### Blogging On Differentiation rule

In this Chapter, I found the most difficult stuff was relates rates problems.

We need to read the question and find a formula, or even probably two relate to the information that question told us. We need to know everything that might relate to the question, and solve the problem.

Exp: Water is flowing into a cone-shaped tank at the rate of 5 cubic inches per second. If the cone has an attitude of 4 inches and a base radius of 3 inches, how fast is the water level rising when the water is 2 inches deep?

The problem is given us the rate of change volume, dv/dt =5, r = 3, and asked to determine the rate change of height when h is 2, dh/dt when h=2.

We know the formula for conical volume is: V = 1/3 pai (r)^2 h

By similar triangle we have r/3=h/4,

So, r=3/4 h

V=1/3 pai r^2 h

V=1/3 pai (3/4h)^2 h

V= 1/3 pai 9/16 h^2 h

V= 3/16 pai h^3

Defferentiate implicitly:

dv/dt = 3/16*pai* 3h^2 (dh/dt)

5 = 3/16 pai 3(2)^2 (dh/dt)

20/9pai = dh/dt

The water level is rising at a rate of 20/9pai inches per second when the water is 2 inches deep.

We need to read the question and find a formula, or even probably two relate to the information that question told us. We need to know everything that might relate to the question, and solve the problem.

Exp: Water is flowing into a cone-shaped tank at the rate of 5 cubic inches per second. If the cone has an attitude of 4 inches and a base radius of 3 inches, how fast is the water level rising when the water is 2 inches deep?

The problem is given us the rate of change volume, dv/dt =5, r = 3, and asked to determine the rate change of height when h is 2, dh/dt when h=2.

We know the formula for conical volume is: V = 1/3 pai (r)^2 h

By similar triangle we have r/3=h/4,

So, r=3/4 h

V=1/3 pai r^2 h

V=1/3 pai (3/4h)^2 h

V= 1/3 pai 9/16 h^2 h

V= 3/16 pai h^3

Defferentiate implicitly:

dv/dt = 3/16*pai* 3h^2 (dh/dt)

5 = 3/16 pai 3(2)^2 (dh/dt)

20/9pai = dh/dt

The water level is rising at a rate of 20/9pai inches per second when the water is 2 inches deep.

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