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AP Calculus AB

An interactive log for students and parents in my AP Calculus class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

Tuesday, November 22, 2005

Related rates of change

In today’s class, Mr. K told us about the exam. Woo... Which we know it will be really hard. And Mr. K gave us a quiz. It had 4 multiple questions on that sheet. We got only 8 minutes to do with yet, which every question you only gave two minutes to do with it. And we were not allowed to use our calculator. We need to do a little practice to get familiar with those questions which will appear on our final exam.
I can image how hard the exam will be, we need to do a lot of exercise to be comfortable when we white that exam which will be on May.

There were three questions on the white board. It was about related rates of change.
Air is blown into a spherical balloon at a rate of 12In^3/ sec. How fast is the radius increasing at the instant the diameter is 1 foot.

From the question that we know the rate of change volume dV/dt=12
1 foot is equal to 12 inch. So, the radius is 6 inch.
And the question is to find the rate of change radius dr/dt.
Volume of Sphere formula: V=4/3 pai r^3
Up to here, we know to fine the rate of change; we need to find the derivative of the function.
According to the Product and chain role:
dV/dt = 4/3pai* 3 r^2 (dr/dt)
dV/dt = 4 pai r^2 dr/dt
12 = 4 pai 6^2 dr/dt

Two questions left, we didn’t have enough time to finish it. And the homework will be on the Bolg tonight.

Nest Scribe is Steve:P

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