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.

  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.

nope

step-by-step explanation:

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.