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Check the picture below, notice those three quadrilaterals.
the square, is really a rectangle and is also a rhombus, but with right-angles and equal sides.
the square, is really a rectangle and is also a rhombus, but with right-angles and equal sides.
2) The formula for the area of a circle is: A = 
Differentiate both sides to get:
where dA/dt is the rate of change of the area of the circle with respect to time, and dr/dt is the rate of change of the radius of the circle with respect to time.
We want to know dA/dt when r = 3 and dr/dt = 2, so plug those into the equation to get:
3) The amount of revenue gained in a week is equal to the price per good times the number of goods sold, or R = x*p. Thus, R = x(150-.002x) = 150x - .002x^2. Differentiate both sides to get:
, where dR/dt is the rate of change of revenue and dx/dt is the rate of change of production.
We want dR/dt when dx/dt = 200 and x = 2000, so plug those in to get:
Differentiate both sides to get:
where dA/dt is the rate of change of the area of the circle with respect to time, and dr/dt is the rate of change of the radius of the circle with respect to time.
We want to know dA/dt when r = 3 and dr/dt = 2, so plug those into the equation to get:
3) The amount of revenue gained in a week is equal to the price per good times the number of goods sold, or R = x*p. Thus, R = x(150-.002x) = 150x - .002x^2. Differentiate both sides to get:
We want dR/dt when dx/dt = 200 and x = 2000, so plug those in to get: