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
algebra - kay, Monday, November 26, 2012 at 10:39am
If H=x then W=6-2.5x and L=1.5x
v(x)=L*H*W= x(1.5x)(6-2.5x)= 9x^2-3.75x^3
For stationary point; V'(x)=0 so x=0 reject or 18=11.25x so x=18/11.25= 1.6
check if it's a max: V''(x)=18-22.5x at x=1.6 V''(1.6)= -18<0 so yes
H=1.6, W=2, L= 2.4
YOUR ANSWER IS CORRECT. JUST IN LINE V(X)=9X^2-3.73X^3 you've made a mistake as it's 3.75 not 3.73
algebra - lee, Monday, November 26, 2012 at 7:07pm
Answer This Question
More Related Questions
- Algebra 2 - I've been stuck on this problem forever. Can someone please explain ...
- algebra - A rectangular box has Dimensions 16 inches and 22 inches and volume ...
- Math - 2.)The volume of a box can be found by multiplying the length times width...
- College Algebra - On a rectangular piece of cardboard with perimeter 11 inches, ...
- Algebra 2 - The dimensions in inches of a shipping box can be expressed as width...
- algebra - carl has a box with a length width and height of 12 inches. she needs ...
- Calculus- PLEASE HELP - A rectangular piece of tin has an area of 1334 square ...
- Algebra 1 check answers - A box has dimensions of 17 inches long, 1.3 feet wide...
- Algebra 2 - A box with no top is to be constructed from a piece of cardboard ...
- math - You are going to build a glass box. The length of the box is 8 inches ...