calc

A cone has its pointy end at the bottom, a height of 15 cm. and a radius of 5 cm.
Water is trickling in at a constant rate of 10 cm3 per hour but a small hole at the
bottom of the cone is allowing water to leak out at a rate proportional to the height of
the water in the cone. When the volume is π cm3, the instantaneous rate of change of 
the total amount of water in the tank is 3
2cm
−  per hour. 
a)  Determine the constant of proportionality for the rate at which water is escaping.
b)  Determine the rate at which the height is changing when the volume of water is
the cone is changing at a rate of 1 cm3 per hour. 
c)  At some position, water will cease to decrease. That is to say, the amount of water
in the cone will stabilize. Find the height of the water in the cone when that
happens.


answer w/ work plz?

-2 cm^3 per hour
10 cm3 = 10 cm^3
pi cm3 = pi cm^3
in case any of that needed clarifying.

lrn2calculus

First of all, diff eq, newb...

so torrichelli's law states that dV/dt=c*h, for some c ∋ c ∈ R
r/h=1/3, r=h/3
V=1/3(πr^2)*h=(1/27)πh^3
(27V/π)^(1/3)=h
now you can find the constant using the data you have (if you're to lazy to plug the numbers in yourself, you clearly don't deserve the help)

ok so now you know dV/dt, so take (27V/π)^(1/3)=h and differentiate both sides, and since you know dV/dt at the point you want, plug in that 1 cubic-centemeter/hr there.

So now for c... dVtotal/dt=10 - c*V, I'm not going to waste my time finishing it out... if you can't figure it out you deserve to fail.

P.S. there are girls on the interwebz

>>4 There a boys and men on the `interwebz' too, what's your point?

On occasion I get crap about being a female math/physics major, so I like to take every opportunity possible to rub it in people's face, before they have a chance to give me crap about it.

Also to make sexist men feel even more insecure.

>>6  nobody cares

>>6 nobody really gives a shit

>>6
no me importa.

>>6
I just came to you. How do you feel about that?

>>6
Do you have any idea what "Anonymous" means?

Well if you bothered posting you must have cared in some way, even if strictly out of annoyance.

>>6
Uptight much?

>>13
Being annoyed with attention whores != caring about their gender. Think before you type.