A box with a square cross section is to be sent by a delivery service, there are
ID: 3143869 • Letter: A
Question
A box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by V = x^2 (- 2x), where x is the length of each side of the section (in (a) Is V a function of x? Yes, V is a function of x. No, V is not a function of x. (b) If V = V (x), find V (5) and V (21). (If is not a function of x, enter DNE.) V (S) = in^3 V (21) = in^3 (c) What restrictions must be placed on x (the domain) so that the problem makes physical sense? (Enter your answer using interval . If V is not a function of x, enter DNE.)Explanation / Answer
(a) V is a function which is given by V = x2 (81-3x)
(b) V(5) = 52 (81-3*5)
= 25 * 66
= 1650
V(21) = 212 (81-3*21)
= 441 * 18
= 7938
(c) We have V = x2 (81-3x)
The value of x and V should both be positive.
=> x > 0
Since x > 0, x2 > 0
V > 0 => x2 (81-3x) > 0
=> 81 - 3x > 0
=> 81 > 3x
=> x < 27
The answer is (0,27)
Note: Interval notation is asked!
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