juanarev04
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The volume of a crate with length of x feet, width of 8 - x feet, and a height of x - 3 feet is given by V(x)=x(8−x)(x−3) find the maximum volume of the crate and the dimensions for this volume

The Volume Of A Crate With Length Of X Feet Width Of 8 X Feet And A Height Of X 3 Feet Is Given By Vxx8xx3 Find The Maximum Volume Of The Crate And The Dimensio class=

Sagot :

przemyslawstefaniak
First, we need to find the maximum volume. In order to do this, we will first look at the dimensions of x and 8-x in the equation for volume. We can see that as x increases, so does 8-x. This means that there is a positive correlation between them. This also tells us that as x continues to increase, there will be a point where 8-x will equal 0. The maximum volume will occur when 8-x equals 0.

Therefore, the dimensions for the maximum volume are x=8 and x=-3.

Now we can solve for the actual maximum volume:

V max =(8)(8)-(3)(8)=64.

The maximum volume is 64 cubic feet and the dimensions for this volume are 8x=-3
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