anonymous
  • anonymous
A conical salt spreader is spreading salt at a rate of 1 cubic feet per minute. The diameter of the base of the cone is 4 feet and the height of the cone is 5 feet. How fast is the height of the salt in the spreader decreasing when the height of the salt in the spreader (measured from the vertex of the cone upward) is 3 feet? Give your answer in feet per minute.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
I understand the first part, but confused about the second.
anonymous
  • anonymous
|dw:1332930077648:dw| you want dh/dt so replace the r in the volume equation in terms of h.
anonymous
  • anonymous
take V' with r replaced in terms of h in the volume equation...

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anonymous
  • anonymous
Im having problems with the cancelation at the beinging of plugging in my variables
dumbcow
  • dumbcow
\[\frac{dh}{dt} = \frac{dV}{dt}*\frac{dh}{dV}\] \[\frac{dV}{dt} = -1\] \[V = \frac{1}{3}\pi r^{2}h\] ratio of radius to height is 2:5 so r = 2/5h \[V = \frac{4}{75}\pi h^{3}\] \[\frac{dV}{dh} = \frac{4}{25}\pi h^{2} \rightarrow \frac{dh}{dV} = \frac{25}{4\pi h^{2}}\] \[\frac{dh}{dt} = -1*\frac{25}{4\pi h^{2}}\] plug in value for h
anonymous
  • anonymous
looks good
anonymous
  • anonymous
thank you, i understand it better now
anonymous
  • anonymous
dumbcow did all the work... but yw anyway :)
anonymous
  • anonymous
what is the value for h that you plug in??
dumbcow
  • dumbcow
@jsands, its the height of 3 ft given, they want to know the rate the height is decreasing when the salt level is at 3 ft
anonymous
  • anonymous
then i get -176.714 and that isn't correct?
anonymous
  • anonymous
how would i simplify that then? once i plug 3 in for h
dumbcow
  • dumbcow
?? you should get dh/dt = -.221 when h=3
anonymous
  • anonymous
got it thanks!
dumbcow
  • dumbcow
\[-\frac{25}{4\pi 3^{2}} = -\frac{25}{36\pi} = -0.221\]

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