SOLUTION: Hello! Help on the following please: The frame for a shipping crate is to be constructed from 22 feet of 2x2 lumber. a) If the crate is to have square ends of side x

Question 443125: Hello!
Help on the following please:
The frame for a shipping crate is to be constructed from 22 feet of 2x2 lumber.
a) If the crate is to have square ends of side x feet, express the outer volume Vof the crate as a function of x (disregard the thicknessof the lumber).
b) Sketch the graph of V for x>0
Thanks
Mak
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The frame for a shipping crate is to be constructed from 22 feet of 2x2 lumber.
:
a) If the crate is to have square ends of side x feet, express the outer volume V of the crate as a function of x.
:
The two square sides = 8x
The four lengths = 4L
8x + 4L = 22 ft
Simplify, divide by 4
2x + L = 5.5
L = -2x + 5.5
:
Vol = x * x * L
Replace L with (-2x+5.5)
V(x) = x^2 * (-2x+5.5)
V(x) = -2x^3 + 5.5x
:
b) Sketch the graph of V for x>0
Graph the positive portion of an equation y = -2x^3 + 5.5x, y = V(x)

:
Check our work assume x=2 then L = = 1.5 is the length
Find the vol 2 * 2 * 1.5 = 6 cu ft, which agrees with the graph green line
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