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Chapter 1: Problem 39
Find all real values of \(x\) such that \(f(x)=0\). $$f(x)=\frac{3 x-4}{5}$$
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The median sale prices \(p\) (in thousands of dollars) of an existing one-family home in the United States from 2000 through 2010 (see figure) can be approximated by the model \(p(t)=\left\\{\begin{array}{ll}0.438 t^{2}+10.81 t+145.9, & 0 \leq t \leq 6 \\ 5.575 t^{2}-110.67 t+720.8, & 7 \leq t \leq 10\end{array}\right.\) where \(t\) represents the year, with \(t=0\) corresponding to \(2000 .\) Use this model to find the median sale price of an existing one-family home in each year from 2000 through \(2010 .\) (Source: National Association of Realtors) (GRAPH CAN'T COPY)
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) Use Hooke's Law for springs, which states that the distance a spring is stretched (or compressed) varies directly as the force on the spring.
Find the difference quotient and simplify your Answer: $$f(t)=\frac{1}{t-2}, \quad \frac{f(t)-f(1)}{t-1}, \quad t \neq 1$$
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(F\) is jointly proportional to \(r\) and the third power of \(s\) \((F=4158 \text { when } r=11 \text { and } s=3 .)\)
Match the data with one of the following functions $$f(x)=c x, g(x)=c x^{2}, h(x)=c \sqrt{|x|}, \quad \text {and} \quad r(x)=\frac{c}{x}$$ and determine the value of the constant \(c\) that will make the function fit the data in the table. $$\begin{array}{|c|c|c|c|c|c|}\hline x & -4 & -1 & 0 & 1 & 4 \\\\\hline y & -32 & -2 & 0 & -2 & -32 \\\\\hline \end{array}$$
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