \textcolor{w h i t e}{{a}^{2}} 32$
$\textcolor{w h i t e}{a a} + 4 = + 4$
$4 x = 36$
$\frac{4 x}{4} = \frac{36}{4}$
$x = 9 f t$ is the length of the side of the painting.
$x - 2 = 9 - 2 = 7 f t$ is the length of the side of the mirror.<|endoftext|>
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# Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.11
## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.11
Question 1.
Solve the following quadratic equations by completing the square method
(i) 9x2 – 12x + 4 = 0
(ii) $$\frac{5 x+7}{x-1}$$ = 3x + 2
Solution:
Question 2.
Solve the following quadratic equations by formula method
(i) 2x2 – 5x + 2 = 0
(ii) $$\sqrt{2} f^{2}$$ – 6f + $$3 \sqrt{2}$$
(iii) 3y2 – 20y – 3 = 0
(iv) 36y2 – 12 ay + (a2 – b2) = 0
Solution:
(i) 2x2 – 5x + 2 = 0
The formula for finding roots of a quadratic equation ax2 + bx + c = 0 is
Question 3.
A ball rolls down a slope and travels a distance d = t2 – 0.75t feet in t seconds. Find the time when the distance travelled by the ball is 11.25 feet.
Solution:
Distance d = t2 – 0.75 t,
Given that d = 11.25 = t2 – 0.75 t.
t2 – 0.75t – 11.25 = 0<|endoftext|>
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### Counting Factors
Is there an efficient way to work out how many factors a large number has?
### Repeaters
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
### Oh! Hidden Inside?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
# American Billions
##### Stage: 3 Challenge Level:
Alison and Charlie are playing a divisibility game with a set of $0-9$ digit cards.
They take it in turns to choose and place a card to the right of the cards that are already there.
• After two cards have been placed, the two-digit number must be divisible by $2$.
• After three cards have been placed, the three-digit number must be divisible by $3$.
• After four cards have been placed, the four-digit number must be divisible by $4$.
And so on!
They keep taking it in turns until one of them gets stuck.
Click here to see an example of a game:
Alison places the $5$.
Charlie puts down the $8$ to make $58$, which is a multiple of $2$.
Alison puts down the $2$ to make $582$, which is a multiple of $3$.
Charlie puts down the $0$ to make $5820$, which is a multiple of $4$.
Alison now has to choose from $1, 3, 4, 6, 7,$ or $9$ to make a multiple of $5$.
Convince yourself that Alison is stuck, and that Charlie has won.
Play the game a few times on your own or with a friend.
Are there any good strategies to help you to win?
After a while, Charlie and Alison decide to work together to make the longest number that they possibly can that satisfies the rules of the game.
They very quickly come up with the five-digit number $12365$. Can they make their number any longer using the remaining digits? When will they get stuck?
What's the longest number you can make that satisfies the rules of the game?
Is it possible to use all ten digits to create a ten-digit number?
Is there more than one solution?
Please send us your explanation of the strategies you use to create long numbers.<|endoftext|>
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My Math Forum Solve second order differential equation(Euler's method)
Differential Equations Ordinary and Partial Differential Equations Math Forum
April 18th, 2011, 06:56 AM #1
Newbie
Joined: Apr 2011
Posts: 2
Thanks: 0
Solve second order differential equation(Euler's method)
Please, help me with solve of this equation:
Attached Images
Image 1.jpg (9.9 KB, 3231 views)
April 18th, 2011, 06:29 PM #2 Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 y"(1) = 2e
April 18th, 2011, 11:05 PM #3 Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Solve second order differential equation(Euler's method) First, let's find the solution satisfying the given conditions, then we'll employ Euler's method for comparison. a) Find the solution to the corresponding homogeneous solution. The auxiliary equation is: $r^2-2r=0\:\therefore\:r=0,2$ thus: $y_h(x)=c_1+c_2e^{2x}$ b) Find a particular solution, we can assume it will be of the form: $y_p(x)=Ae^x=y_p'(x)=y_p'#39;(x)$ Substituting into the ODE gives: $Ae^x-2$$Ae^x$$=2e^x$ $-Ae^x=2e^x\:\therefore\:A=-2$ $y_p(x)=-2e^x$ Thus, the general solution is: $y(x)=y_h(x)+y_p(x)=c_1+c_2e^{2x}-2e^x$ $y'(x)=2c_2e^{2x}-2e^x$ Now, we use initial conditions to determine the parameters: (1) $-1=c_1+c_2e^2-2e$ (2) Solving (2) for $c_2$ we find: $c_2=\frac{1}{e}$ Substituting into (1) we get: $c_1=e-1$ Thus, the solution satisfying the given conditions is: $y(x)=e-1+e^{2x-1}-2e^x$ $y(2)=e-1+e^{3}-2e^2=e^3-2e^2+e-1\approx7.025706553785$ To use Euler's method, we begin by converting the given IVP into an IVP for a system of first order equations. First, we express the ODE as: $y''=2y#39;+2e^x$ Setting: $u_1(x)\equiv y(x)$ $u_2(x)\equiv y'(x)$ we obtain: $u_1'(x)=u_2(x)$ $u_2'(x)=2u_2(x)+2e^x$ The initial conditions given transform to: $u_1(1)=-1$, $u_2(1)=0$ Recall, Euler's method is given recursively by: $x_{n+1}=x_n+h$ $y_{n+1}=y_n+hf$$x_n,y_n$$$ Extending this to the system of equations, we have: $x_{n+1}=x_n+h$ $u_{n+1,1}=u_{n,1}+hu_2$$x_n$$$ $u_{n+1,2}=u_{n,2}+2h$$u_{n,2}+e^{x_n}$$$ With h = 0.1, we have: $x_{n+1}=x_n+0.1$ $u_{n+1,1}=u_{n,1}+0.1u_{n,2}$ $u_{n+1,2}=1.2u_{n,2}+0.2e^{x_n}$ Step 0: $x_0=1$ $u_{0,1}=-1$ $u_{0,2}=0$ Step 1: $x_1=1.1$ $u_{1,1}=-1+0.1(0)=-1$ $u_{1,2}=1.2(0)+0.2e^{1}=0.5436563656918$ Step 2: $x_2=1.2$ $u_{2,1}=-1+0.1(0.543656365691=-0.94563436343082" /> $u_{2,2}=1.2(0.543656365691+0.2e^{1.1}=1.25322084 36194465" /> Step 3: $x_3=1.3$ $u_{3,1}=-0.94563436343082+0.1(1.2532208436194465)=-0.8203122790688753$ $u_{3,2}=1.2(1.2532208436194465)+0.2e^{1.2}=2.16788 83968906453$ Step 4: $x_4=1.4$ $u_{4,1}=-0.8203122790688753+0.1(2.1678883968906453)=-0.6035234393798108$ $u_{4,2}=1.2(2.1678883968906453)+0.2e^{1.3}=3.33532 5409792623$ Step 5: $x_5=1.5$ $u_{5,1}=-0.6035234393798108+0.1(3.335325409792623)=-0.26999089840054846$ $u_{5,2}=1.2(3.335325409792623)+0.2e^{1.4}=4.813430 485120082$ Step 6: $x_6=1.6$ $u_{6,1}=-0.26999089840054846+0.1(4.813430485120082)=0.21135 215011146$ $u_{6,2}=1.2(4.813430485120082)+0.2e^{1.5}=6.672454 3962117115$ Step 7: $x_7=1.7$ $u_{7,1}=0.21135215011146+0.1(6.6724543962117115)=0 .8785975897326312$ $u_{7,2}=1.2(6.6724543962117115)+0.2e^{1.6}=8.99755 1760333078$ Step 8: $x_8=1.8$ $u_{8,1}=0.8785975897326312+0.1(8.99755176033307= 1.778352765765939" /> $u_{8,2}=1.2(8.99755176033307+0.2e^{1.7}=11.89185 1590745134" /> Step 9: $x_9=1.9$ $u_{9,1}=1.778352765765939+0.1(11.891851590745134)= 2.9675379248404523$ $u_{9,2}=1.2(11.891851590745134)+0.2e^{1.8}=15.4801 51401776748$ Step 10: $x_{10}=2$ $u_{10,1}=2.9675379248404523+0.1(15.480151401776748 )=4.5155530650181275$ $u_{10,2}=1.2(15.48015140177674+0.2e^{1.9}=19.913 360570588" /> I expected a closer approximation than that. I don't know whether I've made an error or if the first order numerical method's convergence is to blame.
April 19th, 2011, 07:57 AM #4 Newbie Joined: Apr 2011 Posts: 2 Thanks: 0 Re: Solve second order differential equation(Euler's method) Dear MarkFL, I am so profoundly grateful to you for your help.
Tags differential, equationeuler, method, order, solve
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# euler method for 2nd order ode
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How do I change, delete, or insert a line in a file, or append to the beginning of a file? O and the “f” issues: filehandles, flushing, formats, and footers. Perl normally buffers output so it doesn’t make a system call option binary tree every bit of output.
By saving up output, it makes fewer expensive system calls. For instance, in this little bit of code, you want to print a dot to the screen for every line you process to watch the progress of your program. For more information on output layers, see the entries for binmode and open in perlfunc, and the PerlIO module documentation. The basic idea of inserting, changing, or deleting a line from a text file involves reading and printing the file to the point you want to make the change, making the change, then reading and printing the rest of the file. Within that basic form, add the parts that you need to insert, change, or delete lines. To prepend lines to the beginning, print those lines before you enter the loop that prints the existing lines. To change existing lines, insert the code to modify the lines inside the while loop.
In this case, the code finds all lowercased versions of “perl” and uppercases them. The happens for every line, so be sure that you’re supposed to do that on every line! First read and print the lines up to the one you want to change. Next, read the single line you want to change, change it, and print it. To skip lines, use the looping controls. The next in this example skips comment lines, and the last stops all processing once it encounters either __END__ or __DATA__ .
Do the same sort of thing to delete a particular line by using next to skip the lines you don’t want to show up in the output. Modules such as Path::Tiny and Tie::File can help with that too. If you can, however, avoid reading the entire file at once. Perl won’t give that memory back to the operating system until the process finishes. You can also use Perl one-liners to modify a file in-place. To delete lines, only print the ones that you want. How do I count the number of lines in a file?
