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Chapter 2 / Exercise 17
Trigonometry
McKeague/Turner Expert Verified Unformatted text preview: 10/14/2018 2.8 Related Rates Priscila Ribeiro MTH 2207 ­ Fall 2018, section TMWC, Fall 2018 2.8 Related Rates (Homework) Instructor: Alassane Ngaide Current Score : 14 / 19 Due : Sunday, October 14 2018 11:59 PM EDTLast Saved : n/a Saving... WebAssign 1. 2/2 points | Previous AnswersLarApCalc10 2.8.001. Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. y = x (a) Find dy/dt, when x = 9, given that dx/dt = 9. 3/2 (b) Find dx/dt, when x = 81, given that dy/dt = 6. 108 2. 2/2 points | Previous AnswersLarApCalc10 2.8.003. Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. xy = 4 (a) Find dy/dt, when x = 8, given that dx/dt = 12. ‑3/4 (b) Find dx/dt, when x = 1, given that dy/dt = −6. 3/2 1/5 10/14/2018 2.8 Related Rates 3. 2/2 points | Previous AnswersLarApCalc10 2.8.005.MI. The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of the area when r = 7 inches and r = 24 inches. (a) r = 7 inches 42π in2/min (b) r = 24 inches. 144π in2/min 4. 2/2 points | Previous AnswersLarApCalc10 2.8.009. A spherical balloon is inflated with gas at a rate of 14 cubic feet per minute. How fast is the radius of the balloon changing at the instant the radius is 1 foot and 8 feet? (a) 1 foot 72π ft/min (b) 8 feet 7128π ft/min 2/5 10/14/2018 2.8 Related Rates 5. 2/3 points | Previous AnswersLarApCalc10 2.8.012. A company that manufactures pet toys calculates that its costs and revenue can be modeled by the equations 2 C = 15,000 + 1.25x and R = 500x − x 25 where x is in the number of toys produced in 1 week. Production during one particular week is 5000 toys and is increasing at a rate of 350 toys per week. Find the rate at which the cost, revenue, and profit are changing. (a) cost dC = dt dollars/week (b) revenue dR = dt dollars/week 437.5 35000 (c) profit dP = dt dollars/week 6. 2/2 points | Previous AnswersLarApCalc10 2.8.015. All edges of a cube are expanding at a rate of 9 centimeters per second. How fast is the volume changing when each edge is 2 centimeters and 13 centimeters? (a) 2 centimeters 108 cm3/sec (b) 13 centimeters 4563 cm3/sec 3/5 10/14/2018 2.8 Related Rates 7. 2/2 points | Previous AnswersLarApCalc10 2.8.016.MI. All edges of a cube are expanding at a rate of 4 centimeters per second. How fast is the surface area changing when each edge is 8 centimeters and 14 centimeters? (a) 8 centimeters 384 cm2/sec (b) 14 centimeters 672 cm2/sec 8. –/1 pointsLarApCalc10 2.8.020. A (square) baseball diamond has sides that are 90 feet long (see figure). A player running from second base to third base at a speed of 23 feet per second is 20 feet from third base. At what rate is the player's distance from home plate changing? (Round your answer to two decimal places.) ft/sec 9. –/2 pointsLarApCalc10 2.8.021.MI. An air traffic controller spots two airplanes at the same altitude converging to a point as they fly at right angles to each other. One airplane is 150 miles from the point and has a speed of 600 miles per hour. The other is 200 miles from the point and has a speed of 800 miles per hour. (a) At what rate is the distance between the planes changing? mph (b) How much time does the controller have to get one of the airplanes on a different flight path? min 4/5 10/14/2018 2.8 Related Rates 10.–/1 pointsLarApCalc10 2.8.024. A company is increasing the production of a product at the rate of 25 units per week. The demand and cost functions for the product are given by p = 50 − 0.03x and C = 4000 + 30x − 0.04x2, where x is the number of units produced per week. Find the rate of change of the profit with respect to time (in dollars per week) when the weekly sales are x = 500 units. \$ per week 5/5 ...
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