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Chapter 1: Problem 28
Find the \(x\) - and \(y\) -intercepts of the graph of the equation. $$y=-|x+10|$$
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Graph each of the functions with a graphing utility. Determine whether the function is even, odd, or neither. $$\begin{aligned}&\begin{array}{ll}f(x)=x^{2}-x^{4} & g(x)=2 x^{3}+1 \\\h(x)=x^{5}-2 x^{3}+x & j(x)=2-x^{6}-x^{8}\end{array}\\\&k(x)=x^{5}-2 x^{4}+x-2 \quad p(x)=x^{9}+3 x^{5}-x^{3}+x \end{aligned}$$
The cost per unit in the production of an MP3 player is 60 dollars. The manufacturer charges 90 dollars per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by 0.15 dollars per MP3 player for each unit ordered in excess of 100 (for example, there would be a charge of 87 dollars per MP3 player for an order size of 120 ). (a) The table shows the profits \(P\) (in dollars) for various numbers of units ordered, \(x .\) Use the table to estimate the maximum profit. $$\begin{array}{|l|c|c|c|c|c|}\hline \text { Units, } x & 130 & 140 & 150 & 160 & 170 \\\\\hline \text { Profit, } P & 3315 & 3360 & 3375 & 3360 & 3315 \\\\\hline\end{array}$$ (b) Plot the points \((x, P)\) from the table in part (a). Does the relation defined by the ordered pairs represent \(P\) as a function of \(x ?\) (c) Given that \(P\) is a function of \(x,\) write the function and determine its domain. (Note: \(P=R-C\) where \(R\) is revenue and \(C\) is cost.)
The percents \(p\) of prescriptions filled with generic drugs in the United States from 2004 through 2010 (see figure) can be approximated by the model \(p(t)=\left\\{\begin{array}{ll}4.57 t+27.3, & 4 \leq t \leq 7 \\ 3.35 t+37.6, & 8 \leq t \leq 10\end{array}\right.\) where \(t\) represents the year, with \(t=4\) corresponding to \(2004 .\) Use this model to find the percent of prescriptions filled with generic drugs in each year from 2004 through \(2010 .\) (Source: National Association of Chain Drug Stores) (GRAPH CAN'T COPY)
The frequency of vibrations of a piano string varies directly as the square root of the tension on the string and inversely as the length of the string. The middle A string has a frequency of 440 vibrations per second. Find the frequency of a string that has 1.25 times as much tension and is 1.2 times as long.
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) Use the fact that 14 gallons is approximately the same amount as 53 liters to find a mathematical model that relates liters \(y\) to gallons \(x\) Then use the model to find the numbers of liters in 5 gallons and 25 gallons.
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