Those can be rather inefficient though. However, that doesn’t work if the line ending isn’t a newline. How do I delete the last N lines from a file? Most often, the real question is how you can delete the last N lines without making more than one pass over the file, or how to do it without a lot of copying. The easy concept is the hard reality when you might have millions of lines in your file. That module provides an object that wraps the real filehandle to make it easy for you to move around the file.<|endoftext|>
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Imagine a Ferris wheel, filled with water and boats
FALKIRK, Scotland — There was a time, a couple of centuries ago, when the best way to move people and freight across the land was on canals.
Scotland, surrounded by water on three sides, became the first nation in the world to dig intersecting cross-country canals. They connected the North Sea, near Edinburgh on the east, with the Atlantic Ocean, a few miles to the west of Glasgow.
That was in 1790, and the trip took most of a day, including the 6-10 hours to move through 11 locks needed to raise or lower the boats 115 feet.
But in the next century, an enhanced steam engine greatly cut the transit time — and also opened other routes, on land and sea. The railroad further reduced the need for canals.
Finally, widespread use of the internal combustion engine meant trucks and cars could take people and cargo much faster than could boats.
What had been a busy canal system was largely abandoned in 1933. In the 1960s, it was closed when two major highways were constructed through the canals.
But everything old is new again, and then some.
The national government spent the equivalent of $124-million to eliminate the need for the original 11 locks by creating the world’s first “rotating boat lift.” Opened in May 2002, it is named the Falkirk Wheel, after the middle-of-the-nation town where it was constructed.
The structure is futuristic in appearance, yet it uses an ancient law of physics to operate. Basically, a huge wheel is fixed to an axis, and on either side of the wheel are two boxes that hold water. Each box, called a gondola, is 70 feet long by 21 feet wide.
This is when Archimedes’ Principle comes into use. This states that an item placed in water displaces its own weight; thus one or more boats push out of the gondola an amount of water equivalent in weight to the boat’s weight.
The opposing gondola has the same weight, whether it is water only or also boats. A number of electric motors turn a cleverly designed series of gears that rotate both the large wheel and lesser gears that keep the gondolas level while the big wheel turns.
The gondola on the bottom is filled with water from a basin, and boats glide in before a water-tight door is closed behind them. The gondola at top opens onto an aqueduct that connects through a tunnel to the original, higher canal.
When both gondolas are closed, the wheel rotates — eerily quiet, considering the size of the structure. What was below goes up and what was up comes down.
When the big wheel’s half-rotation is complete, the water doors are opened and the boats glide out, to continue their canal journey in either direction. The cross country canal is about 68 miles long.
Since it opened, thousands of pleasure craft and more than 1-million visitors have come through the gates to watch it happen, with many of them booking rides on the 40-passenger tour boats kept in the basin.
The half-rotation takes about 15 minutes; the tour boats going up send their boats into the 330-foot-long aqueduct, which leads to a 475-foot-long tunnel beneath an ancient Roman wall. From there the tour boats enter a small lake, turn around and come back.
If you go
GETTING THERE: Several trains a day from Edinburgh and Glasgow stop in Falkirk; the ride takes little more than a half-hour. Phone your departure train station for the schedule.
The Falkirk Wheel is on a bus route from Falkirk’s Grahamston and High train stations. The No. 3 Red Line Bus, operated by First Bus, runs about every 15 minutes from stops near both stations to the Wheel site. Or, cabs can be hired at the stations.<|endoftext|>
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The rand function can be used to print a random number in Perl.
This will print something like this.
Set highest possible number
By default, the rand function without any options will print 0 followed by a decimal. Placing an integer inside of the parenthesis will tell the rand function to print an integer that will not exceed the value inside of the parenthesis. For example, if 10 is placed inside of the parenthesis, rand will print an integer somewhere between 0 and 10.
In this example, the non-decimal integer is 7.
Whole number / No decimal
To only print whole numbers with no decimal, use the int override. In this example, a whole number between 0 and 1000 will be printed.
361 was printed.<|endoftext|>
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Endangered Species Day: May 19th
May 19th is Endangered Species Day, and what better way to celebrate than by helping endangered wildlife in our area. According to the US Fish and Wildlife Service, there are five different species of sea turtles that are either endangered or threatened in Virginia: Loggerhead sea turtles, leatherback sea turtles, green sea turtles, hawksbill sea turtles, and the Kemp’s ridley sea turtle, which is the most endangered and rarely seen.
One of the major threats to sea turtles is marine pollution and debris, especially plastics. Sea Turtle Conservancy estimates that over 100 million marine animals are killed each year due to plastic debris in the ocean, and more than 80% of this plastic comes from land. Polluted waterways kill off a sea turtle’s natural food source and plastic debris is commonly mistaken for food. This is a problem you can help solve.
How you can help:
- Reduce your use of plastic in addition to reusing and recycling. A great way to start is to avoid using plastic straws and politely request no straw with your drink order.
- Properly dispose of trash and make sure it is secure to prevent fly-away plastic debris
- Host or participate in a beach clean-up event
- Do not leave behind any fishing gear, line, or netting. If you bring it in, take it out.
- Reduce marine pollution by using less chemical fertilizers
- Avoid releasing balloons into the air
- Be aware when out on the water, especially in a boat. Sea turtles are hard to spot and can be critically injured by boat propellers.
- When in nature, don’t leave any items behind, and leave rocks, plants and other natural objects as you find them.<|endoftext|>
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If you dual 3/4 the a cup, you"ll gain 6/4 cups, which can be streamlined as 3/2 cups or 1 1/2 cups. In decimals, 3/4 of a cup is .
You are watching: What is 2/3 cup doubled
Furthermore, what is half of 3/4 in cups? If you desire to include half the 3/4 cup sugar (3/8 cup) to a recipe, you deserve to use a couple of different methods to measure up this amount. Measure half the 3/4 cup sugar by using a tablespoon. The number of tablespoons that adds as much as 3/4 cup is 12, so division 12 in half and add 6 tablespoons of sugar to your recipe because that half that 3/4 cup.
likewise Know, what is fifty percent of 1/3 cup?
Half the 1/3 cup is 1/2 * 16 tsp = 8 tsp.
See more: " Every Time A Bell Rings An Angel Gets His Wings, Every Time A Bell Rings An Angel Gets Its Wings T
How many 2/3 cups does it take to make 1 cup?
One way would be to have two cups one that is 2/3 and also one the is specifically 1 cup. Fill the 2/3 cup up through what ever before you want to measure.. Prefer water and also put that in the north cup. To fill the 2/3 cup again and also fill the partly filled cup through water again.
### How have the right to I measure 3/4 cup that water?
The various other simple method to measure up 3/4 cup is as adheres to : to fill a cup through the thing you desire to measure. To water or take it out fifty percent of it into one more cup(this is 1/2 cup,). Currently from either of the cup take out fifty percent of the point you are measuring(it is 1/4 cup) .
### How much is 3 4 in a cup?
enter your birthdate come continue: 1 tablespoon (tbsp) = 3 teaspoons (tsp) 3/8 cup = 6 tablespoons 1/2 cup = 8 tablespoons 2/3 cup = 10 tablespoons + 2 teaspoons 3/4 cup = 12 tablespoons
### What 3/4 lb doubled?
What is 3/4 doubled? - Quora. 3/4 doubled method that friend are adding another 3/4 come the original 3/4: 3/4 + 3/4 = 6/4 which simplifies to 1 1/2 (read together 1 and also a half).
### What is fifty percent of 2/3 cup that flour?
reducing the size of Recipes 1/3 cup 2 tablespoons + 2 teaspoons 1/2 cup 1/4 cup 2/3 cup 1/3 cup 3/4 cup 6 tablespoons
### How many 1 4 cups perform I need to make 3 4 cups?
Volume (liquid) 1/4 cup or 2 fluid ounces 59 ml 1/3 cup 79 ml 1/2 cup 118 ml 2/3 cup 158 ml
### How lot is 1/8 Cup doubled?
doubling Ingredients A B ingredient: 1/8 cup doubled: 1/4 cup ingredient: 1 teaspoons doubled: 2 teaspoons ingredient: 1/2 tablespoons doubled: 1 tablespoon ingredient: 2/3 cup doubled: 4/3 cup
### How numerous 3rds are in a cup?
Explanation: 13 rd that a cup method there room three 13 the a cup, every cup.
### What is 1.5 of a cup?
Answer and Explanation: half of 1.5 cup is 0.75 cups, or 3/4 cups.
### What is fifty percent of 1/3 in fraction?
Thus, "half of precisely 1/3" is same to “1/2 × 1/3”. Come multiply two or any variety of fractions, we need to multiply the molecule together and the platform together.
### What is fifty percent of 1/3 cup in grams?
Dry goods Cups Grams Ounces 2 tbsp 25 g .89 oz 1/4 cup 50 g 1.78 oz 1/3 cup 67 g 2.37 oz 1/2 cup 100 g 3.55 oz
### What is enlarge 1 3 cup or 1 4 cup?
“How plenty of 1/3 cup make a 1/4 cup?” When splitting fractions, invert the denominator, in this case, 1/3 i do not care 3/1. We know it takes less than 1/3 the a cup to fill a 1/4th cup because 1/3 cup is bigger 보다 a 1/4th cup.
### What is one fifty percent of a 3rd cup?
When separating by a fraction, invert that fraction (the denominator) and also multiply. When multiplying two fractions, main point the two numerators. Climate multiply the 2 denominators. So, fifty percent of a third cup = 1/6 (one sixth).
### What is .375 together a fraction?
fountain to decimal to Inches to MM Conversion chart Fractions Decimal millimeter 11/32 .3437 8.731 23/64 .3594 9.128 3/8 .375 9.525 25/64 .3906 9.921
### What is fifty percent of half a cup?
half the a cup, equal to 4 fluid ounces (0.1 liter) or 8 tablespoons.<|endoftext|>
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# NCERT solutions for class 10 Mathematics
## NEET-UG 2021
10,000+ Daily Practice Questions
(only at ₹ 299/- in myCBSEguide App)
## myCBSEguide App
Complete Guide for CBSE Students
NCERT Solutions, NCERT Exemplars, Revison Notes, Free Videos, CBSE Papers, MCQ Tests & more.
