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# Postal Restrictions

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Postal Restrictions If a box with square cross section is to be sent by the postal service, there are restrictions on its size such that its Volume is given by V= x²(108-4x), where x ist the length of each side of the cross section (in inches).

(a) Is V a function of x?
(b) If V= V(x), find V(10) and V(20).
(c) What restrictions must be placed on x (the domain) so that the problem makes physical sense?

https://brainmass.com/math/geometry-and-topology/postal-restrictions-15331

## SOLUTION This solution is FREE courtesy of BrainMass!

a) Yes. V is a function of x , The relation is given by V = x^2 (108-4x).
<br>
<br>b) V(10) = 10^2 ( 108 - 4*10) ( replacing x by 10)
<br> = 100* 68
<br> = 6800 Cubic Inches
<br>
<br> V (20) = 20^2 ( 108 - 80)
<br> = 11200 cubic inches
<br>
<br>c) For the problem to make physical sense the Volume (V) should be greater than 0. A box with x dimensions as square cross section doesnt makes sense for a 0 Volume.
<br>
<br>Therefore x^2 (108 -4x) &gt;0
<br>Since x is not equal to 0 , therefore 108 -4x &gt;0
<br>or x &lt; 27 inches.
<br>
<br>Hope it is clear.

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