## anonymous 3 years ago Solve for r

1. anonymous

$\large 0=\frac{ r-2700 }{ r^2 }+62 \pi r$

2. calculusxy

You are trying to find the area of a radius?

3. calculusxy

Sorry I meant the area of a circle.

4. anonymous

No it's an optimization problem I am trying to do, I just need to solve for 'r'

5. calculusxy

Oh I thought that because the formula to finding the area of a circle,you have to first square the radius and then multiply it by pi (r^2)3.14.

6. anonymous

Multiply everything by r^2. Then factor out an r. From there it's a quadratic.

7. anonymous

Oh my bad. You actually get a cubic.

8. anonymous

top and bottom or just top?

9. anonymous

Multiply everything by r^2. When you multiply the fraction, multiply on top.

10. anonymous

$r^2 or \frac{ r^2 }{ r^2 }$

11. anonymous

Just r^2

12. anonymous

yeah so woulnt that cancel out with the fraction

13. anonymous

Yes =) That's the point. It gets r out of the denominator.

14. anonymous

ohh i thought you were also telling me to muktiply the top by r^3 so the function would be diff, i misunderstood

15. anonymous

$$\huge 0 = \frac{r-2700}{r^2} + 62\pi*r$$ multiply everything by r^2 $$\huge (0)*r^2 = (\frac{r-2700}{r^2})*r^2 + (62\pi*r)*r^2$$

16. anonymous

Gives: $$\huge 0 = r-2700 + 62\pi*r^3$$

17. anonymous

And honestly from there your best bet is to use a cubic solver of some sort. Wolfram Alpha should do just fine.

18. anonymous

|dw:1371520632051:dw| yeah but the thing is like during an exam i cant use it :P

19. anonymous

Are you sure the question is correct?

20. anonymous

21. anonymous

I suggest you double check, because you will not solve this without the aid of wolfaplha

22. anonymous

here is the question and my solution

23. anonymous

I suggest you take a look at this http://gbbservices.com/math/cubic.html

24. anonymous

Okay on the step where you take C', you make incorrect use of the quotient rule. The derivative of the top will be 0.

25. anonymous

The correct derivative is: $$\Large C' = \frac{-27900}{r^2} + 62\pi*r$$

26. anonymous

Set the derivative equal to 0 and solve: $$\Large \frac{-27900}{r^2} + 62\pi*r = 0$$ $$\Large (\frac{-27900}{r^2} + 62\pi*r)*r^2 = 0*r^2$$ $$\Large -27900 + 62\pi*r^3 = 0$$ $$\Large 62\pi*r^3 = 27900$$ You good from there?