## NCERT Solution Chapter 8: Introduction to Trigonometry
You have already studied about triangles, and in particular, right triangles, in your earlier classes. Let us take some examples from our surroundings where right triangles can be imagined to be formed. For instance : Suppose the students of a school are visiting Qutub Minar. Now, if a student is looking at the top of the Minar, a right triangle can be imagined to be made, as shown in Fig 8.1. Can the student find out the height of the Minar, without actually measuring it? Suppose a girl is sitting on the balcony of her house located on the bank of a river. She is looking down at a flower pot placed on a stair of a temple situated nearby on the other bank of the river. A right triangle is imagined to be made in this situation as shown in Fig.8.2. If you know the height at which the person is sitting, can you find the width of the river?.
Suppose a hot air balloon is flying in the air. A girl happens to spot the balloon in the sky and runs to her mother to tell her about it. Her mother rushes out of the house to look at the balloon. Now when the girl had spotted the balloon intially it was at point A. When both the mother and daughter came out to see it, it had already travelled to another point B. Can you find the altitude of B from the ground? In all the situations given above, the distances or heights can be found by using some mathematical techniques, which come under a branch of mathematics called ‘trigonometry’. The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). In fact, trigonometry is the study of relationships between the sides and angles of a triangle. The earliest known work on trigonometry was recorded in Egypt and Babylon. Early astronomers used it to find out the distances of the stars and planets from the Earth. Even today, most of the technologically advanced methods used in Engineering and Physical Sciences are based on trigonometrical concepts. In this chapter, we will study some ratios of the sides of a right triangle with respect to its acute angles, called trigonometric ratios of the angle. We will restrict our discussion to acute angles only. However, these ratios can be extended to other angles also. We will also define the trigonometric ratios for angles of measure 0° and 90°. We will calculate trigonometric ratios for some specific angles and establish some identities involving these ratios, called trigonometric identities.
## NCERT Solutions for Class 10th Mathematics
NCERT Solutions Class 10 Mathematics PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 10 Mathematics includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 10 Mathematics have total 13 chapters. Class 10 Mathematics ncert Solutions in pdf for free Download are given in this website. Ncert Mathematics class 10 solutions PDF and Mathematics ncert class 10 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.
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# Partial correlation
Partial correlation measures the strength and direction of the relationship between two variables while controlling for the effect of one or more additional variables.
By:
Updated: Jun 27, 2024
## 3 key takeaways:
• Partial correlation isolates the relationship between two variables by removing the influence of other variables, providing a clearer understanding of their direct connection.
• It helps in identifying whether the observed correlation between two variables is due to their direct association or influenced by a third variable.
• Partial correlation is commonly used in statistical analysis and research to control for confounding factors and obtain more accurate results.
## What is partial correlation?
Partial correlation is a statistical technique used to understand the relationship between two variables while controlling for the influence of one or more additional variables. By accounting for the effects of these other variables, partial correlation provides a clearer picture of the direct association between the variables of interest. This method is useful in determining whether the observed correlation between two variables is genuine or if it is influenced by the presence of other factors.
For example, in a study examining the relationship between exercise and weight loss, partial correlation can control for diet, ensuring that the observed relationship between exercise and weight loss is not confounded by dietary habits.
## Calculating partial correlation
To calculate the partial correlation between two variables (X) and (Y) while controlling for a third variable (Z), the following steps are generally taken:
1. Compute the correlation between (X) and (Z), denoted as (r_{XZ}).
2. Compute the correlation between (Y) and (Z), denoted as (r_{YZ}).
3. Compute the correlation between (X) and (Y), denoted as (r_{XY}).
4. Use the partial correlation formula:
[ r_{XY.Z} = \frac{r_{XY} – r_{XZ} \cdot r_{YZ}}{\sqrt{(1 – r_{XZ}^2) \cdot (1 – r_{YZ}^2)}} ]
For example, if we want to find the partial correlation between hours studied and exam scores while controlling for sleep hours, we would first find the correlations between each pair of variables and then apply the formula to isolate the direct relationship between studying and exam performance.
## Applications of partial correlation
• Research studies: Partial correlation is used to control for potential confounding variables, providing more accurate results in research studies.
• Medical research: In clinical studies, partial correlation helps isolate the effects of a treatment by controlling for other factors such as age, gender, or pre-existing conditions.
• Social sciences: Researchers use partial correlation to understand complex relationships between variables by accounting for the influence of other socio-demographic factors.
For instance, in a study on the impact of education on income, partial correlation can control for factors like work experience and socio-economic background to better understand the direct effect of education.
## Benefits of partial correlation
• Control for confounding: It helps control for confounding variables, providing a clearer understanding of the direct relationship between variables.
• Improved accuracy: By accounting for the influence of additional variables, partial correlation can lead to more accurate and reliable results.
• Enhanced analysis: It allows researchers to disentangle complex relationships and better interpret the data.
For example, controlling for age when studying the relationship between physical activity and heart health ensures that the observed effects are not merely due to differences in age.
## Challenges of partial correlation
• Complexity: Calculating partial correlations can be complex, especially when controlling for multiple variables.
• Interpretation: The results of partial correlation analysis can be difficult to interpret without a thorough understanding of the underlying statistical principles.
• Data requirements: Partial correlation requires accurate and comprehensive data on all relevant variables to provide meaningful results.
For instance, if the data on a confounding variable is incomplete or inaccurate, the partial correlation results may be misleading.
## Examples of partial correlation
• Health studies: Examining the relationship between smoking and lung function while controlling for age and exercise.
• Education research: Analyzing the link between study habits and academic performance while controlling for socio-economic status.
• Economic analysis: Investigating the relationship between inflation and unemployment while controlling for government policies.
For example, in a health study, researchers might use partial correlation to understand the direct impact of a new drug on blood pressure by controlling for patients’ dietary habits and exercise routines.
• Correlation
• Multiple regression
• Confounding variable
• Statistical control
• Path analysis
Understanding these related topics can provide a broader context for partial correlation, highlighting its importance in controlling for confounding factors and obtaining more accurate and reliable results in various fields of research and analysis.
Sources & references
Risk disclaimer
AI Financial Assistant
Arti is a specialized AI Financial Assistant at Invezz, created to support the editorial team. He leverages both AI and the Invezz.com knowledge base, understands over 100,000... read more.<|endoftext|>
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Birch bark, which is found in many parts of the U.S., Canada, Europe and China, is a great way to start a campfire. Rich in terpenoids, the paper-thin material ignites easily. The heat it releases provides enough activation energy to set small twigs ablaze, which of course should be placed in a tee-pee arrangement, so as to let in more oxygen. All of this should take place in a pit surrounded by stones, not to let wind take heat away from the young fire and not to burn the forest down.
The hues of a flame are rarely constant for a second, a hint that something complex is occurring within them. There is a set of chain mechanisms involving intermediate molecules that are needed for subsequent steps. Many of the in-between products are radicals, reactive molecules with unpaired electrons. Radicals are often created in the high temperature regions of the flame, but they diffuse back into the colder regions where they are needed to generate the final products. To reveal more details, laser-based investigative techniques have been used so as not to disturb the flame. Even when burning as simple a molecule as diatomic hydrogen, radicals like O, H, OH and HO2 form. When the combustion of hydrocarbons like cellulose and lignin in wood takes place, we get a greater variety of radicals, some of them carbon-centered. C2 and the radical CH arise in excited form and release blue and green light. Lignin-derived radicals involving benzene structures are not the healthiest things to inhale, but mere occasional exposure is probably nothing to worry about, unless there’s a concentration of wood-burning stoves in a particular area. All of this underlines the fact that whenever we write an overall equation for a fuel consumed in a fire, it’s like we are seeing only the ingredients of a recipe and the final product without witnessing the cooking.
Hot, gaseous products of combustion expand and rise, stretching flames vertically. The ascension leads to pressure gradients, and fresh air is pushed into the fire. The circulation supplies it with more oxygen, the electron-thief that campfires depend on to release heat as more tightly bonded products like water and carbon dioxide are created. There’s energy needed to drive molecular fragments of cellulose apart, in the same way that you need to exert force against gravity if you want to push a ball up a hill. But once at the top, the ball can roll further down on the other side. With chemicals, it’s not the combination of mass, gravity and varying heights that accounts for differences in potential energy but Coulombic forces acting over a variety of distances between positive atomic nuclei and valence electrons.
Why is a wood flame predominantly yellow-orange? It has been proposed that it’s not the result of electron transitions; what’s supposedly responsible is incandescence of particles at about 1100 to 1200 oC. Since the combustion of wood is incomplete, the flame’s soot particles, some of which are elemental carbon(others are polymers), emit part of their vibrational energy as photons. How fast the molecules vibrate depends on their temperature, and the hotter the surface, the higher the frequency of the photons emitted. The same mechanism would account for the red glow of logs at the base of a fire. But the temperature is lower, in the neighborhood of 700 to 1000oC, hence a color of a longer wavelength and a lower frequency. Different parts of the charcoal emit light of slightly different frequencies, intermittently and in different directions. A point on the surface of the charcoal particle that has just emitted photons will have lost energy and cooled slightly. Although exothermic reactions quickly compensate, from that same spot, the temperature will not necessarily be identical, especially in light of air movement and the exact frequency of photons is not necessarily replicated.
It’s well known that the ease of ignition and burning rate of wood vary greatly with moisture content. Specifically, a drop in moisture content of 10% results in an increase of 20–30% in burning rate. When wood is too dry the combustion rate increases, but an inadequate oxygen supply leads to more undesirable emissions. The combustion rate also depends on boundary conditions and the species being burnt. Why does it vary with tree type? Wood composition is not constant. Wood is essentially a matrix of cellulose and other carbohydrate fibers (hemi cellulose) reinforced by the adhesive binding action of lignin. But hardwoods can have anywhere from 18 to 25% lignin along with varying amounts of hemicellulose, usually a partly acetylated, acidic xylan. Softer woods have other hemicellulose fibers and more “binder”, 25 to 35% lignin. There is also an assortment of oils and other secondary products present.
