Ricardo is building a rectangular wooden box to ship a large item in. He needs the length of the box to be 30 inches longer than the width. He also needs the height of the box to be 5 inches shorter than the width. Create an equation to represent the volume of the wooden box in terms of the width. The question wants me to fill in the blank y=_+_x^2-_x. It also asks what the largest width would be.

Question

Mathematics

Alec

20 April, 02:16

Ricardo is building a rectangular wooden box to ship a large item in. He needs the length of the box to be 30 inches longer than the width. He also needs the height of the box to be 5 inches shorter than the width. Create an equation to represent the volume of the wooden box in terms of the width. The question wants me to fill in the blank y=_+_x^2-_x. It also asks what the largest width would be.

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Answers (2)

Know the Answer?

Miguel Short · Answer 1

Answer: y = x^3 + 25x^2 - 150x

It is possible for the width of the box to be : 5.2 inches

Cherokee · Answer 2

x³ + 25x² - 150x

Step-by-step explanation:

It is given that, the length of the box to be 30 inches longer than the width. He also needs the height of the box to be 5 inches shorter than the width.

To find the equation to represent volume

Let 'x' be the width of the rectangle

Length = x + 30

Height = x - 5

Volume of rectangle = Length * width * height

= (x + 30) * x * (x - 5)

= x (x + 30) (x - 5)

= x (x² - 25x - 150)

= x³ + 25x² - 150x