#ATTENDANCE QUIZ for Lecture 11 of Math251(Dr. Z.)
#EMAIL  RIGHT AFTER YOU WATCHED THE VIDEO
#BUT NO LATER THAN  Oct. 12, 2020, 8:00PM (Rutgers time)
#EXTENDED TO Oct. 17
#THIS .txt FILE (EDITED WITH YOUR ANSWERS)
#TO:
#DrZcalc3@gmail.com
#Subject: aq11
#with an ATTACHMENT CALLED:
#aq11FirstLast.txt
#(e.g. aq11DoronZeilberger.txt)




#LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS


#Lecture Problem 1:

#Who proved every positive solution can be written as a sum of four squares


Answer: Lagrange

#Lecture Problem 2:

#Use Lagrange multipliers to find the largest value that x + 3y + 5z can be given x^2 + 3y + z = 35

graidents. L<1,3,5> <2x,3,1>.  

2x = L , 3=3L, 1=5L

x = 15 L/6

15L/6 = 35 

L = 14

x = 7

7 + 3 + 5 = 15

Answer: 15

#Lecture Problem 3: Find the maximum value of x^2 + 5xy + 3y^2 on the curve 5x^3 +6xy + 2y^3 = 2

<2x + 5y, 5x + 6y> <15x^2+6y, 6x + 6y^2> 

15x^2 + 6y = 2x + 5y

Y = 2x - 15x^2

5x + 6y= 6x + 6y^2

6y^2-6y = x

(2x+5y)(5x+6y) = L^2(15x^2+6y)(6x + 6y^2)

L = 1/3 x + 5/6 y

7L^3 = 2

 L^2 + 5LL + 3L^2

2/7 + 10/7 + 6/7 = 18/7

Answer: 18/7


#Lecture Problem 4:

#Finish the problem

x = (3/2)*sqrt(8/3)

4 * (9/4)(8/3) + 9 * (64/9)

72/3 + 64 = 88 

Answer: 88