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Section 4.6 – Related Rates 5.5 I can use implicit differentiation to solve related rate word problems. Day 1: Find the slope the following at x = 1:

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A 14 foot ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2 ft/s, how fast will the end be moving away from the wall when the top is 6 ft above the ground? 14 6 x y L The ladder is moving away at a rate of

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A man 6 ft tall is walking at a rate of 2 ft/s toward a street light 16 ft tall. At what rate is the size of his shadow changing? 6 16 x y The size of his shadow is reducing at a rate of 6/5.

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A boat whose deck is 10 ft below the level of a dock, is being drawn in by means of a rope attached to a pulley on the dock. When the boat is 24 ft away and approaching the dock at ½ ft/sec, how fast is the rope being pulled in? x y R 26 The rope is being pulled in at a rate of 6/13

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A pebble is dropped into a still pool and sends out a circular ripple whose radius increases at a constant rate of 4 ft/s. How fast is the area of the region enclosed by the ripple increasing at the end of 8 seconds. At t = 8, r = (8)(4) = 32 The area is increasing at a rate of

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A spherical container is deflated such that its radius decreases at a constant rate of 10 cm/min. At what rate must air be removed when the radius is 5 cm? 5 Air must be removed at a rate of

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A ruptured pipe of an offshore oil platform spills oil in a circular pattern whose radius increases at a constant rate of 4 ft/sec. How fast is the area of the spill increasing when the radius of the spill is 100 ft? The area of the spill is increasing at a rate of

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Sand pours into a conical pile whose height is always one half its diameter. If the height increases at a constant rate of 4 ft/min, at what rate is sand pouring from the chute when the pile is 15 ft high? 15 The sand is pouring from the chute at a rate of

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Liquid is pouring through a cone shaped filter at a rate of 3 cubic inches per minute. Assume that the height of the cone is 12 inches and the radius of the base of the cone is 3 inches. How rapidly is the depth of the liquid in the filter decreasing when the level is 6 inches deep? 12 3 h r The depth of the liquid is decreasing at a rate of

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If and x is decreasing at the rate of 3 units per second, the rate at which y is changing when y = 2 is nearest to: a. –0.6 u/s b. –0.2 u/s c. 0.2 u/s d. 0.6 u/s e. 1.0 u/s

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When a wholesale producer market has x crates of lettuce available on a given day, it charges p dollars per crate as determined by the supply equation If the daily supply is decreasing at the rate of 8 crates per day, at what rate is the price changing when the supply is 100 crates?

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