The different wood recipes not only affect kinetics but thermochemistry. Softwoods, compared to hardwoods, release on average an extra 5% of heat, a maximum of 21 instead of 20 MJ/kg, to be precise. From the point of view of carbon dioxide emissions, it’s not a good idea to rely on wood as a primary fuel. For every MJ of heat obtained from wood, on average, 80 g of CO2 are emitted. In contrast, natural gas combustion only puts out 50 g per MJ.
Finally, when the fire dies and we’re left with ashes, what exactly are we staring at? In general the ash is of an alkaline nature, with a pH of about 12, mostly due to the presence of carbonates of calcium and potassium, specifically CaCO3 and K2Ca(CO3)2. At higher temperatures about 1300 oC, calcium and magnesium oxides are ashes’ main compounds. Those alkaline compounds were not originally present in plant tissue. Neutral metals weren’t either, so the carbonates must have formed indirectly, perhaps ions precipitating with carbonic acid, derived from water and carbon dioxide.
In the same way that the nature of flames and soot depends on the type of wood, the more detailed composition of ash also varies. According to a fairly recent study, it matches the needs of trees growing in a particular area. Among ashes of all conifers and broadleaves tested, that of birch trees, whose bark started this discussion, has the most calcium, the 2nd most phosphorus and is the only one without aluminum. But birch ash only has a fraction of the potassium and magnesium ions found within that of poplars and maples, respectively. Like cremated people and exploding suns, trees leave a signature in their ashes.
- Chung. K Law Combustion Physics http://books.google.ca/books?
- Kurt Nassau. The Physics and Chemistry of Color: the 15 Causes of Color. Wiley-Interscience. 1983
- Study on the characteristics of Waste Wood Ash. 2011 http://www.uctm.edu/journal/j2011-1/3_Mladenov.pdf
- Rona Pitman. Use of Wood Ash In Forestry http://www.forestry.gov.uk/pdf/Use_of_ash_in_forestry.pdf/
- bark photo: http://www.millsonforestry.com/shop/index.php?main_page=product_info&cPath=8&products_id=21
- Hao C. Tran and Robert H. White Burning Rate of Solid Wood http://184.108.40.206/documnts/pdf1992/tran92b.pdf
- Wood Combustion Basics http://www.epa.gov/burnwise/workshop2011/WoodCombustion-Curkeet.pdf
- T.E. Timell. Recent Progress in the Chemistry of Wood http://www.springerlink.com/content/k7716255rq375805/<|endoftext|>
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THE NATION CLASSROOM
History as It Happened
RACE RELATIONS and CIVIL RIGHTS
Below, you’ll discover articles and reporting taken from the pages of The Nation magazine—history reported on as it happened. You will be able to explore primary and secondary sources on key historical events. The material is organized into three modules, each covering an important period in the story of US race relations and civil rights.
Each module includes an introduction to the time period; a short list of vocabulary words—phrases you will need to know; and numerous brief excerpts from original Nation articles. Under “As You Read,” you’ll also find questions about the excerpts that can help develop your analytical skills.
The short excerpts for each time period are presented in a DBQ (document-based question) format that resembles the DBQ requirement on AP US History exams. Working with your teacher, in class groups, or on your own, you can practice the skills necessary for the DBQ section of the AP US History test.
To get started, choose a module and begin exploring that time period.
CHOOSE YOUR MODULE:
- 1865–77: The Post–Civil War Era and Realities of Reconstruction
- 1919–29: Return From World War I, Jim Crow, Harlem Renaissance
- 1945–65: Civil Rights, Civil Strife: Landmark Movement Moments
You can also access another resource—a collection of Nation articles covering race relations and civil rights in recent years—here.
*A NOTE ABOUT OUTMODED LANGUAGE
As you read original articles in this archive, you will come across phrases that may sound unfamiliar, archaic, even offensive. Words such as “Negro’ and ‘colored person’ were commonly used to describe African Americans during The Nation’s first 100-plus years. Other terms, including now-discredited terms, appear occasionally, especially in reported pieces. We have retained these terms in the interests of historical accuracy, and we hope that readers will understand their usage as part of the complex record of the American story.<|endoftext|>
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Also known as the Jack Pine Warbler.
Your purchase is helping Expedition Art and Saving Species purchase land in Sumatra! Learn more about the project.
This warbler nests only in stands of young jack pines in central Michigan, a habitat that grows up only briefly after fires. In migration, they are seen in thickets and deciduous trees. During winter, rarely seen, found only in dense undergrowth of pine forests of the Bahamas.
Males arrive on breeding grounds in mid-May, a few days before the females, and establish large territories. They tend to be loosely colonial (lone pairs are rare), and males tend to return to the same colony in which they previously nested. Males sometimes have more than one mate. The young are fed by both parents.
Kirtland’s warblers have a short life span--about two years.
These birds forage for insects near the ground and in lower parts of pines and oaks. They eat mostly small insects, some berries. Adults also feed on pine sap.
From record lows of 167 in 1987, the number of singing males increased to around 2,000 in 2012.
The Kirtland warbler is one of the rarest songbirds.
This songbird is one of 56 species of wood warblers found in North America.
It nests in just a few counties in Michigan's northern Lower and Upper peninsulas.
Why Are They Endangered?
Always known as a scarce bird with a limited range, Kirtland's Warbler apparently began to decline seriously in the 1960s. Today, Kirtland's warblers face two significant threats: lack of crucial young jack pine forest habitat and the parasitic brown-headed cowbird. Through most of the 1970s and 80s, the annual counts hovered around 200 males, twice dropping as low as 167. Since 1990, the numbers have gradually increased, and the total of singing males hit 2,000 in 2012.<|endoftext|>
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# How to simplify a square root
How can the following:
$$\sqrt{27-10\sqrt{2}}$$
Be simplified to:
$$5 - \sqrt{2}$$
Thanks
If you're faced with a question that says "Prove that $\sqrt{27-10\sqrt{2}}$ $=5 - \sqrt{2}$", then it's just a matter of squaring $5 - \sqrt{2}$ and seeing that you get $27-10\sqrt{2}$. But suppose the question your faced with is to find a square root of $27-10\sqrt{2}$ of the form $a+b\sqrt{2}$, where $a$ and $b$ are rational. Then you have $$27-10\sqrt{2}=\left(a+b\sqrt{2}\right)^2 = a^2 + 2ab\sqrt{2} + 2b^2$$ so \begin{align} 27 & = a^2+2b^2 \\[8pt] -10 & = 2ab \end{align} From the second equation we get $a=-5/b$, then the first equation becomes $$27 = \frac{25}{b^2} + 2b^2$$ or $$2(b^2)^2 -27b^2 + 25 = 0.$$ A solution is $b^2=1$, and you can go on from there to find $b$ and then $a$.
(And remember that the number will have two square roots.)
Later note: In order for all this to work, we have to rely on the fact that $\sqrt{2}$ is irrational. That enables us to conclude that the rational parts are equal and the irrational parts are equal, so we have two equations.
• It might be worth to mention that $5-\sqrt 2>0$. Commented Mar 13, 2013 at 23:31
No lucky guesses are needed, there is a simple denesting algorithm for $\rm\:\sqrt{a+b\sqrt{n}}$
Simple Denesting Rule $\rm\ \ \ \color{#0A0}{subtract\ out}\ \sqrt{norm}\:,\ \ then\ \ \color{brown}{divide\ out}\ \sqrt{trace}$
$\begin{array}{lll}\rm Recall\ \ \ w = a + b\sqrt{n}\ \ \ has\!\!\! &{\bf norm} &\!\!\!\rm=\: w\:\cdot\: w' = &\!\!\!\!\rm(a + b\sqrt{n})\ \cdot\: (a - b\sqrt{n})\ =\: a^2 - n\: b^2 \\ \\ \rm and,\ furthermore,\ \ w\ \ has \!\!\!&{\bf trace} &\!\!\!\!\rm =\: w+w' = &\!\!\!\!\rm (a + b\sqrt{n}) + (a - b\sqrt{n})\: =\: 2\:a\end{array}$
Here $\:27-10\sqrt{2}\:$ has norm $= 23^2.\,$ $\rm\, \color{#0A0}{Subtracting\ out}\ \sqrt{norm}\ = -23\$ yields $\ 50-10\sqrt{2}\:$
and this has $\rm\ \sqrt{trace}\: =\: 10,\ \ hence\ \ \ \color{brown}{dividing\ it\ out}\$ of this yields $\rm\ 5 - \sqrt{2} =\:$ sought sqrt.
Remark $\$ The sign of the norm sqrt was chosen to make the trace sqrt rational. The same answer would arise using the opposite sign, but with slightly more work (rationalizing a denominator). $\$ For many further examples see other posts on radical denesting.
• Nice technique and a good example of why there are really two solutions when taking the square root, contrary to what most mathematicians would like it to be (a single-valued function), and that it doesn't matter much whether you take the square root of an unknown or a "simple number".
– SasQ
Commented Dec 14, 2014 at 22:26
• Where does these names come from? ("norm" and "trace") I see that the first one is similar to calculating the norm of a complex number, but there's no $i$ in it, so why does it still work similarly to complex conjugates? And why is the norm subtracted instead of divided out? Why is it the trace which is divided out instead? The trick is really nice, but it would be nicer if you explained why does this magic work so well.
– SasQ
Commented Dec 14, 2014 at 22:29
• Oh, and one thing you wrote is a bit misleading: You put this in a way suggesting that one has to divide by the trace of the original square-rooted number ($w$), but when I tried this, it didn't work. One has to divide out by the trace of the partial answer obtained along the way instead, which is not the original $w$, but $w - \sqrt{norm}$.
– SasQ
Commented Dec 14, 2014 at 22:32
• Even if you link to the source, I think it's bad practice to just copy and paste someone else's answer... Commented Sep 30, 2018 at 13:41
Note that $27=5^2+\sqrt2^2$ and $10\sqrt2=2\times5\times\sqrt2$
Hint: Compare the squares of both expressions.
Notice that \begin{align}27-10\sqrt{2} & = 25 - 2\cdot 5\sqrt{2} + 2 \\ & = 5^2 - 2\cdot5\sqrt2 + \left(\sqrt2\right)^2\\ & = \left(5 - \sqrt 2\right)^2 \end{align}
I don't know any way to notice this except to just get lucky and notice it; I didn't realize it could happen until sometime in high school when I was astounded to discover that $\sqrt{7+4\sqrt3} = 2+\sqrt3$.
