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Derivatives to Physical Systems:
A stone is dropped into a quiet lake, & waves move within circles outward from the location of the splash at a constant velocity of 0.5 feet per second. Determine the rate at that the area of the circle is increasing when the radius is 4 feet.
Solution:
Using the formula for the area of a circle,
A = πr2
obtain the derivative of both sides of this equation along with respect to time t.
dA/dt = 2πr (dr/dt)
But, dr/dt is the velocity of the circle moving outward which equals 0.5 ft/s and dA /dt is the rate at which the area is increasing, that is the quantity to be determined. Set r equal to 4 feet, substitute the known values into the equation, and solve for dA /dt.
dA/dt = 2πr(dr/dt)
dA/dt = (2)(3.1416)(4 ft)(0.5 ft/s)
dA/dt = 12.6 ft2/s
Therefore, at a radius of 4 feet, the area is raising at a rate of 12.6 square feet per second.
Explain Congruum?
Longer- Term Forecasting Moving averages, exponential smoothing and decomposition methods tend to be utilized for short to medium term forecasting. Longer term forecasting is
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2x-3x=6
how to play
x=ct,y=c/t d^2/dx^2
A telephone exchange has two long distance operators.The telephone company find that during the peak load,long distance calls arrive in a poisson fashion at an average rate of 15 p
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