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+1
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Who can finish it first??

ProMagma  Nov 4, 2017
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6+0 Answers

 #1
avatar+499 
+1

Is anyone going to try?

ProMagma  Nov 4, 2017
 #2
avatar+304 
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
avatar+499 
+1

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

 

Good Luck

 

laugh

ProMagma  Nov 4, 2017
 #4
avatar+499 
+1

The derivative of the surface area of a cone..

ProMagma  Nov 4, 2017
 #5
avatar+78762 
+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

 

 

 

cool cool cool 

CPhill  Nov 5, 2017
 #6
avatar+499 
+1

Good Job CPhill!!

 

I am VERY impressed!!

 

laughlaughlaugh

ProMagma  Nov 6, 2017

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