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

Algebra ->  Expressions-with-variables -> 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       Log On


   

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) About Me  (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)
+graph%28+300%2C+200%2C+-1%2C+6%2C+-1%2C+10%2C+-2x%5E3%2B5.5x%5E2%2C+6%29+
:
Check our work assume x=2 then L = %2822-8%282%29%29%2F4 = 1.5 is the length
Find the vol 2 * 2 * 1.5 = 6 cu ft, which agrees with the graph green line