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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?
$A=πr^2\ \ and\ \ C=2πr$
$C=2πr$
$A=πr^2$
$A=πr^2\ \ and\ \ \ C\ =πd$
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?
$\frac{dC}{dt}=40$
$\frac{dr}{dt}=40$
$\frac{dA}{dt}=40$
$\frac{dπ}{dt}=40$
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?
$\frac{dA}{dt}\ when\ C=100π$
$\frac{dC}{dt}\ when\ A\ =\ 100π$
$\frac{dA}{dt}\ when\ A\ =\ 100π$
$\frac{dC}{dt}\ when\ r\ =\ 100π$
What is the derivative of circumference with respect to time?
$\frac{dC}{dt}=2π\cdot\frac{dr}{dt}$
$\frac{dC}{dt}=2π$
$\frac{dC}{dt}=2πr$
$\frac{dC}{dt}=π\cdot\frac{dr}{dt}$
What is the derivative of area with respect to time?
$\frac{dA}{dt}=2πr\cdot\frac{dr}{dt}$
$\frac{dA}{dt}=2πr$
$\frac{dA}{dt}=πr\cdot\frac{dr}{dt}$
$\frac{dA}{dt}=πr^2\cdot\frac{dr}{dt}$
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 is the length of the radius when the circumference is 100π ft?
$r=50\ ft$
$r=100\ ft$
$r=\sqrt{50}ft$
cannot be determined
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?
At what rate is the radius changing when the circumference is 100π ft?
$\frac{dr}{dt}=\frac{20}{π}$
$\frac{dr}{dt}=\frac{50}{π}$
$\frac{dr}{dt}=50$
$\frac{dr}{dt}=20$
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?
$\frac{dA}{dt}=2000\ \frac{ft^2}{\sec}$
$\frac{dA}{dt}=40\ \frac{ft^2}{\sec}$
$\frac{dA}{dt}=100\ \frac{ft^2}{\sec}$
$\frac{dA}{dt}=200\ \frac{ft^2}{\sec}$
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