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Section 6.6 Related Rates

Section 6.6 Related Rates. 1. When a circular plate of metal is heated in an oven its radius increases at a rate of 0.01 cm/min . At what rate is the plate’s area increasing when the radius is 50 cm ?.

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Section 6.6 Related Rates

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  1. Section 6.6 Related Rates

  2. 1. When a circular plate of metal is heated in an oven its radius increases at a rate of 0.01 cm/min. At what rate is the plate’s area increasing when the radius is 50 cm?

  3. 2. The length L of a rectangle is decreasing at the rate of 2 cm/sec and the width W is increasing at the rate of 2 cm/sec. When L = 12 cm and W = 5 cm, find the rates of change of: (a) the area

  4. 2. The length L of a rectangle is decreasing at the rate of 2 cm/sec and the width W is increasing at the rate of 2 cm/sec. When L = 12 cm and W = 5 cm, find the rates of change of: (b) the perimeter The perimeter does not change

  5. 2. The length L of a rectangle is decreasing at the rate of 2 cm/sec and the width w is increasing at the rate of 2 cm/sec. When L = 12 cm and w = 5 cm, find the rates of change of: (c) the lengths of the diagonals of the rectangle?

  6. 3. Sand falls from a conveyor belt onto a conical pile at the rate of 10 cubic feet per minute. The radius of the base of the pile is always equal to ½ of the altitude. How fast is the altitude of the pile increasing when the pile is 5 feet high?

  7. 4. A point moves on the curve so that its y-coordinate increases at a constant rate of 6 meters per second. a. At what rate is the x-coordinate changing when x = 4 meters? b. What is the slope of the curve when x = 4 m?

  8. 5. A spherical balloon is inflated with gas at the rate of 100 cubic feet per minute. a. Assuming that the gas pressure remains constant, how fast is the radius of the balloon increasing at the instant when the radius is three feet? b. How fast is the surface area increasing?

  9. 6. A point P moves from left to right along the curve at a constant horizontal speed of 3 units per second. Howfast does the y-coordinate of P increase at the moment when P passes through (2, 4)?

  10. 7. The length of the base of a right triangle is increasing at the rate of 2 inches per minute. At the same time, the height of the triangle is decreasing in such a way that the length of the hypotenuse remains 10 inches. When the length of the base is 6 inches, how quickly is the height of the triangle changing?

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