Mathematics

12th -

University

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Derivative Real World Apps

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11 questions

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  • 1. Multiple Choice
    30 seconds
    1 pt

    Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?


    What equation(s) should be used?

    A=πr2 and C=2πrA=πr^2\ \ and\ \ C=2πr

    C=2πrC=2πr

    A=πr2A=πr^2

    A=πr2 and C =πdA=πr^2\ \ and\ \ \ C\ =πd

  • 2. Multiple Choice
    30 seconds
    1 pt

    Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?

    What rate is given in the problem?

     dCdt=40\frac{dC}{dt}=40 

     drdt=40\frac{dr}{dt}=40 

     dAdt=40\frac{dA}{dt}=40 

     dπdt=40\frac{dπ}{dt}=40 

  • 3. Multiple Choice
    30 seconds
    1 pt

    Oil spilled from a tanker spreads in a circle whose circumference increases at a rate of 40 ft/sec. How fast is the area of the spill increasing when the circumference of the circle is 100π ft?

    What rate are we looking for and when?

     dAdt when C=100π\frac{dA}{dt}\ when\ C=100π 

     dCdt when A = 100π\frac{dC}{dt}\ when\ A\ =\ 100π 

     dAdt when A = 100π\frac{dA}{dt}\ when\ A\ =\ 100π 

     dCdt when r = 100π\frac{dC}{dt}\ when\ r\ =\ 100π 

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