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Chapter 2: Problem 82
Simplify the rational expression by using long division or synthetic division. \(\frac{x^{3}+x^{2}-64 x-64}{x+8}\)
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Solve the inequality and graph the solution on the real number line. \(x^{2}>2 x+8\)
The cost \(C\) (in millions of dollars) of removing \(p \%\) of the industrial and municipal pollutants discharged into a river is given by \(C=\frac{255 p}{100-p}, \quad 0 \leq p<100\) (a) Use a graphing utility to graph the cost function. (b) Find the costs of removing \(10 \%, 40 \%,\) and \(75 \%\) of the pollutants. (c) According to this model, would it be possible to remove \(100 \%\) of the pollutants? Explain.
Use a graphing utility to graph the equation. Use the graph to approximate the values of \(x\) that satisfy each inequality. \(y=-x^{2}+2 x+3 \quad\) (a) \(y \leq 0 \quad\) (b) \(y \geq 3\)
The game commission introduces 100 deer into newly acquired state game lands. The population \(N\) of the herd is modeled by \(N=\frac{20(5+3 t)}{1+0.04 t}, \quad t \geq 0\) where \(t\) is the time in years (see figure). (a) Find the populations when \(t=5, t=10,\) and \(t=25 .\) (b) What is the limiting size of the herd as time increases?
Determine whether each value of \(x\) is a solution of the inequality. Inequality. \(\frac{3 x^{2}}{x^{2}+4}<1 \quad\) (a) \(x=-2 \quad\) (b) \(x=-1\) (c) \(x=0\) (d) \(x=3\)
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