Several questions regarding rate of change.

May 2010
1
0
I have a test coming up and we received a practice packet, and I want to make sure I got everything right.


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1) Assuming that a soap bubble retains its spherical shape as it expands, how fast is its radius increasing when its radius is 5 inches, if air is blown into it at the rate of 3 cubic inches per second?

I got \(\displaystyle dr/dt\) = \(\displaystyle 3/100pi
\)

2) The top of a 25 foot ladder is sliding down a vertical wal at a constant rate of 3 feet per minute when the top of the ladder is 7 feet from the ground. What is the rate of change of the distance between the bottom of the ladder and the wall?

I got dx/dt = 7/8


3) Area of a rectangle is increasing at a constant rate of 100 square meters per second. The length of the rectangle is increasing at a rate of 4 meters per second when the area equals 10 meters and the length equals 2 meters. How fast is the width increasing at this instant?

I got 40


4) The area of a circle is increasing at a rate of 4 ft squared per minute. How fast is the radius of this circle increasing at the instant the radius equals 4 feet?

I got 1/2 pi


5)The volume of a cube is increasing at the rate of 15.6 cubic centimeters per second. How fast is the surface area of the cube increasing at the instant when each edge of the cube is 12 centimeters long?

I got da/dt = 5.2


6) The area of a circle is increasing at the rate of 20 cm squared per second. At what rate is the circumference of the circle increasing when the circumference equals 10pi?

I got 4





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I know it's a lot but even just I could just be checked on a few of them that would be great.
 

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
--
1) Assuming that a soap bubble retains its spherical shape as it expands, how fast is its radius increasing when its radius is 5 inches, if air is blown into it at the rate of 3 cubic inches per second?

I got \(\displaystyle dr/dt\) = \(\displaystyle 3/100pi
\)
This one is correct. Don't forget your units, in this case "inches per second"

Assuming you followed similar logic and using the chain rule you should have some confidence the remaining questions are on the right track.
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
I have a test coming up and we received a practice packet, and I want to make sure I got everything right.


--
1) Assuming that a soap bubble retains its spherical shape as it expands, how fast is its radius increasing when its radius is 5 inches, if air is blown into it at the rate of 3 cubic inches per second?

I got \(\displaystyle dr/dt\) = \(\displaystyle 3/100pi
\)

2) The top of a 25 foot ladder is sliding down a vertical wal at a constant rate of 3 feet per minute when the top of the ladder is 7 feet from the ground. What is the rate of change of the distance between the bottom of the ladder and the wall?

I got dx/dt = 7/8


3) Area of a rectangle is increasing at a constant rate of 100 square meters per second. The length of the rectangle is increasing at a rate of 4 meters per second when the area equals 10 meters and the length equals 2 meters. How fast is the width increasing at this instant?

I got 40


4) The area of a circle is increasing at a rate of 4 ft squared per minute. How fast is the radius of this circle increasing at the instant the radius equals 4 feet?

I got 1/2 pi


5)The volume of a cube is increasing at the rate of 15.6 cubic centimeters per second. How fast is the surface area of the cube increasing at the instant when each edge of the cube is 12 centimeters long?

I got da/dt = 5.2


6) The area of a circle is increasing at the rate of 20 cm squared per second. At what rate is the circumference of the circle increasing when the circumference equals 10pi?

I got 4





--

I know it's a lot but even just I could just be checked on a few of them that would be great.
your numerical answers are correct ... you might want to pay attention to units in your solutions.