) The diameter of a circle is increasing at a rate of 5 cm/sec. How fast is the area changing with time when the diameter is 20 cm

50π cm²/s

Step-by-step explanation:

Area of the circle A = πd²/4

Rate at which the area is changing with time is expressed as;

dA/dt = dA/dd*dd/dt

dd/dt is the rate at which the diameter is changing with time

dd/dt = 5cm/sec

dA/dd = 2πd/4

dA/dd = πd/2

Given that d = 20cm

dA/dt = dA/dd*dd/dt

dA/dt = πd/2*5

dA/dt = 20π/2 *5

dA/dd = 10π * 5

dA/dd = 50π cm²/s

Hence the area is changing at the rate of  50π cm²/s

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,

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