To encourage buyers to place 100-unit orders, your firm's sales department applies a continuous discount that makes the unit price a function p(x) of the number of units x ordered. the discount decreases the price at a rate of $0.01 per unit ordered. the price per unit for a 100-unit order is p(100) = $20.09. a. find p(x) by solving the following initial value problem: differential equation: dp/dx = -p/100 initial condition: p(100) = 20.09b. find the unit price for a 10-unit order and the unit price for a 90-unit order. c. the sales department has asked you to find out if it is discounting so much that the firm's revenue, r(x)=x. p(x), will actually be less for a 100-unit order than say for a 90-unit order

Several processes form metal ore. match each process to its description. volcanic activity weathering hydrothermal energy rocks break down as they interact with air and water. arrowright density differences and other factors cause metals to concentrate in igneous rocks. arrowright seawater heats up from contact with hot rock, and metals dissolve in it. the water rises and contacts cooler water, causing metal ores to settle on the ocean floor. arrowright

The man fires an 80 g arrow so that it is moving at 80 m/s when it hits and embeds in a 8.0 kg block resting on ice. how far will the block slide on the ice before stopping? a 7.1 n friction force opposes its motion.

Na food processing facility, a spherical container of inner radius r1 5 40 cm, outer radius r2 5 41 cm, and ther- mal conductivity k 5 1.5 w/m · k is used to store hot water and to keep it at 100°c at all times. to accomplish this, the outer surface of the container is wrapped with a 800-w electric strip heater and then insulated. the temperature of the inner surface of the container is observed to be nearly 120°c at all times. as- suming 10 percent of the heat generated in the heater is lost through the insulation, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the container, (b) obtain a relation for the variation of temperature in the container material by solving the differential equation, and (c) evaluate the outer surface tempera- ture of the container. also determine how much water at 100°c this tank can supply steadily if the cold water enters at 20°c.