Set the nested radical as the difference of two square roots so that $$\sqrt{27-10\sqrt{2}}=(\sqrt{a}-\sqrt{b})$$ Then square both sides so that $$27-10\sqrt{2}=a-2\sqrt{a}\sqrt{b}+b$$ Set (1) $$a+b=27$$ and set (2) $$-2\sqrt{a}\sqrt{b}=-10\sqrt{2}$$ Square both sides of (2) to get $$4ab= 200$$ and solve for $b$ to get $$b=\frac{50}{a}$$ Replacing $b$ in (1) gives $$a+\frac{50}{a}=27$$ Multiply all terms by $a$ and convert to the quadratic equation $$a^2-27a+50=0$$ Solving the quadratic gives $a=25$ or $a=2$. Replacing $a$ and $b$ in the first difference of square roots formula above with $25$ and $2$ the solutions to the quadratic we have $$\sqrt{25}-\sqrt{2}$$ or $$5-\sqrt{2}$$
• What if the solutions to the quadratic were also irrational, so that $a$ and $b$ become nested inside their radicals again? Or is this possibility somehow excluded?
– SasQ
Commented Dec 14, 2014 at 22:22
$$\sqrt{27 - 10\sqrt{2}}$$ $$= \sqrt{25 + 2 - 2.5.\sqrt{2}}$$ $$= \sqrt{5^{2} - 2.5.\sqrt{2} +{\sqrt{2}}^2}$$ $$= \sqrt{{(5 - \sqrt{2})}^2}$$
$$= (5 - \sqrt{2})$$ $$= R.H.S$$
• You need equals signs rather than arrows. I would have written something similar as $$\sqrt{27-10\sqrt{2}} = \sqrt{27-2\sqrt{ 25 \times 2}} = \sqrt{25-2\sqrt{ 25 }\sqrt{2} +2} = \sqrt{(\sqrt{25} - \sqrt{2})^2}$$ Commented Mar 14, 2013 at 8:51
• @Henry: Thanks corrected. Its been ages I am solving some math problem Commented Mar 14, 2013 at 9:13
• But then you have to "guess" how to split that $27$.
– SasQ
Commented Dec 14, 2014 at 22:23<|endoftext|>
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Multiplying and Dividing Real Numbers Objective: To multiply and divide real numbers.
Presentation on theme: "Multiplying and Dividing Real Numbers Objective: To multiply and divide real numbers."— Presentation transcript:
Multiplying and Dividing Real Numbers Objective: To multiply and divide real numbers.
Essential Understanding The rules for multiplying real numbers are related to the properties of real numbers and the definitions of operations.
Essential Understanding The rules for multiplying real numbers are related to the properties of real numbers and the definitions of operations. The product of two positive numbers is positive. The product of two negative numbers is positive. The product of a positive and a negative is negative.
Problem 1 Find each product. 12(-8) = -96 24(0.5) = 12
Problem 2 Simplify each square root.
Problem 4 Divide the following fractions.
Class Work Page 42 8-18 even
Homework Page 42 9-47 odd
The Distributive Property Let a, b, and c be real numbers. a(b+c) = ab + ac (b+c)a = ba + ca a(b – c) = ab – ac (b – c )a = ba - ca
Problem 1 3(x + 8) = 3x + 24 (5b – 4)(-7) = -35b + 28
Got it? a)5(x + 7) b) c)
Got it? a)5(x + 7) = 5x + 35 b) c)
Got it? a)5(x + 7) = 5x + 35 b) c)
Got it? a)5(x + 7) = 5x + 35 b) c)
Problem 2 What sum or difference does this represent?
Problem 2 What sum or difference does this represent?
Got it? What sum or difference does each expression represent?
Got it? What sum or difference does each expression represent?
Got it? What sum or difference does each expression represent?
Got it? What sum or difference does each expression represent?
Problem 3 What is the simplified form of ?
Problem 3 What is the simplified form of ? Distribute the negative to both terms.
Got it? What is the simplified form of each expression?
Got it? What is the simplified form of each expression?
Like Terms You can simplify an algebraic expression by combining the parts of the expression that are alike.
Like Terms You can simplify an algebraic expression by combining the parts of the expression that are alike. Term- A number, variable, or the product of a number and one or more variables.
Like Terms You can simplify an algebraic expression by combining the parts of the expression that are alike. Term- A number, variable, or the product of a number and one or more variables. Constant- A term that has no variable.
Like Terms You can simplify an algebraic expression by combining the parts of the expression that are alike. Term- A number, variable, or the product of a number and one or more variables. Constant- A term that has no variable. Coefficient- A numerical factor of a term.
Like Terms You can simplify an algebraic expression by combining the parts of the expression that are alike. Term- A number, variable, or the product of a number and one or more variables. Constant- A term that has no variable. Coefficient- A numerical factor of a term. Like terms have the same variable factors.
Problem 5 Combine like terms.
Problem 5 Combine like terms.
Problem 5 Combine like terms.
Got it? Simplify by combining like terms.
Got it? Simplify by combining like terms.
Homework Page 50 9-63 odd
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The study of STEM (Science, Technology, Engineering, and Math) is vital for all 21st-century kids. When you consider that probably over half of the children today will be doing jobs that are not even invented yet, as a parent, you need to make sure they are fully up-to-speed with all the latest tech. They need to have all the right skills as well.
Your children can do all these by studying STEM. STEM will equip them with the tools they will need to build an exciting future for themselves.
It’s never too early to start fostering a love of STEM; even the youngest of children can benefit from taking part in some STEM activities. The extra-curricular study of STEM can vastly improve your children’s problem-solving skills and give them a better understanding of the world around them. It can also open a wider area of incredible career opportunities and boost their school grades.
Putting your children in a different setting, away from the pressures of their normal classroom environment, can work wonders by sparking new interests in STEM. STEM summer camps are perfect for this: children see them as recreational. In addition, these camps provide kids with many hands-on activities which will help them to forget any preconceptions they may have had about ‘hating math’ or ‘being rubbish at science’.
Summer camps also allow your children access to new inspirational, technological tools that they may not have had a chance to use at school. Teachers will also possess a high degree of specialism, putting them in the perfect position to inform and inspire your kids.
In the camp environment, the emphasis is on hands-on. If your children love to experiment, takes things apart and put them back together, STEM courses are perfect. They will leave camp with a much deeper, more practical knowledge of how machines and technology work.
Recommended STEM Summer Camps for Kids
Here are three particularly awesome STEM summer camp activities that are virtually guaranteed to foster a lifelong love of the subject:
Nothing is more futuristic than robots so the chance to study robotics is bound to wow your child.
Under robotics, kids will have the chance to design, build, and program a robot. This is usually a collaborative process so your children’s social skills will also be developed, alongside their tech skills.
Robotics is closely linked with subjects such as mechanical engineering, electronics, and software programming. As such, so they will finish camp with a broad range of skills they can apply to other areas of their learning too.
The future demand for graduates with advanced coding skills is certain, so giving your kids the chance to have fun with coding this summer could be setting them up for an incredible career later on.
Coding involves instructing computers to perform functions using computer-based languages. At one end of the spectrum, incredibly advanced coding controls every electronic device in existence: from sat-nav systems to smartphones. However, even young children can learn basic code and coding is rapidly being adopted into national curriculums across the globe.
Coding is brilliant for developing problem-solving skills. To complete tasks successfully, kids will need to learn to troubleshoot, or ‘debug’ in coding terms. This skill can have a significant impact on their performance across the curriculum.
Coding activities at summer camp are guaranteed to have fun at their core for all ages, with lots of emphasis on games and fun app development.
3. 3D Printing
3D printing technology has recently become much more widely available and talked about, so your kid will be delighted to have the opportunity to take part in hands-on 3D printing activities.
Kids typically learn to create a model using the specially-designed software. Additionally, they will know how to prepare and troubleshoot ready for printing and to print and evaluate their creation. There are crossover links with all areas of the curriculum, from art to engineering.
3D printing at camp is a great chance for kids to fire up their imagination and to create something to take home and be proud of.
With the variety of STEM summer camps your kids can choose from, they will learn, have fun and be fully prepared to excel in this field in the future.
Maloy Burman is the Chief Executive Officer and Managing Director of Premier Genie FZ LLC. He is responsible for driving Premier Genie into a leadership position in STEM (Science, Technology, Engineering and Mathematics) Education space in Asia, Middle East and Africa and building a solid brand value. Premier Genie is currently running 5 centers in Dubai and 5 centers in India with a goal to multiply that over the next 5 years.<|endoftext|>
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Revision Notes: Relations & Functions
# Relations and Functions Class 11 Notes Maths Chapter 2
## Mathematics (Maths) for JEE Main & Advanced
209 videos|443 docs|143 tests
## FAQs on Relations and Functions Class 11 Notes Maths Chapter 2
1. What is the difference between a relation and a function?
Ans. A relation is a set of ordered pairs, while a function is a special type of relation where each element in the domain is associated with exactly one element in the range. In other words, every input (domain) value in a function corresponds to a unique output (range) value.
2. How can you determine if a relation is a function?
Ans. To determine if a relation is a function, you can use the vertical line test. If a vertical line intersects the graph of the relation at more than one point, then it is not a function. However, if no vertical line intersects the graph at more than one point, then the relation is a function.
3. Can a function have more than one output for a single input?
Ans. No, a function cannot have more than one output for a single input. In a function, each input value must be associated with only one output value. If an input value is associated with multiple output values, then it violates the definition of a function.
4. What is the domain and range of a function?
Ans. The domain of a function is the set of all possible input values for the function. It represents the values for which the function is defined. The range of a function is the set of all possible output values that the function can produce. It represents the values that the function can take on.
5. How can you represent a function algebraically?
Ans. A function can be represented algebraically using an equation or a formula. For example, if we have a function f(x), we can represent it as f(x) = 2x + 3, where 2x + 3 is the formula that relates the input values (x) to the output values (f(x)). This algebraic representation allows us to calculate the value of the function for different input values.
