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Chapter 2: Problem 32
Use synthetic division to divide. \(\left(9 x^{3}-16 x-18 x^{2}+32\right) \div(x-2)\)
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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) \(x=3\)
Determine whether the statement is true or false. Justify your answer. The solution set of the inequality \(\frac{3}{2} x^{2}+3 x+6 \geq 0\) is the entire set of real numbers.
The revenue and cost equations for a product are \(R=x(50-0.0002 x)\) and \(C=12 x+150,000\) where \(R\) and \(C\) are measured in dollars and \(x\) represents the number of units sold. How many units must be sold to obtain a profit of at least \(\$ 1,650,000 ?\) What is the price per unit?
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.
(a) find the interval(s) for \(b\) such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients. \(3 x^{2}+b x+10=0\)
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