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Supply and Demand The demand and supply equations for a cordless screwdriver are given by
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Chapter 1 Solutions
CALCULUS: APPLIED APPROACH LOW COST MA
- The resistance of a copper wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. A copper wire with a diameter of 0.0126inch has a resistance of 64.9ohms per thousand feet. What length of 0.0201-inch-diameter copper wire will produce a resistance of 33.5ohms?arrow_forwardThe rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the original substance, x is the amount of substance formed, and k is a constant of proportionality. Factor the expression.arrow_forwardDemand A company has found that the daily demand x for its boxes of chocolates is inversely proportional to the price p. When the price is $5, the demand is 800 boxes. Approximate the demand when the price is increased to $6.arrow_forward
- The maximum weight M that can be supported by a beam is jointly proportional to its width w and the square of its height h and inversely proportional to its length L. a Write an equation that expresses this proportionality. b Determine the constant of proportionality if a beam 4 in. wide, 6 in. high, and 12 ft long can support a weight of 4800 lb. c If a 10-ft beam made of the same material is 3 in. wide and 10 in. high, what is the maximum weight it can support?arrow_forwardXander’s new business found that the daily demand for its product was inversely proportional to the price, p. When the price is $5, the demand is 700 units. (a) Write the equation of variation. (b) What is the demand if the price is raised to $7?arrow_forwardElectrical resistance The resistance of a wire varies directly as the length of the wire and inversely as the square of its diameter. A 1000-foot length of wire, 0.05 inch in diameter, has a resistance of 200 ohms. What would be the resistance of a 1500-foot length of wire that is 0.08 inch in diameter.arrow_forward
- A car’s value varies inversely with its age. Elena bought a two-year-old car for $20,000. a. Write the equation of variation. b. What will be the value of Elena’s car when it is 5 years old?arrow_forwardThe time required to empty a pool varies inversely as the rate of pumping. It took Lucy 2.5 hours to empty her pool using a pump that was rated at 400 gpm (gallons per minute). a. Write the equation of variation. b. How long will it take her to empty the pool using a pump rated at 500 gpm?arrow_forwardRoad Trip The number of hours it takes Jack to drive from Boston to Bangor is inversely proportional to his average driving speed. When he drives at an average speed of 40 miles per hour, it takes him 6 hours for the trip. a. Write the equation that relates the number of hours, h, with the speed, s. b. How long would the trip take if his average speed was 75 miles per hour?arrow_forward
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