Homework11 8-14
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University of Southern Mississippi *
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Mathematics
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Apr 3, 2024
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docx
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Homework11 Homework11: Problem 8 Previous Problem Problem List Next Problem (1 point) A 14 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 4 ft/s, how fast will the foot be moving away from the wall when the top is 13 feet above the ground? The foot will be moving at 10.007 ft/s. Previous Problem Problem List N\ [Sad g (elol [y (1 point) A street light is at the top of a 18 foot tall pole. A 6 foot tall woman walks away from the pole with a speed of 6 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 30 feet from the base of the pole? The tip of the shadow is moving at 9 ft/sec. (1 point) Aboat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 9 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 12 ft/min, at what rate will the boat be approaching the dock when 100 ft of rope is out? The boat will be approaching the dock at 12.04 ft/min. Hint: Sketch a diagram of this situation. (1 point) Gravel is being dumped from a conveyor belt at a rate of 30 ft* /min. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 20 ft high? The height is increasing at 3/(10pi) ft/min. (1 point) The altitude (i.e., height) of a triangle is increasing at a rate of 1.5 cm/minute while the area of the triangle is increasing at a rate of 3 square cm/minute. At what rate is the base of the triangle changing when the altitude is 10 centimeters and the area is 87 square centimeters? The base is changing at 0.04383 cm/min. Submit Answers (1 point) If two resistors with resistances R; and R, are connected in parallel, as in the figure, then the total resistance R, measured in Ohms (£2), is given by: 1_1,1 R R, R, If R, and R, are increasing at rates of .3 (/s and .2 /s, respectively, how fast is R increasing when R; = 80 and R, = 100 Q? 0.132 Q/s (1 point) A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.4 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 9 cm. (Note the answer is a positive number). 50.89
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