1. Let the height of the box be x
then the length is 1.5x
let the width be y
so x + 1.5x + y = 6
y = 6 - 2.5x
volume = V = x(1.5x)(y) = 1.5 x^2 y
= 9x^2 - 3.75x^3
dV/dx = 18x - 11.25x^2
= 0 for a max of V
x(18-11.25x) = 0
x = 0 --- > makes no sense (would give us minimum V)
x = 18/11.25 = 8/5
height = 8/5
length = 1.5(8/5) = 12/5
width = 6-2.5(8/5) = 6-4 = 2
x^4 - 41x^2 + 400) = 0
(x^2 - 25)(x^2 - 16) = 0
x^2 = 25 ----> x = ± 5
x^2 = 16 ----> x = ± 4
Thank you Reiny for your help.
Help... Can you give me answers for the unit test??
To Derr - You have made a couple of uncalled for comments to a couple of ...
Algebra - Have a couple questions was wondering if someone could check my work? ...
Algebra 1B - This Question is in multiple sections. f(x)= -2x^2+2x+10 is the ...
APA Format - Hi i have a couple of dumb questions :) I know the good websites ...
math - I have a couple of math questions that i cant seem to get to work out. ...
algebra - in my workbook it says give the opposite of each expression and the ...
Algebra - Can someone help me on these questions, please.
Music - I have a couple of questions... 1. I have to transpose a musical piece ...
chemistry - Chromatography seperating mixtures; A couple questions I'm not sure ...
algebra - I have a couple questions I need help on. Which model is most ...