help please .. it is about derivatives application

Question

anonymous · Answer

attachment

xapproachesinfinity · Answer

Related rates!
first what the Area of a circle?

xapproachesinfinity · Answer

First Break thing down to know what you are looking for
they want the rate of change of the radius meaning they looking for 
$\large \frac{d}{dt}(r)$

xapproachesinfinity · Answer

Yes?

anonymous · Answer

ok

xapproachesinfinity · Answer

Hey you there! @forzamilan

xapproachesinfinity · Answer

do you got what i did just know?

xapproachesinfinity · Answer

So what is the area of circle? the formula

anonymous · Answer

I'm trying to figure it out

anonymous · Answer

a=pie(r)^2

xapproachesinfinity · Answer

yes $\large A=\pi~r^2$
Now take the derivative of that with respect to t (time)

xapproachesinfinity · Answer

differentiate the equation implicitly

anonymous · Answer

so the answer is 3?

anonymous · Answer

m/s

xapproachesinfinity · Answer

I don't know what the answer is! do the step and will see

xapproachesinfinity · Answer

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kainui · Answer

So both area and radius are changing over time right? Then this means Area and Radius are both functions of time. And we also know they're related by the unforgettable A=pi*r^2

So let's write them as being functions of time: $$\LARGE A(t)=\pi [r(t)]^2$$ Now let's take the derivative of this equation with respect to time. $$\LARGE A'(t)=2 \pi *r(t) * r'(t)$$ I just used the chain rule. Now why did I take the derivative? Because I knew from the question we were given that at a specific time, which I will just call t_0 to distinguish it as being a specific moment in time,  $$\LARGE A'(t_0)=150 \frac{m^2}{s}$$ and $$\LARGE r(t_0)=25 m$$

So now we have everything we need to solve for $$\LARGE r'(t_0)$$

anonymous · Answer

thnx everyone i got it :)

xapproachesinfinity · Answer

@Kainui  has explained in details^_^