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3.7 Related Rates

Learn how to solve various related rate problems involving area, ladder movement, sand pouring, and distance changes with step-by-step solutions.

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3.7 Related Rates

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  1. 3.7 Related Rates

  2. 3.7 Related Rates #6. Let A be the area of a circle of radius r,and assume that r increases with the time t. (a)Draw a picture of the circle with the labels A and r placed appropriately. (b) Write an equation that relates A and r. (c)Usethe equation in part (b) to find an equation that relates dA/dt and dr/dt. (d) At a certain instant the radius is 5 cm and increasing at the rate of 2 cm/s. How fast is the area increasing at that instant?

  3. 3.7 Related Rates • #16. A 17-ft ladder is leaning against a wall. If the bottom of the ladder is pulled along the ground away from the wall at a constant rate of 5 ft/s, how fast will the top of the ladder be moving down the wall when it is 8 ft above the ground?

  4. 3.7 Related Rates • #27. Sand pouring from a chute forms a conical pile whose height is always equal to the diameter. If the height increases at a constant rate of 3 ft/min, at what rate is sand pouring from the chute when the pile is 10 ft high?

  5. 3.7 Related Rates • #39. A point P is moving along the line whose equation is y = 2x. How fast is the distance between P and the point (3,0) changing at the instant when P is at (3,6) if x is decreasing at the rate of 2 units/s at that instant?

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