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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: An Applied Approach (Providence College: MTH 109)
- The 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_forwardThe 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_forward
- Xander’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_forwardThe force needed to break a board varies inversely with its length. Richard uses 24 pounds of pressure to break a 2-foot long board. a. Write the equation of variation. b. How many pounds of pressure is needed to break a 5-foot long board?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_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_forwardThe kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?arrow_forward
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