12th
-
University

Mathematics

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JUSTIN MEIDENBAUER

4 years

Mathematics

12th -

University

Derivative Real World Apps

JUSTIN MEIDENBAUER

64
plays

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?
$A=πr^2\ \ and\ \ C=2πr$
$C=2πr$
$A=πr^2$
$A=πr^2\ \ and\ \ \ C\ =πd$
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?
$\frac{dC}{dt}=40$
$\frac{dr}{dt}=40$
$\frac{dA}{dt}=40$
$\frac{dπ}{dt}=40$
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?
$\frac{dA}{dt}\ when\ C=100π$
$\frac{dC}{dt}\ when\ A\ =\ 100π$
$\frac{dA}{dt}\ when\ A\ =\ 100π$
$\frac{dC}{dt}\ when\ r\ =\ 100π$
4. Multiple Choice
30 seconds
1 pt
What is the derivative of circumference with respect to time?
$\frac{dC}{dt}=2π\cdot\frac{dr}{dt}$
$\frac{dC}{dt}=2π$
$\frac{dC}{dt}=2πr$
$\frac{dC}{dt}=π\cdot\frac{dr}{dt}$
5. Multiple Choice
30 seconds
1 pt
What is the derivative of area with respect to time?
$\frac{dA}{dt}=2πr\cdot\frac{dr}{dt}$
$\frac{dA}{dt}=2πr$
$\frac{dA}{dt}=πr\cdot\frac{dr}{dt}$
$\frac{dA}{dt}=πr^2\cdot\frac{dr}{dt}$
6. 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 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
7. 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?

At what rate is the radius changing when the circumference is 100π ft?
$\frac{dr}{dt}=\frac{20}{π}$
$\frac{dr}{dt}=\frac{50}{π}$
$\frac{dr}{dt}=50$
$\frac{dr}{dt}=20$
8. 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?
$\frac{dA}{dt}=2000\ \frac{ft^2}{\sec}$
$\frac{dA}{dt}=40\ \frac{ft^2}{\sec}$
$\frac{dA}{dt}=100\ \frac{ft^2}{\sec}$
$\frac{dA}{dt}=200\ \frac{ft^2}{\sec}$
9. Multiple Choice
5 minutes
1 pt
If y=2x-8, what is the minimum value of the product xy?
-16
-8
-4
2
10. Multiple Choice
30 seconds
1 pt
1
-1
0
DNE
11. Multiple Choice
1 minute
1 pt
0
5/3
e^5x
DNE
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Derivative Real World Apps

12th - University

Mathematics

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Derivative Real World Apps

64 plays

11 questions

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