- #1
EricPowell
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Homework Statement
32) A stone dropped into a pond at time t=0 seconds causes a circular ripple that ravels out from the point of impact at 5 metres per second. At what rate (in square metres per second) is the area within the circle increasing when t=10?
Homework Equations
I need to use the chain rule dy/dx = dy/du x du/dx
The Attempt at a Solution
The area of a circle is A=∏r2
Differentiating this formula will tell me the rate at which the area increases for a specific radius
dA/dr=2∏r
The rate at which the radius increases is 5 metres per second, so I think that would be expressed as
dr/dt=5m/s
I need to find the rate of change of the area of the circle at 10 seconds. Using this chain rule, I think this would be found with
dA/dt=dA/dr x dr/dt
where dA/dt is the derivative of area as a function of time. So multiplying these derivatives gives me
dA/dt=dA/dr x dr/dt
=(2∏r)(5m/s)
=(50∏rm)/s
The radius at 10 seconds by multiplying 5m/s x 10s =50m. So I substitute 50m in for r.
=(50∏(50m)m)/s
=(2500∏m2)/2
I'm struggling a bit in my calculus class and I'm a bit unsure about all of this. Am I going in the right direction with my solution attempt above?
Also I noticed on these forums that people are entering equations and formulas in "fancy text", if I may call it that. What I mean is making math stuff look like what one would see in a textbook, as opposed to using unicode characters like I did above. How can I do that?