anonymous
  • anonymous
Ms. Davis loves a good cup of coffee. If she puts on a pot of coffee using coneshaped coffee filter of radius 6 cm and depth 10 cm, and the water begins to drip out through the hole at the bottom at a constant rate of 1.5 cm^3 per second, determine how fast the water level is falling when the depth is 8 cm. Help? :/
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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myininaya
  • myininaya
volume=V depth=d r=radius we want to find d' when d=8cm V=1/3 *pi*r^2*d find derivative we have V'=1/3*pi*2rr'*d+1/3*pi*r^2*d' ..
anonymous
  • anonymous
Can you show me how you find the derivative?
myininaya
  • myininaya
you use the product rule we have two triangles so there is a way we can write this with just d' or d without r or r'

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myininaya
  • myininaya
we have to triangles inside the cone so we have 6/r=10/d so r=6d/10=3d/5 so r'=3d'/5
myininaya
  • myininaya
so we have V'=1/3*pi*2*3d/5*3d'/5*d+1/3*pi*9r^2/5*d' so we can find d' plug in the values for V' and d and then solve for d'
anonymous
  • anonymous
so I just plug in 8 to V' ?
myininaya
  • myininaya
i gave us the rate of the volume which was _____________
myininaya
  • myininaya
mean it gave you*
anonymous
  • anonymous
1.5cm^3
myininaya
  • myininaya
yes and the volume is decreasing so it would be negative 1.5cm^3/sec
myininaya
  • myininaya
they wanted us to find d' when d=8cm
myininaya
  • myininaya
so we have everything we need to solve for d'
anonymous
  • anonymous
SO what do I do next?

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