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May 28, 2015

Homework Help: algebra

Posted by kevin on Monday, November 26, 2012 at 7:17am.

I need someone to check my work not sure if I'm doing this right.

The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be? HINT: Let x represent one of the dimensions, then define the other dimensions in terms of x.

I got h=1.6 in
w=2in
l=2.4in
l+w=H=6
L=1.5H
1.5H+W+H=6
2.5W=6
W=6-2.5H
H=X
L=1.5X
V(X)=(1.5X)(X)(6-2.5X)
V(X)=9X^2-3.73X^3
V1(X)=18X-11.25X^2
X=1.6, (X=0)
V2(X)=18-2.25X
V2(16)=-18<0
X=16
H=1.6
W=2
L=2.4

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