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Chapter 0: Problem 42
Give an example of a number that is a rational number, an integer, and a real number.
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Describe ways in which solving a linear inequality is similar to solving a linear equation.
a. A mathematics professor recently purchased a birthday cake for her son with the inscription $$ \text { Happy }\left(2^{\frac{5}{2}} \cdot 2^{\frac{3}{4}} \div 2^{\frac{1}{4}}\right) \text { th Birthday. } $$ How old is the son?b. The birthday boy, excited by the inscription on the cake, tried to wolf down the whole thing. Professor Mom, concerned about the possible metamorphosis of her son into a blimp, exclaimed, "Hold on! It is your birthday, so why not take \(\frac{8^{-\frac{4}{3}}+2^{-2}}{16^{-\frac{3}{4}}+2^{-1}}\) of the cake? I'll eat half of what's left over." How much of the cake did the professor eat?
Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A company manufactures and sells blank audiocassette tapes. The weekly fixed cost is \(\$ 10,000\) and it costs \(\$ 0.40\) to produce each tape. The selling price is \(\$ 2.00\) per tape. How many tapes must be produced and sold each week for the company to generate a profit?
The rational expression $$\frac{130 x}{100-x}$$ describes the cost, in millions of dollars, to inoculate \(x\) percent of the population against a particular strain of flu. a. Evaluate the expression for \(x=40, x=80,\) and \(x=90\) Describe the meaning of each evaluation in terms of percentage inoculated and cost. b. For what value of \(x\) is the expression undefined? c. What happens to the cost as \(x\) approaches \(100 \% ?\) How can you interpret this observation?
What is a quadratic equation?
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