Solve the problem,
1) A stack of poles has 22 poles in the bottom row, 21 poles in the next row, and so on, with 6 poles in the top row. How many poles are there in the stack?
2) In the formula N = Iekt> N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a ce n country to double if its annual growth rate is 2.5%? Round to the nearest year.
3) A rectangular piece of cardboard measuring 26 inches by 42 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the sides.
Let x represent the length of a side of each such square. What is the maximum volume of this box? If necessary, round to 2 decimal places.
4) A rectangular piece of cardboard measuring 15 inches by 24 inches is to be made into a boxwith an open top by cutting equal size squares from each comer and folding up the sides.
Let x represent the length of a side of each such square. For what value of x will the volume be a maximum? If necessary, round to 2 decimal places.
5) Northwest Molded molds plastic handles which cost $0.70 per handle to mold. The fixed cost to run the molding machine is $5799 per week. If the company sells the handles for $ 3.70 each, how many handles must be molded weekly to break even?
6) The volume V of a 19-gram object varies inversely with the density Q in grams per milliliters, V = 19/Q. Find lim V.
7) At what interest rate must $4800 be compounded annually to equal $9051.12 after 13 yr? 11) (Round to the nearest percent.)
8) The volume V of a given mass of gas varies directly as the temperature T and inversely as the pressure P. If V = 550.0 in.3 when T = 500° and P = 10 lb/in .2, what is the volume when T = 350° and P = 15 lb/in.2?
9) The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 36 hours for 9 carpenters to frame a house, then how long will it take 63 carpenters to do the same job?
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?
10) 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.
11) Sketch a graph that depicts the amount of water in a 50-gallon tank during the course of 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.
12) 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.
13) Suppose the government wants to impose a tax on fossil fuels to reduce carbon emissions. 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.
14) 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?
15) 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?
16) Assume that the sales of a certain appliance dealer are approximated by a linear function.Suppose that sales were $8500 in 1982 and $51,000 in 1987. Let x = 0 represent 1982. Find the equation giving yearly sales y.
17) Employees of a publishing company received an increase in salary of 6% plus a bonus of $500. Find the new salary if the old salary was $23,000.
18) Georgianna Petrillo's Pizza Parlor had startup costs of $5900, The material for each pizza cost $4.50. She sells each pizza for $10. Express the revenue R as a function of x, where x is the number of pizzas sold.
19)The graph below depicts the annual coat production at the Warm Fuzzy Coat Factory during the years from 1988 to 1997. Solve the problem.
Use interval notation to represent the years when production of wool sport coats was greater than or equal to the production of polyester sport coats. Include both endpoints of the interval.
20) Vertex: (2,3) point: (1,4) Find the linear equation that meets the stated criteria.
21) The linear equation y = 243x + 6320 provides an approximation of the annual cost (in dollars) to rent an apartment at the Leisure Village Retirement Community, where x = 1 represents 1985, x = 2 represents 1986, and so on. prepare an equation that yields the same y-values when the exact year number is entered. Provide an appropriate response.