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anonymous

  • one year ago

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 ?

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  1. anonymous
    • one year ago
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    |dw:1443498489098:dw|

  2. jim_thompson5910
    • one year ago
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    is there a typo? `The area of the circle is increasing at a constant rate^2/sec`

  3. anonymous
    • one year ago
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    yep sorry about that " the area of the circle is increasing at a constant rate of 15pi in^2/sec

  4. jim_thompson5910
    • one year ago
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    oh ok that makes more sense now

  5. anonymous
    • one year ago
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    ;P , alright so for the area of the square im getting (2r)^2 , not sure where to go on frem there

  6. jim_thompson5910
    • one year ago
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    |dw:1443498822076:dw| hopefully you see how the diameter d is equal to the side length of the square

  7. jim_thompson5910
    • one year ago
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    yes the side length is 2r

  8. jim_thompson5910
    • one year ago
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    A = (2r)^2 = 4r^2

  9. jim_thompson5910
    • one year ago
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    if A = 4r^2, then what is dA/dt ?

  10. anonymous
    • one year ago
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    8r dr/dt

  11. jim_thompson5910
    • one year ago
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    yes

  12. anonymous
    • one year ago
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    okay but we dont have dr/dt we only have da/dt of the circle

  13. jim_thompson5910
    • one year ago
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    Circle Ac = pi*r^2 dAc/dt = 2*pi*r*dr/dt 15pi = 2*pi*r*dr/dt

  14. jim_thompson5910
    • one year ago
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    Rectangle Ar = 4r^2 dAr/dt = 8r*dr/dt try to connect dAc/dt and dAr/dt somehow

  15. anonymous
    • one year ago
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    15/2r = dr/dt

  16. jim_thompson5910
    • one year ago
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    I'm thinking to divide the two so maybe dAc/dt divided by dAr/dt

  17. jim_thompson5910
    • one year ago
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    (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

  18. anonymous
    • one year ago
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    okay one sec let me process this

  19. anonymous
    • one year ago
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    okay nvm i found an easier way

  20. anonymous
    • one year ago
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    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

  21. jim_thompson5910
    • one year ago
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    60 is correct

  22. jim_thompson5910
    • one year ago
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    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

  23. anonymous
    • one year ago
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    yep didn't see that , thanks for your help really appreciate it :D

  24. jim_thompson5910
    • one year ago
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    no problem

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