anonymous
  • anonymous
....
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
I think its 4000 but I'm not sure
misty1212
  • misty1212
HI!!
misty1212
  • misty1212
calc question?

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anonymous
  • anonymous
Hello and Yes
misty1212
  • misty1212
|dw:1443580022426:dw|
misty1212
  • misty1212
area is \(x^2+4xh\) with no top
misty1212
  • misty1212
set \[x^2+4xh=1200\] and solve for\(h\)
misty1212
  • misty1212
i get \[h=\frac{1200-x^2}{x}\]
anonymous
  • anonymous
Okay
misty1212
  • misty1212
oops i made a mistake
misty1212
  • misty1212
\[x^2+4xh=1200\\ h=\frac{1200-x^2}{4x}\]
misty1212
  • misty1212
volume is \[V=x^2h\] or now \[V(x)=x^2\left(\frac{1200-x^2}{4x}\right)\]or \[V(x)=\frac{1}{4}x(1200-x^2)\]
misty1212
  • misty1212
find the critical points by taking the derivative, setting it equal to zero, etc
anonymous
  • anonymous
Okay 1200x^2-x^4/4x^3 =0
misty1212
  • misty1212
hmm lets multiply out first
misty1212
  • misty1212
\[V(x)=300x-\frac{1}{4}x^3\]
misty1212
  • misty1212
the derivative is a lot simpler than that, it is just \[V'(x)=300-\frac{3}{4}x^2\]
anonymous
  • anonymous
Okay and then plug my numbers in?
misty1212
  • misty1212
set that equal to zero and solve
misty1212
  • misty1212
\[300-\frac{3}{4}x^2=0\]
misty1212
  • misty1212
don't fret the solution, solve \[\frac{3}{4}x^2=300\] forget the negative solution
misty1212
  • misty1212
you get \(x=20\) yet?
anonymous
  • anonymous
Yes

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