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Numerade Educator

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Problem 60 Hard Difficulty

Find a formula for the described function and state its domain.

A closed rectangular box with volume $ 8 ft^3 $ has length twice the width. Express the height of the box as a function of the width.

Answer

$h(w)=\frac{4}{w^{2}}$

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Video Transcript

for this kind of problem. It's always nice to draw, sketch and label it and figure out what you know and what you're trying to find. So we have a rectangular box and its dimensions are length with and height, and we know that the length is two times the width. So what if I call the length to W and the width W and the height H? We also know the volume is eight cubic feet and we know to get volume, you would multiply the length, width and height together so you would have to W times W Times age equals eight, so that might come in handy as we go. Our goal here is to express the height as a function of the width. So we want a function that looks like this h of w equals something. Okay, so at this point, we have our volume equation, which has age and w in it. If we just isolate H in that equation, then we'll have what we're looking for. So let's divide both sides of the equation by to w squared that will isolate the H. So now we have aged equals eight divided by two w squared, and we can reduce that. And that is a CI equals four divided by W. Squared. And if we write that using function notation each of w equals four divided by W squared. Now, what about the domain? Well, w is the length of a side of a box, and so w has got to be positive.