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Related Rates

Related Rates. An application of the derivative. Formulas you should know. Trust me!. Formulas. Formulas. Right Circular Cone. If one of these is on the test, I’ll give you the formula!. Example #1.

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Related Rates

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  1. Related Rates An application of the derivative

  2. Formulas you should know Trust me!

  3. Formulas

  4. Formulas

  5. Right Circular Cone If one of these is on the test, I’ll give you the formula!

  6. Example #1 • A circular pool of water is expanding at the rate of 16π in2/sec. At what rate is the radius expanding when the radius is 4 inches?

  7. Example #2 • A 25-foot ladder is leaning against a wall and sliding toward the floor. If the foot of the ladder is sliding away from the base of the wall at a rate of 15 ft/sec, how fast is the top of the ladder sliding down the wall when the top of the ladder is 7 feet from the ground?

  8. Example #3 • A spherical balloon is expanding at a rate of 60π in3/sec. How fast is the surface area of the balloon expanding when the radius of the balloon is 4 inches?

  9. Example #4 • An underground conical tank, standing on its vertex, is being filled with water at a rate of 18π ft3/min. If the tank has a height of 30 feet and a radius of 15 feet, how fast is the water level rising when the water is 12 feet deep?

  10. Example #5 • A circle is increasing in area at a rate of 16π in2/sec. How fast is the radius increasing when the radius is 2 inches?

  11. Example #6 • A rocket is rising vertically at a rate of 5400 mph. An observer on the ground is standing 20 mi from the launch point. How fast (in radians/hr) is the angle of elevation b/w the ground and the observers line of sight is the rocket increasing when the rocket is at an elevation of 40 miles?

  12. Example #7 • Water is being drained out of a conical tank. Suppose the height is changing at a rate of -.2 ft/min and the radius is changing at a rate of -.1 ft/min. What is the rate of change in the volume when the radius is 1 and the height is 2?

  13. Example #8 • A pebble is dropped into a calm pond causing ripples in the form of circles. The radius of the outer ripple is increasing at a constant rate of 1 ft/sec. When the radius is 4 feet, at what rate is the area of the disturbed water changing?

  14. Example #9 • Air is being pumped into a spherical balloon at a rate of 4.5 cubic in/min. Find the rate of change of the radius when the radius is 2 inches.

  15. Example #10 • An airplane is flying on a flight path that will take it directly over a radar station. If the distance between the radar and the plane is decreasing at a rate of 400 mi/hr when that distance is 10 miles, what is the speed of the plane? The plane is traveling at an altitude of 6 miles.

  16. Example: From text #11(will have variables in answer) • Find the rate of change of the distance between the origin and a moving point on the graph of y=x2+1 if dx/dt = 2 cm/sec

  17. Example #12 • Suppose a spherical balloon is inflated at the rate of 10 cubic cm per min. How fast is the radius of the balloon increasing when the radius is 5 cm?

  18. Example #13 • One end of a 13-ft ladder is on the floor and the other end rests against a vertical wall. If the bottom of the ladder is drawn away from the wall at 3 ft/sec, how fast is the top of the ladder sliding down the wall when the bottom of the ladder is 5 feet from the wall?

  19. Example #14 • Water is poured into a conical paper cup at the rate of 2/3 cubic inches per sec. If the cup is 6 in tall and the top of the cup has a radius of 2 in, how fast does the water level rise when the water is 4 in deep?

  20. Example #15 • Pat walks at the rate of 5 ft/sec toward a street light whose lamp is 20 ft above the base of the light. If Pat is 6 ft tall, determine the rate of change of the length of Pat’s shadow at the moment when Pat is 24 feet from the base of the lamppost.

  21. Example #16

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