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Hie gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 4 lb when the masses are 3 ft apart, what
is the attraction when the masses are 6 ft apart?
John has a jarful of quarters and nickels. There are 111 coins in the jar. The value of the coins is $16.75. How many of each type of coin are there?
Suppose the government wants to impose a tax on fossil fuels to reduce carbon emissions. 22)
The cost benefit is modeled by ln(l - P) = -0.0025 - 0.0056x, where x represents the dollars of tax per ton of carbon emitted and P represents the percent reduction in emissions of carbon. (P is in decimal form.) Determine P when x = 44. Round to three decimal places.
In September 1998 the population of the country of West Goma in millions was modeled 21) by f(x) = 16.9e0-0019x_ At the same time the population of East Goma in millions was modeled by g(x) = 13.5e0-0106x_ In both formulas x is the year, where x = 0 corresponds to September 1998. Assuming these trends continue, estimate what the population will be when the populations are equal.
Jim has gotten scoi*es of 64 and 98 on his first two tests. What score must he get on his third test to keep an average of 75 or greater?
The density Q of an object with a mass of 18 grams varies inversely with the volume V in 18) milliliters, q = m/V. Find lim q.
V^0+
Sketch a graph that depicts the amount of water in a 50-gallon tank during the course of 17) the described pumping operations. The tank is initially full, and then a pump is used to take water out of the tank at a rate of 4 gallons per minute. The pump is turned off after 5 minutes. At that point, the pump is changed to one that will pump water into the tank. The change takes 2 minutes and the water level is unchanged during the switch. Then, water is pumped into the tank at a rate of 3 gallons per minute for 3 minutes.
The intensity I of light varies inversely as the square of the distance D from tine source. If 16) the intensity of illumination on a screen 5 ft from a light is 4 foot candles, find the intensity ■ on a screen 20 ft from the light.
The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches: M(x) = 4x - x2. What rainfall produces the maximum number of mosquitoes?
Find the effective rate if the nominal rate is 4.0% and interest is compounded daily (n 365). (If r is the nominal rate and n is the number of times interest is compoundedn
annually, then R =
1 +■
- 1 is the effective rate.)*
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