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Chapter 1: Problem 19
Determine the quadrant(s) in which \((x, y)\) is located so that the condition(s) is (are) satisfied. $$ y<-5 $$
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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 \(x\). $$ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & 10 & 15 & 20 & 25 \\ \hline y & 24 & 12 & 8 & 6 & \frac{24}{5} \\ \hline \end{array} $$
On a yardstick with scales in inches and centimeters, you notice that 13 inches is approximately the same length as 33 centimeters. Use this information to find a mathematical model that relates centimeters \(y\) to inches \(x\). Then use the model to find the numbers of centimeters in 10 inches and 20 inches.
Use the given value of \(k\) to complete the table for the inverse variation model $$y=\frac{k}{x^{2}}$$ Plot the points on a rectangular coordinate system. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=\frac{k}{x^{2}} & & & & & \\ \hline \end{array}$$ $$ k=2 $$
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. $$\begin{array}{|l|l|l|l|l|l|} \hline x & 2 & 4 & 6 & 8 & 10 \\ \hline y=k x^{2} & & & & & \\ \hline \end{array}$$ $$ k=\frac{1}{2} $$
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 \(f^{-1}\)
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