## burhan101 Group Title Solve for r one year ago one year ago

1. burhan101 Group Title

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

2. calculusxy Group Title

You are trying to find the area of a radius?

3. calculusxy Group Title

Sorry I meant the area of a circle.

4. burhan101 Group Title

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

5. calculusxy Group Title

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. SmoothMath Group Title

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

7. SmoothMath Group Title

Oh my bad. You actually get a cubic.

8. burhan101 Group Title

top and bottom or just top?

9. SmoothMath Group Title

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

10. burhan101 Group Title

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

11. SmoothMath Group Title

Just r^2

12. burhan101 Group Title

yeah so woulnt that cancel out with the fraction

13. SmoothMath Group Title

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

14. burhan101 Group Title

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

15. SmoothMath Group Title

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

16. SmoothMath Group Title

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

17. SmoothMath Group Title

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

18. burhan101 Group Title

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

19. Bad2zBone Group Title

Are you sure the question is correct?

20. burhan101 Group Title

21. Bad2zBone Group Title

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

22. burhan101 Group Title

here is the question and my solution

23. Bad2zBone Group Title

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

24. SmoothMath Group Title

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. SmoothMath Group Title

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

26. SmoothMath Group Title

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?