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Chapter 1: Problem 69
Write the standard form of the equation of the circle with the given characteristics. Center: (0,0)\(;\) Radius: 4
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Find a mathematical model for the verbal statement. The rate of growth \(R\) of a population is jointly proportional to the size \(S\) of the population and the difference between \(S\) and the maximum population size \(L\) that the environment can support.
Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\sqrt{x-2} $$
Find a mathematical model for the verbal statement. \(V\) varies directly as the cube of \(e\).
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 \(x\). $$ \begin{array}{|c|c|c|c|c|c|} \hline x & 5 & 10 & 15 & 20 & 25 \\ \hline y & 1 & \frac{1}{2} & \frac{1}{3} & \frac{1}{4} & \frac{1}{5} \\ \hline \end{array} $$
Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=3 x+5 $$
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