anonymous
  • anonymous
Related rates question!!! A circle is inscribed in a square. The area of the circle is increasing at a constant rate^2/sec. As the circle expands the square expands to keep the circle inscribed at what rate is the area of the square increasing in in^2/sec ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1443498489098:dw|
jim_thompson5910
  • jim_thompson5910
is there a typo? `The area of the circle is increasing at a constant rate^2/sec`
anonymous
  • anonymous
yep sorry about that " the area of the circle is increasing at a constant rate of 15pi in^2/sec

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jim_thompson5910
  • jim_thompson5910
oh ok that makes more sense now
anonymous
  • anonymous
;P , alright so for the area of the square im getting (2r)^2 , not sure where to go on frem there
jim_thompson5910
  • jim_thompson5910
|dw:1443498822076:dw| hopefully you see how the diameter d is equal to the side length of the square
jim_thompson5910
  • jim_thompson5910
yes the side length is 2r
jim_thompson5910
  • jim_thompson5910
A = (2r)^2 = 4r^2
jim_thompson5910
  • jim_thompson5910
if A = 4r^2, then what is dA/dt ?
anonymous
  • anonymous
8r dr/dt
jim_thompson5910
  • jim_thompson5910
yes
anonymous
  • anonymous
okay but we dont have dr/dt we only have da/dt of the circle
jim_thompson5910
  • jim_thompson5910
Circle Ac = pi*r^2 dAc/dt = 2*pi*r*dr/dt 15pi = 2*pi*r*dr/dt
jim_thompson5910
  • jim_thompson5910
Rectangle Ar = 4r^2 dAr/dt = 8r*dr/dt try to connect dAc/dt and dAr/dt somehow
anonymous
  • anonymous
15/2r = dr/dt
jim_thompson5910
  • jim_thompson5910
I'm thinking to divide the two so maybe dAc/dt divided by dAr/dt
jim_thompson5910
  • jim_thompson5910
(dAc/dt)/(dAr/dt) = [ 2*pi*r*dr/dt ] / [8r*dr/dt] the 'r' and 'dr/dt' terms will cancel to get (dAc/dt)/(dAr/dt) = pi/4
anonymous
  • anonymous
okay one sec let me process this
anonymous
  • anonymous
okay nvm i found an easier way
anonymous
  • anonymous
okay so we know that dr/dt = 15/2r and we know that dAr/dt = 8r dr/dt so if you just plug in dr/dt into the dAr/dt formula you get 120r/2r which gives us 60 which i know to be the answer
jim_thompson5910
  • jim_thompson5910
60 is correct
jim_thompson5910
  • jim_thompson5910
alternatively, you can let x = dAr/dt, so (dAc/dt)/(dAr/dt) = pi/4 (15pi)/(x) = pi/4 15pi*4 = pi*x 60pi = pi*x x*pi = 60pi x = 60
anonymous
  • anonymous
yep didn't see that , thanks for your help really appreciate it :D
jim_thompson5910
  • jim_thompson5910
no problem

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