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Simple circle problem involving area and circumference

  • Thread starter astrololo
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  • #26
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OK. Let's do it using limits. Let A(t) = the area at time t, and let A(t+Δt) = area at time t + Δt. Also, let C(t) = circumference at time t, and let C(t+Δt) be the circumference at time t+Δt. Starting with your general equation for A in terms of C, write an equation for A(t+Δt) - A(t) in terms of C(t+Δt) and C(t).
Ok, I need to go now. I'll answer you when I get time. I'm very sorry :/
 
  • #27
SteamKing
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Yeah sorry about that :

$$\frac{c}{2*\pi}$$
Then, if c is the circumference of the circle, the expression above can be simplified further still.
 
  • #28
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Then, if c is the circumference of the circle, the expression above can be simplified further still.
The problem statement implies expressing dA/dt entirely in terms of the circumference and its time derivative.

Chet
 
  • #29
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Then, if c is the circumference of the circle, the expression above can be simplified further still.
How ? I don't know what there is to do next.
 
  • #30
SteamKing
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How ? I don't know what there is to do next.
What's the formula for the circumference of a circle?
 
  • #31
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What's the formula for the circumference of a circle?
c=2*##\pi##*r
 
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  • #32
SteamKing
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c=2*##\pi##*r
Sigh... and what happens when you divide C by 2π ?
 
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  • #33
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Sigh... and what happens when you divide C by 2π ?
You obtian the radius. Btw why are you desesperate lol
 
  • #34
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I was hoping you would start working this problem using the method I was leading you to in post #25. This method involves using limits (which is the main requirement for your teacher). If you do what I suggested in post #25 (which is the first step in the derivation), I can lead you through, step by step, to the final result. But I need you to start.

Chet
 
  • #35
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$$A(t)=\frac{C^2(t)}{4\pi}$$
$$A(t+Δt)=\frac{C^2(t+Δt)}{4\pi}$$
$$A(t+Δt)-A(t)=\frac{C^2(t+Δt)-C^2(t)}{4\pi}$$
Do you know how to factor the numerator of the right hand side?
 

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