## Mathematics (Maths) for JEE Main & Advanced
209 videos|443 docs|143 tests
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A team of scientists has created a new model explaining the origin of Saturn's rings: their hypotheses were theorized based on a series of computer simulations.
The results are applicable to the rings of other giant planets as well, explaining the particular phenomenon of compositional differences between the rings of Saturn and Uranus.
The study was published in the online journal Icarus on Oct. 6.
The giant planets inside our solar system have very different rings from each other. Based on the results of observations so far, Saturn's rings are made of more than 95 percent icy particles, while Uranus' and Neptune's have darker rings, which could be explained through a higher rock content.
The first time the rings of Saturn were observed was back in the 17th century; since then, generations of astronomers have tried to understand the rings' properties and origins. However, despite the evolution in observational methods, the probes and the visual data, little was known about the rings' origin until recently.
The current research was aimed at understanding the Late Heavy Bombardment period, which is believed to have happened approximately 4.1 to 3.8 billion years back. The period is also known as lunar cataclysm, and it's an event during which an extraordinary number of asteroids are theorized to have collided with the early planets in our solar system. Mercury, Venus, Earth and Mars are the ones that, it is believed, were most affected during the period.
The study takes this orbital migration theory and contextualizes it. It is believed that a large number of celestial objects, roughly the size of Pluto, existed beyond Neptune's location. The scientists discovered that Saturn, Uranus and Neptune had close encounters with the objects many times during that period, suggesting that it was possible for them to have destroyed the large objects through their tidal force.
Then, computer simulations recreated the disruptions of the objects, and their results depended on a series of initial conditions, among which the minimum approach distance to the planet. What the study discovered is that up to 10 percent of the mass of the Kuiper belt objects was captured into orbits around the planet, which would further explain the rings around the two giant planets.
The model serves as a good explanation for the compositional difference between the rings of the two planets. Provided the Kuiper objects were to have layered structures, each of the planets captured a distinct layer.
The discovery comes after Saturn's moon, Titan, was found to have an impossible cloud, making it the most Earth-like world we have encountered until now, according to NASA.<|endoftext|>
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Sun January 24th, 2016
When satellite imagery of the Brazilian rainforest shows lush, dense forests, most of us likely expect that those trees are packed with wildlife. But what if what we are actually seeing is an empty forest?
According to a recent study published in Conservation Letters, this possibility is already becoming a reality in the pre-frontier areas of Amazonia in Brazil — defined as municipalities with over 90 percent of their original forest cover still intact.
Where are the animals going? Many are being eaten by city dwellers.
Native species are at risk of becoming endangered, or even going extinct, as a result of over-hunting due to the prevalence of bushmeat consumption in the pre-frontier Brazilian Amazon, say the researchers. “Rapid growth of cities and inadequate resources to deter illegal consumption in this urbanized wilderness,” is the crux of the problem.
“A representative survey of two pre-frontier cities indicated that virtually all urban households consume wildlife, including fish (99%), bushmeat (mammals and birds; 79%), chelonians (48%) and caimans (28%) — alarming evidence of an underreported wild-meat crisis in the heart of Amazonia,” write UK researcher Luke Parry, and Brazilian researchers, Jos Barlow and Heloisa Pereira.
The paper proposes several solutions to curb the problem: “Innovative environmental governance could limit wildlife consumption to only harvest-tolerant species,” with decision-makers implementing policies and strategies “that promote poverty alleviation and supply poor city dwellers with affordable alternatives to eating wildlife.”
Tropical forests contain high levels of biodiversity and house countless endangered species. As urbanization of the Brazilian Amazon has increased over time, many environmentalists assumed that over-hunting of wildlife would decline. However, research has shown that many rainforest wildlife species continue to decline due to hunting, and that city-dwellers commonly incorporate these species into their diet.
One reason for this is poverty: Throughout the world, bushmeat consumption has been linked to lack of income, because hunting is a less expensive and time-consuming way to obtain food than keeping domestic livestock or fish, which also can’t easily be raised in urban areas. Poverty is widespread in the urban cities of the Brazilian Amazon, which likely explains the ongoing consumption of native wildlife.
Parry and his team set out to gain some insight into urban eating habits in regard to bushmeat by surveying two cities in Amazonas State, Brazil: Borba and Novo Aripuana. They distributed questionnaires to 153 households that asked questions delineating socioeconomic factors as well as wildlife consumption habits in the previous year. They also engaged the households in games to clearly show their food preferences.
The results found that bushmeat consumption is definitely not in decline in these urban settings. According to the study, about half of urban households in the two cities eat bushmeat at least once per month, and nearly 80% of urban households had eaten bushmeat in the last year.
That’s not to say that all rainforest species are threatened equally by hunting. The study showed that the consumption practices varied greatly among different animals, and largely depended on taste preferences. Whereas 99% of households had consumed fish in the last year, only 28% had eaten caiman, for example.
“Tapir and white-lipped peccary, both large-bodied ungulates, are widely consumed in Amazonian cities and perhaps are favored by hunters due to their size (lots of meat) and by consumers for their taste… [whereas] urban demand for consuming monkeys is relatively limited,” Parry told Mongabay.
There was also a great disparity in the types of families doing the consuming. Parry and his team found that wildlife consumption is inherently linked to economic status, with impoverished families doing significantly more fishing and hunting than wealthier families.
Now that the scale of the problem has been identified, Parry and his team are proposing solutions. Most significantly, they urge that environmental regulations and enforcement be put in place to limit consumption to more harvest-tolerant species. This would help protect threatened species. Furthermore, impoverished city-dwellers need to be offered affordable dietary alternatives to bushmeat, and be provided with real opportunities for poverty alleviation.
Though the reduction of wildlife consumption in the Amazon is a large undertaking, it is crucial to maintaining biodiversity in the region, says Parry. “Developing solutions to defaunation is essential in order to prevent extinctions, maintain the integrity of ecosystems and, equally important, maintain the livelihoods of resource harvesters and the well-being and food security of consumers.”
– This report was originally published in Mongabay and is republished by an agreement to share content.<|endoftext|>
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What is Fair Housing Act
The Fair Housing Act is a law that prohibits discrimination in the buying, selling, renting or financing of housing. This includes discrimination based on race, skin color, sex, nationality, religion, disability and children or any other characteristics from a protected class.
3 Most Important Factors In Buying A Home
BREAKING DOWN Fair Housing Act
The Fair Housing Act is also known as Title VIII of the Civil Rights Act of 1968. It guarantees protection from discrimination on the part of any party involved in a real estate transaction. That includes landlords, realtors, sellers, government entities, insurers, or any other person or company that may have an influence in the decision-making process. It prevents them from using any portion of a persons protected class to deny them the ability to obtain housing. It further stipulates that all decisions for housing should be based off a person’s credit worthiness.
The U.S. Department of Housing and Urban Development is the primary enforcer of the Fair Housing Act. The Department of Housing and Urban Development website can provide additional information about what constitutes discrimination and how to proceed if a person feels that their inclusion in a protected class somehow negatively influenced a decision.
The Civil Rights Act of 1964 paved the way for this legislation. The Civil Rights Act was in direct response to changes in the racial and social structure of the United States at the time.
What is creditworthiness
Creditworthiness is determined by reviewing several different factors such as income, debts, assets and credit score. Depending on the type of credit the borrower is applying for, different factors will be given different weight.
For instance, a mortgage company will review income as it compares to debts, credit score and the condition of the property that a borrower is looking to finance. An auto lender may look at the same qualities, but instead of looking at the condition of a property, they would instead review the automobile that the borrower was looking to secure the loan against.
A credit card company may decide that they only need consider a borrower’s credit report. If a borrower has a long history of making their payments on time and keeping their credit extensions low, a credit card company may issue the borrower a credit card without verifying income or available assets.
Some lenders have programs for well-qualified borrowers, using only their credit report to verify their creditworthiness.<|endoftext|>
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A box contains cards bearing numbers 6 to 70.
Question:
A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears
(i) a one-digit number,
(ii) a number divisible by 5,
(iii) an odd number less than 30,
(iv) a composite number between 50 and 70.
Solution:
Given number 6, 7, 8, .... , 70 form an AP with a = 6 and d = 1.
Let Tn = 70. Then,
6 + (n − 1)1 = 70
⇒ 6 + n − 1 = 70
⇒ n = 65
Thus, total number of outcomes = 65.
(i) Let E1 be the event of getting a one-digit number.
Out of these numbers, one-digit numbers are 6, 7, 8 and 9.
Number of favourable outcomes = 4.
$\therefore P$ (getting a one-digit number) $=P\left(E_{1}\right)=\frac{\text { Number of outcomes favourable to } E_{1}}{\text { Number of all possible outcomes }}$
$=\frac{4}{65}$
Thus, the probability that the card bears a one-digit number is $\frac{4}{65}$.
(ii) Let E2 be the event of getting a number divisible by 5.
Out of these numbers, numbers divisible by 5 are 10, 15, 20, ... , 70.
Given number 10, 15, 20, .... , 70 form an AP with a = 10 and d = 5.
Let Tn = 70. Then,
10 + (n − 1)5 = 70
⇒ 10 + 5n − 5 = 70
⇒ 5n = 65
⇒ n = 13
Thus, number of favourable outcomes = 13.
$\therefore \mathrm{P}$ (getting a number divisible by 5$)=\mathrm{P}\left(\mathrm{E}_{2}\right)=\frac{\text { Number of outcomes favourable to } \mathrm{E}_{2}}{\text { Number of all possible outcomes }}$
$=\frac{13}{65}=\frac{1}{5}$
Thus, the probability that the card bears a number divisible by 5 is $\frac{1}{5}$.
(iii) Let E3 be the event of getting an odd number less than 30.
Out of these numbers, odd numbers less than 30 are 7, 9, 11, ... , 29.
Given number 7, 9, 11, .... , 29 form an AP with a = 7 and d = 2.
Let Tn = 29. Then,
7 + (n − 1)2 = 29
⇒ 7 + 2n − 2 = 29
⇒ 2n = 24
⇒ n = 12
Thus, number of favourable outcomes = 12.
$\therefore P($ getting an odd number less than 30$)=P\left(E_{3}\right)=\frac{\text { Number of outcomes favourable to } E_{3}}{\text { Number of all possible outcomes }}$
$=\frac{12}{65}$
Thus, the probability that the card bears an odd number less than 30 is $\frac{12}{65}$.
(iv) Let E4 be the event of getting a composite number between 50 and 70.
Out of these numbers, composite numbers between 50 and 70 are 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68 and 69.
Number of favourable outcomes = 15.
$\therefore P($ getting a composite number between 50 and 70$)=P\left(E_{4}\right)=\frac{\text { Number of outcomes favourable to } E_{4}}{\text { Number of all possible outcomes }}$
$=\frac{15}{65}=\frac{3}{13}$
Thus, the probability that the card bears a composite number between 50 and 70 is $\frac{3}{13}$.<|endoftext|>
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By Md. Arfanuzzaman, BCAS
In Bangladesh, nearly 2.5 billion tonnes of sediment flow through three mighty rivers—the Ganges, the Brahmaputra and the Meghna—each year. All three rivers deposit portions of the sediment flowing through their waters along their respective riverbeds. Over the years, the accumulation of these deposits has resulted in the creation of many shoals or river islands in the river basin areas. These river islands are known as ‘char’ in Bengali. Home to more than 600,000 dwellers, Bangladesh’s many chars are prone to severe erosion and floods. Every year, chars are submerged by their surrounding waters because of the respective rivers’ hydromorphological dynamics. Consequently, the lives and livelihoods of char inhabitants are subject to a variety of stresses that make them socio-economically vulnerable. The Teesta River, a study basin for the HI-AWARE initiative, and also a sub-basin of the mighty Brahmaputra river system, consists of a number of chars in the north-western region of Bangladesh, specifically in the Lalmonirhat, Nilphamari, Kurigram, Rangpur,and Gaibandha districts.
Flooding during the monsoon, and dryness in the pre- and post- monsoon seasons, are common phenomena in the chars of the Teesta basin. Affected chars include Gonai, Bishawnath, Dushmara, Mahimpara, Najirdahand and Jharshinghershor. In the monsoon, when water levels in the rivers rise and flash floods occur, char inhabitants have to take shelter on others’ lands and embankments. When they come to the mainland or their corresponding embankments, they face many problems including those of food, water, sanitation, and energy. They lose the crops they planted on their agricultural land and often don’t find space to shelter their livestock in the areas in which they have shifted. They return to their own char land when the water levels go down. Sometimes, it takes several years for river water levels to go down enough for plots of char land to emerge and become habitable again. In such cases, the respective char inhabitants lose their homes and agricultural lands.
As the incidence of floods and flash floods increases, the agricultural vulnerability of these areas also increases. Floods bring sand, not silt, with them. Sand, once deposited on chars, causes these lands to become barren. Sand deposition reduces soil moisture and degrades the land system. As such deposits increase, more cultivable lands are rendered infertile. This has made farming most challenging in the shoals. Such loss of cultivable land puts the agriculture and livelihoods of entire char communities at risk and pushes them into extreme poverty.
The fact that the Teesta runs dry during the pre- and post- monsoon seasons each year fuels water scarcity in the char regions and restricts the livelihood options available to its inhabitants. Due to the unavailability of river-dependent livelihood options such as fishing and boating, agriculture has emerged as a major means of earning a living. Char communities need to survive and sustain through agriculture as they live through a series of extreme events—floods, droughts, storms, hail storms, char erosion, erratic rainfall, cold waves and climate variability—which obstruct their lives and livelihood practices. Abulkalam Azad, 33, a landless farmer from the Koshimbari village in the Dahagram union says, “The Teesta River has become unpredictable. It is as if it has lost its youth. Flash floods and river erosion have become very common these days.”
Char inhabitants such as Azad live below the poverty line and are forced to live through challenging situations, working hard as they struggle to cope and changing strategies to ensure their survival. Five years ago, most inhabitants cultivated pumpkin on the sandy and loamy soil of their chars. But the market for pumpkins was not good which meant the returns were insignificant. Char farmers have now switched to cultivating maize, peanut, onion and potato, crops that offer them better profit margins. Even the high-yield Boro rice crop has been replaced by maize as sand deposition on chars has made growing Boro unfeasible.
Ten years ago, sand deposition drastically hindered crop cultivation on chars. It was very difficult to grow staples on such barren and degraded land. Today, the persistent endeavours of the people who farm them have made crop cultivation on such sandy, infertile land possible. As a result, the white sandy grounds have turned green. In this regard, the director of the Department of Agriculture Extension (DAE) of Kaunia Upazila says, “The char people are very hard working. They never wait for anyone’s help. They employ one strategy after another until they find one that works best.”
Extreme climate events such as floods, river bank erosion, drought and cold waves often hinder the optimum production of crops on chars. Local farmers say that new varieties of insects attack agricultural crops during droughts and cold waves. Crops grow slowly during cold waves. These days, char farmers have taken to using anti-cold sprays to protect their crop from the fog and are using nets to fence in their plants for the same reason. A good number of char inhabitants now have shallow tube wells to extract ground water irrigation as well. Those who don’t have such an alternative rent irrigation water from others to cultivate their crops. This increases the cost of production but the excess cost can be compensated for if there is a bumper harvest. Char erosion is also a great concern for the people here as it adds to their vulnerability. Lack of improved sanitation, nutrition, education, health care, formal credit, good communication and electricity remain barriers to the socio-economic development of char communities.
Although the conditions char communities live in need drastic improvement, some good things are happening on Bangladesh’s river islands. Governmental and non-governmental organisations are working to assist char inhabitants. Their projects include the introduction of improved agricultural methods and techniques that in turn increase production, efficiency and income. Sanitation has also improved relatively in char habitations and more flood-resilient housing practices are being adopted than in the past. There are NGOs that help locals acquire agricultural credit, livestock, improved seeds and technical support. The DAE has is involved in the dissemination of knowledge, technology, farming techniques, methods, ideas and other useful information. In the recent past, the DAE has run demonstration projects related to vermicomposting, Integrated Crop Management (ICM), Integrated Pest Management (IPM) and Farmer Clubs for Sustainable Agricultural Practice in char areas. Here, IPM has emerged as a sustainable approach to managing pests and crops by combining cultural, biological, genetic, mechanical and chemical methods in a way that minimises economic, health, and environmental risks. Facilities such as these are, however, limited and not as yet available to people living in hard-to-reach areas. Char residents in such places are hence more vulnerable to the impacts of climate change.
Regardless of all the climatic and non-climatic vulnerabilities, the char inhabitants of Bangladesh are optimistic. Whatever disaster they may have to live through, they do not want to leave their chars as they don’t want to live on land that belongs to other people. To us, floods may be disasters but to char communities, floods can be a mixed blessing. Floods help revive soil fertility, reduce land degradation, boost crop production and increase the total land area of chars.
No hazard will stop the hard-working people of Bangladesh’s chars from struggling for their survival. They are brave and determined to sustain themselves. They are determined about cultivating food for themselves and for their nation regardless of the extremities they face. They do so with the help of knowledge that has been passed on to them by their ancestors and with the help of the knowledge they have gained through their own experience. Sometimes, a bumper harvest paradoxically results in lower market prices for their crops, and weak supply chains and poor communications systems impede full access to better markets. Yet the people of the chars endure. They carry on farming and sustaining as they have for generations.<|endoftext|>
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Question
# The consecutive digits of a three digit number are in G.P. If the middle digit is increased by 2 then they form an A.P. If 792 is subtracted from this number then we get the number consisting of the same three digits but in reverse order. Find the number.
Hint: Firstly assume the digits to be $a,ar,a{{r}^{2}}$after that you can apply the conditions accordingly. Use the formula of A.P. given by If a,b,c are in A.P. then , $b=\dfrac{a+c}{2}$ so that you will get a simpler equation. After that use the last condition and solve it to find ‘r’ and on further solving you will get ‘a’.
To solve the given problem we have to assume the digits and as they are in G.P. therefore we have the standard consecutive numbers to be assumed which are given by,
Therefore the three consecutive digits of the number are given by,
$a,ar,a{{r}^{2}}$ …………………………………………… (1)
Where, ‘a’ is the first term and ’r’ is the common ratio of G.P.
$100a+10ar+a{{r}^{2}}$
If we take ‘a’ as common we will get,
$a\left( 100+10r+{{r}^{2}} \right)$ …………………………….. (2)
As given in the problem if the middle digit is increased by 2 then it will form an A.P.
Therefore,
$a,ar+2,a{{r}^{2}}$ form an A.P.
To proceed further we should know the formula given below,
Formula:
If a,b,c are in A.P. then , $b=\dfrac{a+c}{2}$.
