#LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS

Attendance Question #1

Who proved that every positive integer can always be written as a sum of four squares?

Answer to Attendance Question #1

Joseph Louis Lagrange

Attendance Question #2

Use Lagrange multiplies (no credit for other methods) to find the largest value that x+3y+5z can be given that x^2+y^2+z^2=35

Answer to Attendance Question #2

Fx= 1 fy= 3 fy= 5 <1,3,5>
Gx=2x gy=2y gz=2z <2x,2y,2z>
<1,3,5> = L<2x,2y,2z>
1=L2x 3=L2y 5=L2z
15=L^3*8xyz
X= 1/2L y=3/2L z= 5/2L
(1/2L)^2 + (3/2L)^2 + (5/2L)^2 = 35
1/4L^2 + 9/4L^2 + 25/4L^2 = 35
35/4L^2= 35
1= 4L^2
1/2 = L
X= 1/4 y=3/4 z= 5/4
1/4 + 9/4 + 25/4= 35/4

Attendance Question #3

Let a[i] = the i-th digit of your RUID, if it is zero make it 5
Find the maximum value of a[1]*x^2+a[4]*x*y+a[9]*y^2
On the curve a[5]*x^3+a[7]*x*y+a[5]*y^3=a[5]

Answer to Attendance Question #3

202002783
Find the maximum value of 2*x^2+5*x*y+3*y^2
On the curve 5*x^3+7*x*y+5*y^3=5 
Fx= 4x+5y fy= 5x+6y <4x+5y,5x+6y>
Gx= 15x+7y gy= 7x + 15y^2 <15x+7y, 7x+15y^2>
 <4x+5y,5x+6y>= L <15x+7y, 7x+15y^2>
4x+5y=L(15x+7y) 5x+6y=L(7x+15y^2)

(4x+5y) 5x+6y = L^2(15x+7y)(7x+15y^2)
I’m not sure what to do beyond this. 

Attendance Question #4

Finish up problem

Answer to Attendance Question #4

X= 3/2 *square root(8/3) y = squareroot (8/3)

4*x^2+9*y^2 = 4* 9/4* 8/3 +9*8/3= 24+24= 48

X=-12*y /8 = -3/2 y
Y=square root(8/3)
X= -3/2squareroot(8/3)

4*9/4*8/3 +9*8/3 = 24+24 =48

maximum is 48 and no minimum