91Ó°ÊÓ

Given that \(f(x)=x^{2}-3\) and \(g(x)=2 x+1,\) find each of the following, if it exists. $$(f g)(2)$$

Find the variation constant and an equation of variation for the given situation. \(y\) varies inversely as \(x,\) and \(y=0.1\) when \(x=0.5\).

First, graph the equation and determine visually whether it is symmetric with respect to the \(x\) -axis, the \(y\) -axis, and the origin. Then verify your assertion algebraically. $$y=|x+5|$$

The amount of sales tax paid on a product is directly proportional to the purchase price. In lowa, the sales tax on a Nook Glowlight'm that sells for \(\$ 119\) is \(\$ 7.14 .\) What is the sales tax on an e-book that sells for \(\$ 21 ?\)

Graph the function. Estimate the intervals on which the function is increasing or decreasing and any relative maxima or minima. $$f(x)=4-x^{2}$$

Graph the function. Estimate the intervals on which the function is increasing or decreasing and any relative maxima or minima. $$f(x)=5-|x|$$

The time \(T\) required to do a job varies inversely as the number of people \(P\) working. It takes 5 hr for 7 bricklayers to build a park wall. How long will it take 10 bricklayers to complete the job?

The time \(t\) required to empty a tank varies inversely as the rate \(r\) of pumping. If a pump can empty a tank in 45 min at the rate of \(600 \mathrm{kL} / \mathrm{min}\), how long will it take the pump to empty the same tank at the rate of \(1000 \mathrm{kL} / \mathrm{min} ?\)

Test algebraically whether the graph is symmetric with respect to the \(x\) -axis, the \(y\) -axis, and the origin. Then check your work graphically, if possible, using a graphing calculator. $$y^{3}=2 x^{2}$$

The pitch \(P\) of a musical tone varies inversely as its wavelength \(W\). One tone has a pitch of 330 vibrations per second and a wavelength of \(3.2 \mathrm{ft}\). Find the wavelength of another tone that has a pitch of 550 vibrations per second.(IMAGE CAN'T COPY)