The length of a rectangular box is 4 times its width, and its height is 7in more than its width. The volume of the box is 126in3

Question

tester [92]

3 years ago

10

The length of a rectangular box is 4 times its width, and its height is 7in more than its width. The volume of the box is 126in3

. Use the ALEKS graphing calculator to find the width of the box. Round your answer to two decimal places.

Mathematics

1 answer:

Ierofanga [76] · Answer 1 · 2022-07-06T02:14:55+03:00

Answer:

1.88 inches

Step-by-step explanation:

The volume is the product of length, width, and height. If w represents the width of the box, then its length is 4w and its height is w+7. The volume is then ...

V = (4w)(w)(w+7)

We want to find the value of w that makes V=126. It is convenient to use the graphing calculator to look for zeros of a function, so we can write the equation as ...

V - 126 = 0

4w·w·(w+7) -126 = 0

The only positive solution to this equation is near w ≈ 1.883.

The width of the box is about 1.88 inches.

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Attached is output from the DESMOS free graphing calculator. The ALEKS calculator requires a subscription. The method of solution is substantially the same, but requires a little more work on the ALEKS calculator to find the zero-crossing.