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AP Calculus

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The radius of a circle is decreasing at a constant rate of 0.1 centimeters per second. In terms of the circumference C, what is the rate of the area of the circle, in square centimeters per second?

a. -(0.2)pie C
b. -(0.1)C
c. -(0.1)C/2 pie
d. (0.1)^2C
e. (0.1)^2 pie C

  • AP Calculus - ,

    C=2πr

    A=πr²
    dA/dr=2πr=C

    dr/dt=-0.1 cm/sec

    dA/dt
    = dA/dr * dr/dt
    = 2πr (-0.1) cm²/s
    = -0.1C cm²/s

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