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anonymous
 one year ago
Water Runs into a conical tank at the rate of 3 feet^3/min. the tank stands pointing down and has a height of 15ft and a base radius of 4ft. How fast is the water level rising when the water is 8 feet deep.
anonymous
 one year ago
Water Runs into a conical tank at the rate of 3 feet^3/min. the tank stands pointing down and has a height of 15ft and a base radius of 4ft. How fast is the water level rising when the water is 8 feet deep.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443496421968:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure where to go from there

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443496845151:dw first step is to calculate r' (the value I marked), do you know how to do that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea i think i do its, is this right ? \[\frac{ r }{ h } = \frac{ 4 }{ 15 } \] \[r = \frac{ 4h }{ 15 }\]

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2almost, we want the radius when h = 8, so you can plug in h = 8 into your proportion

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2uh, lets leave it as a fraction for now (32/15) now, we just figured out that r = 4h/15, we can substitute that into the volume equation

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2V = (1/3)(pi)(r^2)(h) = (1/3)(pi)(4h/15)^2*(h) now differentiate that with respect to h

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so \[V = \frac{ 1 }{ 3 } \pi (\frac{ 32 }{ 15 }) ^2 h\]

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2actually, forget 32/15, we don't really need that (my mistake)

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443497509872:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait so do we treat the r in the function as a constant = to 32/15 ?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2right, we rewrote r in terms of h, so we've already accounted for r (since r changes proportionally to h)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so dv/dt = 2pi/3 (4h/15) h dh/dt ?

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443497761147:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2then plug in h = 8 and dv/dt = 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait why is h cubed, and also i thought it was 4h/15 not 4/15

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2dw:1443498112065:dw

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2remember your exponent rules

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay and where did the 1/3 go?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the power rule for the h^3 canceled it out

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2remember your derivative rulesdw:1443498227202:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep and the answer is .2098

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay thank you very much!!!

Vocaloid
 one year ago
Best ResponseYou've already chosen the best response.2would be best to write it as a fraction in terms of pi, but yeah
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