That does not have any GLOBAL optimal solution but it does have at least one LOCAL optimal solution; (b). whose set of local optimal solutions coincides with that of the global optimal solutions. 2 Part III (5 points) (a). Suppose that the value of a linear function at [2, 1, 1]T is 4. Which is the value of the same function at [4, 2, 2]T (note that [4, 2, 2]T = 2 · [2, 1, 1]T )? Which property of the function did you use to answer? (b). Suppose that the values of a linear function at [2, 1, −1]T and [2, 0, 1]T are 4 and 7, respectively. Which is the value of the same function at [4, 1, 0]T = [2, 1, −1]T + [2, 0, 1]T ? Which property of the function did you use to answer?

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

a - base

b - exponent

so,

b. would be the answer : )

step-by-step explanation:

step 1: add -16x to both sides.

16x−4y+−16x=64+−16x  

−4y=−16x+64

step 2: divide both sides by -4.

−4y /-4 = -16x + 64/-4

answer:   y=4x−16

hope i'm right