composition of functions: find and interpret (S o r)(t)

[jhawk555]

I was able to do this before, but this problem has me confused.

The surface area S (in square meters) of a hot-air balloon is given by S(r) = 4(pi)r^2, where r is the radius of the balloon (in meters). The radius of the balloon is r(t) = 2/3t^3 where t is the time in seconds after the balloon is starting to be blown up. Find and interpret (S o r)(t).

r(t)=2/3t^3

S(r) = 4(pi)(2/3t^3)squared equalling

4(4/9 t^5) pi

S(r)=16/9t^5pi

I don't think I did this right. Any suggestions?

Thanks

 

[stapel]

Your formatting is ambiguous. Do you mean r(t) to be "2/(3t³)", "2/(3t)³", "(2/3)t³", or something else?

Thank you.

Eliz.

 

[jhawk555]

it is two-thirds t(to the 3rd power) It isn't easy for me to understand how to format this when I am new to this.

 

[skeeter]

\(\displaystyle \L s(r) = 4\pi r^2\)

\(\displaystyle \L r(t) = \frac{2}{3}t^3\)

\(\displaystyle \L s[r(t)] = 4\pi \left[\frac{2}{3}t^3\right]^2 = \frac{16}{9}\pi t^6\)

 

[jhawk555]

I do appreciate you guys looking at my work and helping me understand what I am doing wrong, especially you Eliz. Is there a trick to entering this type of math problem like skeeter has? I'd love to do it right the first time so everyone understands my question.

Thanks again

 

[pka]

At top of this page there is pull-down menu “Forum Help”.
There you will find several topics on “typing mathematics on the web”.
Skeeter is using LaTeX.

 

[jhawk555]

thank you