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Step-by-step explanation:

w and d are the width and diagonal, respectively.

w = d/2 + 1 = (d+2)/2

Pythagorean theorem

w^2 + 8^2 = d^2

substitution

(d+2)^2/4 +64 = d^2

(d+2)^2 + 256 = 4d^2

d^2+4d+4 + 256 = 4d^2

3d^2-4d-260 = 0

Quadratic formula

d = [4±√( 4²-4(3)(-260))]/[2⋅3] = 10, -26/3

-26/3 is an extraneous solution, so d = 10 inches

w=d/2 +1 =6 inches

Ant‘s path = 8+6 = 14 inches

Beetle’s path = 10 inches

14 < 1.5(10)

Ant reaches food first.

395.84

step-by-step explanation:

2πrh+2πr²

2 (pie)(radius)(height)+2(pie)(radius)^2

function 2 has a greater rate of change than function 1

function 2 has a greater y-intercept than function 1

step-by-step explanation: