Gas is escaping from a spherical balloon at the rate of 12 ft3/hr. at what rate (in feet per hour) is the radius of the balloon changing when the volume is 300 ft3?

This is the rate at which the radius of the balloon is changing when the volume is 300

Step-by-step explanation:

Let be the radius and the volume.

We know that the gas is escaping from a spherical balloon at the rate of because the volume is decreasing, and we want to find

The two variables are related by the equation

taking the derivative of the equation, we get

With the help of the formula for the volume of a sphere and the information given, we find  

Substitute the values we know and solve for

c

step-by-step explanation:

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )