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Chapter 2: Problem 90
Cube each complex number. (a) 2 (b) \(-1+\sqrt{3} i\) (c) \(-1-\sqrt{3} i\)
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Solve the inequality and graph the solution on the real number line. \(x^{2}+3 x+8>0\)
Is every rational function a polynomial function? Is every polynomial function a rational function? Explain.
The key numbers of a rational expression are its ___________ and its ____________ _____________.
Use a graphing utility to graph the rational function. Give the domain of the function and identify any asymptotes. Then zoom out sufficiently far so that the graph appears as a line. Identify the line. \(f(x)=\frac{x^{2}+5 x+8}{x+3}\)
A 1000-liter tank contains 50 liters of a \(25 \%\) brine solution. You add \(x\) liters of a \(75 \%\) brine solution to the tank. (a) Show that the concentration \(C,\) the proportion of brine to total solution, in the final mixture is \(C=\frac{3 x+50}{4(x+50)}\) (b) Determine the domain of the function based on the physical constraints of the problem. (c) Sketch a graph of the concentration function. (d) As the tank is filled, what happens to the rate at which the concentration of brine is increasing? What percent does the concentration of brine appear to approach?
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