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jrpalomo · Jun 28, 2010, 05:03 AM

The 12th Annual Balloon contest was held last Friday. The surface area of a balloon is s(r) = 4πr^2 where r is the radius if the balloon in meters.

a. Find the surface area of the balloon as a function of time if the radius is increasing with time t (in seconds) according to the formula r(t) = 2/3t^3

b. What are the dependent and independent variables in function s in terms of r, function s in terms of t and function r?

thanks

jrpalomo · Jun 28, 2010, 05:04 AM

I meant

[QUOTE=jrpalomo;2412618]where r is the radius of the balloon in meters.

ebaines · Jun 28, 2010, 12:41 PM

We'll change your problem around a bit so you can see how to do it, then you can use this technique to solve your specific problem.

Suppose You are given an equation for the volume of the balloon based on it radius:

$ V = \frac 4 3 \pi R^3 $
and an equation for the balloon's radius in terms of time, which suppose is:
$ R = \frac 1 3 t^2 \\ $

To get the volume in terms of time, simply substitute the equation for R into the first equation:

$ S = \frac 4 3 \pi (\frac 1 3 t^2)^3 \ = \frac 4 {81} \pi t^6 $

Do you see how I did that? Now try this same approach on your problem.

The dependent variable is the one that that is the result of the calculation using an equation, and the independent variable is the one that you "know." So for example, the formula for the area of a rectangle is length times width:
$ A = L \times W $

Here A is the dependent variable, as its value "depends on" L and W, which are the independent variables (you can set them to whatever you want). Now, can you complete the problem?