+0

**VERY HARD MATH PROBLEM**

0
2
452
6
+537

Who can finish it first??

Nov 4, 2017

#1
+537
-1

Is anyone going to try?

Nov 4, 2017
#2
+445
0

Did you create this problem and do you know the answer?

What is 'r'? If you give us a number that will make it easier to solve.

Mr.Owl  Nov 4, 2017
edited by Mr.Owl  Nov 4, 2017
#3
+537
-1

The problem is that you are trying to minimize the radius of a cone.. and this is the algebraic problem..

Good Luck

Nov 4, 2017
#4
+537
-1

The derivative of the surface area of a cone..

ProMagma  Nov 4, 2017
#5
+96189
+3

0 = pi  ( r^2  + 900 / [ pi^2 * r^4] )^(1/2) +   (pi *r / 2)( r^2  + 900 / [ pi^2 * r^4] )^(-1/2) *(2r - (3600) / [pi^2*r^5] )

- pi  ( r^2  + 900 / [ pi^2 * r^4] )^(1/2) = (pi *r / 2)( r^2  + 900 / [ pi^2 * r^4] )^(-1/2) *(2r - (3600) / [pi^2*r^5] )

- ( r^2  + 900 / [ pi^2 * r^4] )  =  ( r/2 ) (2r - (3600) / [pi^2*r^5] )

- ( r^6 * pi^2 + 900)  / [ pi^2 * r^4 ]   =   (r/2) (  2r^6 *pi^2 -3600)  / [pi^2 * r^5 ]

- ( r^6 * pi^2 + 900)r   =  (r/2) ( 2r^6 * pi^2 - 3600)

- ( r^6 * pi^2 + 900)r  = r ( r^6 * pi^2  - 1800)

- r^7*pi^2 - 900r  = r^7 * pi^2 - 1800r

2r^7 * pi^2  - 900  r  =   0

r ( r^6 * pi^2  - 450)  = 0

r = 0     [ no good ]       ..... or........

r^6 * pi^2  - 450  = 0

r^6 * pi^2  = 450

r^6   = 450 / pi^2

r^6  =   [225 *2] / pi^2

r^6  =  [2  *  15^2 ] / pi^2

r  =    6√ 2  * 3√ (15 / pi)  ≈  1.8901

Nov 5, 2017
#6
+537
-1

Good Job CPhill!!

I am VERY impressed!!

ProMagma  Nov 6, 2017