Hello i Need Help on mathematical models
11. The surface area of a sphere is a function of its radius. If centimeters is the radius of a sphere and [tex]A(r)[tex] square centimeters is the surface area, then . Suppose a balloon maintains the shape of a sphere as it is being inflated so that the radius is changing at a constant rate of 3 centimeters per second. If centimeters is the radius of the balloon after seconds, do the following:
a.) Compute and interpret your result.
b.) Find the surface area of the balloon after 4 seconds.
14. A rectangular garden is to be fenced off with 100ft of fencing material. a.) Find the mathematical model expressing the area of the garden as a function of its length. b.) what is the domain of your function in part a?
c.) By plotting on your a graphics calculator the graph of your function in part (a), estimate to the nearest foot the dimensions of the largest rectangular garden that can be fenced off with the 100ft of material
Thank you very much!!!
If the length of the garden is , then as we fence it with of fence its width is so
its area is:
The domain is , as the length cannot be less than or greater than .
See attachmentc.) By plotting on your a graphics calculator the graph of your function in part (a), estimate to the nearest foot the dimensions of the largest rectangular garden that can be fenced off with the 100ft of material
RonL
What it said was that the radius was increasing at at rate of , which means that if it starts with a radius (which we are not told) of at , then at its radius must be , as in the radius will have increased by .
Now the existance of an initial radius is based on personal experience with baloons. There is some minimum radius where you have put just sufficient air into them so that they are more-or-less spherical, but the material is not stretched, we can take this as corresponding to time and radius . It makes little sense to assume that at the radius is as the idea of a baloon with a radius of is silly we would be outside the region of validity of the model.
RonL