By using the formula we can write,
$ar+2=\dfrac{a+a{{r}^{2}}}{2}$
$\therefore 2\left( ar+2 \right)=a+a{{r}^{2}}$
$\therefore 2ar+4=a+a{{r}^{2}}$
$\therefore 4=a{{r}^{2}}-2ar+a$
By taking ‘a’ common we will get,
$\therefore 4=a\left( {{r}^{2}}-2r+1 \right)$
To proceed further in the solution we should know the formula given below,
Formula:
${{\left( a-b \right)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}$
By using the above formula we can write,
$\therefore 4=a{{\left( r-1 \right)}^{2}}$
By rearranging the above equation we will get,
$\therefore a{{\left( r-1 \right)}^{2}}=4$ …………………………………….. (3)
To proceed further we should write the number in reverse order therefore, from equation (1) we can write the number in reverse order as,
$100a{{r}^{2}}+10ar+a$
By taking ‘a’ common we will get,
$a\left( 100{{r}^{2}}+10r+1 \right)$ ………………………………. (4)
Now, by using the second condition given in the problem and using equation (2) and equation (4), we will get,
$a\left( 100+10r+{{r}^{2}} \right)-792=a\left( 100{{r}^{2}}+10r+1 \right)$
By taking 792 on the right side of the equation and reverse order number on the left hand side of the equation we will get
$a\left( 100+10r+{{r}^{2}} \right)-a\left( 100{{r}^{2}}+10r+1 \right)=792$
By taking ‘a’ common we will get,
$a\left[ \left( 100+10r+{{r}^{2}} \right)-\left( 100{{r}^{2}}+10r+1 \right) \right]=792$
By opening the parenthesis we will get,
$\therefore a\left[ 100+10r+{{r}^{2}}-100{{r}^{2}}-10r-1 \right]=792$
$\therefore a\left[ 100+{{r}^{2}}-100{{r}^{2}}-1 \right]=792$
$\therefore a\left[ 99-99{{r}^{2}} \right]=792$
By taking 99 common we will get,
$\therefore 99a\left[ 1-{{r}^{2}} \right]=792$
$\therefore a\left[ 1-{{r}^{2}} \right]=\dfrac{792}{99}$
Dividing by 9 to numerator and denominator on the right hand side of the equation we will get,
$\therefore a\left[ 1-{{r}^{2}} \right]=\dfrac{88}{11}$
$\therefore a\left[ 1-{{r}^{2}} \right]=8$
Dividing above equation by equation (3) we will get,
$\therefore \dfrac{a\left( 1-{{r}^{2}} \right)}{a{{\left( r-1 \right)}^{2}}}=\dfrac{8}{4}$
$\therefore \dfrac{\left( 1-{{r}^{2}} \right)}{{{\left( r-1 \right)}^{2}}}=2$
By taking -1 common from denominator of left hand side of the equation we will get,
$\therefore \dfrac{\left( 1-{{r}^{2}} \right)}{{{\left[ -1\left( 1-r \right) \right]}^{2}}}=2$
$\therefore \dfrac{\left( 1-{{r}^{2}} \right)}{{{\left( 1-r \right)}^{2}}}=2$
To proceed further we should know the formula given below,
Formula:
${{a}^{2}}-{{b}^{2}}=\left( a+b \right)\times \left( a-b \right)$
By using above formula we will get,
$\therefore \dfrac{\left( 1-r \right)\left( 1+r \right)}{{{\left( 1-r \right)}^{2}}}=2$
$\therefore \dfrac{\left( 1+r \right)}{\left( 1-r \right)}=2$
$\therefore \left( 1+r \right)=2\left( 1-r \right)$
$\therefore \left( 1+r \right)=2-2r$
$\therefore r+2r=2-1$
$\therefore 3r=1$
$\therefore r=\dfrac{1}{3}$ …………………………………………… (5)
By substituting the value of equation (5) in equation (3) we will get,
$\therefore a{{\left( \dfrac{1}{3}-1 \right)}^{2}}=4$
$\therefore a{{\left( \dfrac{1-3}{3} \right)}^{2}}=4$
$\therefore a{{\left( \dfrac{-2}{3} \right)}^{2}}=4$
$\therefore a\times \dfrac{4}{9}=4$
$\therefore a=4\times \dfrac{9}{4}$
$\therefore a=9$ …………………………………………. (6)
Now if we put the values of equation (5) and equation (6) in equation (2) we will get,
$\therefore$The required number $=a\left( 100+10r+{{r}^{2}} \right)$
$\therefore$The required number $=9\times \left[ 100+10\times \left( \dfrac{1}{3} \right)+{{\left( \dfrac{1}{3} \right)}^{2}} \right]$
$\therefore$The required number $=9\times 100+9\times 10\times \left( \dfrac{1}{3} \right)+9\times {{\left( \dfrac{1}{3} \right)}^{2}}$
$\therefore$The required number $=900+3\times 10\ +9\times \dfrac{1}{9}$
$\therefore$The required number $=900+30+1$
$\therefore$The required number $=931$
Therefore the number which satisfies all the conditions given in the problem is 931.
Note: Don’t assume the digits to be $\dfrac{a}{r},a,ar$, as it will become very much difficult for calculation, it will be better if we use the digits as$a,ar,a{{r}^{2}}$, as it will save your time in solving which is beneficial in competitive exams.<|endoftext|>
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WAYS OF KNOWINg: FAITH
In some contexts, Faith is simply belief without evidence. But this is only a starting point. Faith has two primary meanings. It can be used as a synonym for trust in the secular world, and notably, in a more dogmatic sense, for all-or-nothing belief in, and personal commitment to God or Allah, that is central to most denominations of Christianity and Islam respectively. This is a good example of the polysemy of language.
Students will recall the class activity where different uses of opinion and belief were explored in some detail. This unit is well worth reviewing with students before approaching the class activity below.
Wittgenstein's famous "beetle in a box analogy" provides further insight. It goes some way to finding a cure for confusing private and shared meanings of words.
The class activity is very simple. Arrange students in groups of four and ask them to pinpoint the role of faith/trust in the eight TOK Areas of Knowledge. Also task them to share one real, personal narrative of having faith (or trust) in someone, or something, from their everyday lives.
Groups should appoint a facilitator, two reporters and a scribe. The scribe should capture highlights of the thinking in bullet point notes on the following table. Poetic (or pithy) titles should be formulated collaboratively, and recorded, for each of the personal anecdotes. Allow a timed 15 minutes for the activity.
While the students are working, in preparation for some whole class discussion, divide the white board up into 8 sectors and label them with the Areas of Knowledge. Ensure that you have sufficient colored working marker pens on hand for each group.
Printable pdf. of the table.
After calling the class to order, break the ice by asking a reporter from each group to relate the most compelling personal story that was heard in their group. Insist on starting with the pithy title. Allow clarification questions, and candid responses from the original authors of the stories.
Next, ask the remaining nominated reporter from each group should come to the board and transcribe their bullet points in the Areas of Knowledge sectors. The teacher should erase any duplicates; and then unleash some whole group discussion; encompassing at least one salient example from each Area of Knowledge.
Allow students to take a short break and move around for a few minutes.
Finish the session by changing the frame. Show the Jonestown video and click through the slideshow. Ask a student with some oratory talent to read aloud the Scientific Fundamentalism quote from the New Scientist.
Trust students to make their own connections between the class activity and the stimulus material. Then, after a pause, Discombobulate them with the following Knowledge Question:
- To what extent is faith/trust in strong, charismatic leaders always a negative thing? Justify your thinking with specific examples.
This Knowledge question could be addressed in a whole class discussion and/or assigned as a written assignment.
JONESTOWN MASS SUICIDE: A CAUTIONARY TALE
The Peoples Temple Agricultural Project, or "Jonestown," was a cult settlement in rural Guyana under the messianic leadership of Jim Jones. In November 1978, Jones led his followers in a "revolutionary” mass suicide. 918 died, almost a third were children.<|endoftext|>
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Experiment shows dogs can see colors, not just black and white
Russian scientists say they've shown dogs can differentiate colors, contradicting a long-held assumption they're only able to see in black and white.
For much of history, it has been believed dogs' ability to differentiate between different colored objects was actually due to differences in brightness, not the actual color.
Recent research showing dogs have two types of cones in their eyes led scientists at the Institute for Information Transmission Problems of the Russia Academy of Sciences to suspect they could distinguish colors.
Humans have three kinds of cones, which allows for seeing all three primary colors.
With only two, dogs should be able to see some colors, but not others, the researchers thought -- blues, greens and yellows, for example, but not reds or oranges -- and they designed an experiment to test that.
First they trained several dogs to respond to one of four different colored pieces of paper, light or dark yellow and light or dark blue, by putting paper pairs in front of feed boxes that contained meat.
The dogs soon learned that certain colors meant a treat.
Next, the researchers placed pieces of paper with the color the dogs had been taught to respond to in front of a feed box, along with another piece of paper that was brighter, but of a different color, to see if a dog trained to respond to light blue would respond to dark blue instead of light yellow.
A majority of the dogs went for the color identifier rather than brightness identifier most of the time, the scientists said, proving they were able to distinguish color and were not relying on brightness difference to find their food treat.
The research was reported in the Proceedings of the Royal Society B.<|endoftext|>
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In the last 30 years, obesity has doubled in children and nearly quadrupled in adolescents, with the U.S. having the highest rate in the world. Physical activity is essential for a child’s cardiovascular endurance, strength, and bone health. As such, parents are often curious as to how much is too much when it comes to physical activities for their kids.
Many child fitness experts as well as The Center for Disease Control (CDC) currently recommend 60 minutes per day of physical activity for children ages 7 to 12. Normally, kids are good about regulating their physical activity; they’ll stop when they become tired. Over-exercising in children is often a result of being pushed to keep going by an adult.
Remember, simply asking a child if they’ve had enough of a certain activity is not always effective, though, as children often like to impress coaches and parents and will say they can keep going even if they can’t.
Generally, if a child appears they’re no longer interested or having fun it’s time to stop the activity.
Children who over-exercise face the same injuries or risks as adults such as: over-use and repetitive motion injuries, heat exhaustion. or joint injuries due to fatigue. Another often overlooked problem is burnout. Burnout occurs when a child develops a strong dislike for a particular sport or activity because they have simply been doing it too much and have begun to associate negative feelings with the activity (e.g. they are bored with the game, they are sick of being hot and tired, etc.). It is especially detrimental for kids because play is such an essential part in a child’s physical, emotional, intellectual and social development.
While organized sports offer physical activity and discipline, children’s health experts are warning parents about the disappearance of free play. Free play allows kids the opportunity to experience different types of movements, problem solving and social interactions that they would not obtain from organized sports. Although organized sports can be rewarding for children, they should spend more time in free play.
Maintaining a Healthy Diet
It’s important for children – involved in organized sports or not – to maintain a healthy diet. They need to consume plenty of water and avoid excessive amounts of fatty, processed, sugary foods. Children should eat three meals a day – not skipping breakfast – and one or two snacks; this should include five servings of fruits and vegetables and three servings of dairy or equivalent calcium-rich foods. Giving your child a multivitamin can be beneficial, as vitamin D and iron are two of the most common dietary deficiencies in children. However, supplements, besides vitamin D and iron, have no proven benefit to children and should never be given as a substitute for a well-balanced diet.
If you have questions about your child’s exercise and nutrition needs, please give us a call at (239) 573-2001. Our pediatricians are here to help make sure your child is growing up as healthy as possible.
MacKoul Pediatrics is an amazing local pediatrics office in Cape Coral, FL where caring, compassionate doctors and nurses work with you to keep your children as healthy as possible. MacKoul cares for children from birth to college age, from Cape Coral, Fort Myers, Naples, and beyond.
May 1, 2018<|endoftext|>
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