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Chapter 1: Problem 52
Find a mathematical model for the verbal statement. \(h\) varies inversely as the square root of \(s\).
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Determine whether the statement is true or false. Justify your answer. If the inverse function of \(f\) exists and the graph of \(f \mathrm{~h}\) a \(y\) -intercept, then the \(y\) -intercept of \(f\) is an \(x\) -intercep of \(f^{-1}\)
Use the given value of \(k\) to complete the table for the direct variation model $$y=k x^{2}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=k x^{2} & & & & & \\ \hline \end{array}$$ $$ k=\frac{1}{2} $$
(a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=\frac{x+1}{x-2} $$
Find a mathematical model for the verbal statement. For a constant temperature, the pressure \(P\) of a gas is inversely proportional to the volume \(V\) of the gas.
Determine whether the variation model is of the form \(y=k x\) or \(y=k / x,\) and find \(k .\) Then write \(a\) model that relates \(y\) and \(x\). $$ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & 10 & 15 & 20 & 25 \\ \hline y & 2 & 4 & 6 & 8 & 10 \\ \hline \end{array} $$
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