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I need help question number 6

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Part a

we have that

the volume of the box is equal to

V=L*W*H

so

In this problem

the height H is equal to H=x

L=(10-2x) in

W=(8-2x) in

substitute in the formula

V=(10-2x)(8-2x)(x) in3

apply distributive property

V=(80-20x-16x+4x^2)(x)

V=(4x^3-36x^2+80x) in3

Part b

For x=0.7 in

V=4(0.7)^3-36(0.7)^2+80(0.7)

V=39.732 in3

For x=2.3 in

V=4(2.3)^3-36(2.3)^2+80(2.3)

V=42.228 in3

so

the change in the box volume increases (42.228-39.732)=2.5 in3

For x=3.2 in

V=4(3.2)^3-36(3.2)^2+80(3.2)

V=18.432 in3

the change in the box volume decreases (42.228-18.432)=23.8 in3

User Tun
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