Posted by rachel on Sunday, November 6, 2011 at 10:27pm.
water in a paper conical filter drips into a cup. let x denote the height of the water in the cup. if 10 in^3 of water are poured into the filter, find the relationship between dy/dt and dx/dt
so the paper filter is 4 inches tall
whith a radius of 2 inches. x is the height of the water in the cone.
the cup is 4 inches wide and y is the height of the water in the cup. please help! thanks(:

calculus  Steve, Monday, November 7, 2011 at 12:53pm
If the water in the filter is at depth x, with the surface of radius r,
x/r = 4/2 = 2
x = 2r
r = x/2
now, the volume of the water in the cup, plus that in the filter adds up to 10
cone: v = 1/3 pi r^2 x = pi/12 x^3
cup: v = pi r^2 y = 4pi y
pi/12 x^3 + 4pi y = 10
pi/4 x^2 dx/dt + 4pi dy/dt = 0
multiply by 4/pi to simplify a bit:
x^2 dx/dt + 16 dy/dt = 0
You can massage that into whatever form you need.

calculus  Anonymous, Tuesday, March 31, 2015 at 3:05pm
m,n,mn
Answer This Question
Related Questions
 calculus  water is poured into a conical paper cup so that the height increases...
 Calculus(answer needed immediatly,thanks)  A paper cup has the shape of a cone...
 science  A test liquid has a density of 1.1 g/ml. When you pour some of it into...
 Physics  7. A plastic cup, 15.0 cm in height, is filled to the rim with water. ...
 Chemistry  Materials several black pens of different types 2.0...
 Science  Thanks for everything guys! This really helped! But I have another ...
 Calculus  If water is poured into a cup at a rate of 1 cubic centimeter per ...
 Chemistry  A Test Liquid Has A Density Of 1.1g/ml. When You Pour Some Of It ...
 math  Water is poured into a right circular cone with a height of 10 cm and ...
 MATHS STATISTICS  B. A softdrink vending machine is supposed to pour 8 ounces ...
More Related Questions