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Jana took seven spelling tests, each with ten words, but she could only find the results

Mathematics for the International Student: Mathematics SL | 3rd Edition | ISBN: 9781921972089 | Authors: Sandra Haese, Michael Haese, Robert Haese, Mark Humphries, Marjut Maenpaa ISBN: 9781921972089 446

Solution for problem 16 Chapter 20

Mathematics for the International Student: Mathematics SL | 3rd Edition

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Mathematics for the International Student: Mathematics SL | 3rd Edition | ISBN: 9781921972089 | Authors: Sandra Haese, Michael Haese, Robert Haese, Mark Humphries, Marjut Maenpaa

Mathematics for the International Student: Mathematics SL | 3rd Edition

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Problem 16

Jana took seven spelling tests, each with ten words, but she could only find the results of five of them. These were 9, 5, 7, 9, and 10. She asked her teacher for the other two results and the teacher said that the mode of her scores was 9 and the mean was 8. Given that Jana remembers she only got one 10, find the two missing results.

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MAT 211­ Lecture 6­ 15.3 & 15.4 Section 15.3 Homework #8: ln(x,y)= x​ +y​2­y​x­2 lnx= 0 & lny= 0 1st Derivative:​ lnx= 2x­y​ lny= 2y­2yx I. 2x­y​=0 ­­­­­­­> x=1 2­y​=0 2=y​ y=­ 2 2​ 2y­2yx=0 ­­­­­­­> y=0 2x­y​ =0 2x­0=0 x=0 II. 2y(1­x)= 0 y=0 & x=1 Critical Points: (0,0); (1, ­ 2); (1, + 2) 2nd Derivative:​ lnxx= 2 lnxx (0,0)= 2 lnyy= 2­2x lnyy (0,0)= 2 lnxy= ­2y lnxy (0,0)= 0 H(0,0)= 2 * 2 ­ 0= 4 Since lnxx= 2>0, then we have a relative minimum at (0,0). ­Critical point at (1, ­ 2) : lnxx (1, ­ 2) =2 √ lnyy (1, ­ 2) =0 lnxy (1, ­ 2) =(­2)(­ 2) = 2 2 2 H (1, ­ 2)= 2 * 0 ­ (2 2)​ 0­8= ­8< 0 Since H is negative, we have a saddle point at (1, ­ 2). ­Critical point at (1, + 2) : lnxx (1, + 2)=2 lnyy (1, + 2)=0 lnxy (1, + 2)= ­2( 2) 2​ H(1, + 2) = 2* 0­ (­2 2)​= 0­8= ­8<0 Since H is negative, we have a saddle point at (1, + 2). Homework #11: M(c,f)= 11+8c+4c​ 2­40f­20cf+40f​2 Mc= 8+8c­20f­­­­­­­> 8+8c­20f= 0 divide by 4 2+2c­5f=0 Mf= ­40­20c+80f­­­­> ­40­20c+80f=0 divide by 20 ­2­c+4f=0

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Chapter 20, Problem 16 is Solved
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Textbook: Mathematics for the International Student: Mathematics SL
Edition: 3
Author: Sandra Haese, Michael Haese, Robert Haese, Mark Humphries, Marjut Maenpaa
ISBN: 9781921972089

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Jana took seven spelling tests, each with ten words, but she could only find the results