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Chapter 0: Problem 31
Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$-9 x \geq 36$$
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Use Einstein's special-relativity equation $$ R_{a}=R_{f} \sqrt{1-\left(\frac{v}{c}\right)^{2}} $$ described in the Blitzer Bonus on page \(44,\) to solve this exercise. You are moving at \(90 \%\) of the speed of light. Substitute \(0.9 c\) for \(v,\) your velocity, in the equation. What is your aging rate, correct to two decimal places, relative to a friend on Earth? If you are gone for 44 weeks, approximately how many weeks have passed for your friend?
Use interval notation to express solution sets and graph each solution set on a number line. Solve each linear inequality. $$8 x-2 \geq 14$$
The average rate on a round-trip commute having a one-way distance \(d\) is given by the complex rational expression $$\frac{2 d}{\frac{d}{r_{1}}+\frac{d}{r_{2}}}$$ in which \(r_{1}\) and \(r_{2}\) are the average rates on the outgoing and return trips, respectively. Simplify the expression. Then find your average rate if you drive to campus averaging 40 miles per hour and return home on the same route averaging 30 miles per hour. Explain why the answer is not 35 miles per hour.
Your local electronics store is having an end-of-the-year sale. The price on a plasma television had been reduced by \(30 \%\). Now the sale price is reduced by another \(30 \% .\) If \(x\) is the television's original price, the sale price can be modeled by $$(x-0.3 x)-0.3(x-0.3 x)$$ a. Factor out \((x-0.3 x)\) from each term. Then simplify the resulting expression. b. Use the simplified expression from part (a) to answer these questions. With a \(30 \%\) reduction followed by a \(30 \%\) reduction, is the television selling at \(40 \%\) of its original price? If not, at what percentage of the original price is it selling?
Putting Numbers into Perspective. A large number can be put into perspective by comparing it with another number. For example, we put the \(\$ 18.9\) trillion national debt in perspective (Example 6 ) by comparing this number to the number of U.S. citizens. For this project, each group member should consult an almanac, a newspaper, or the Internet to find a number greater than one million. Explain to other members of the group the context in which the large number is used. Express the number in scientific notation. Then put the number into perspective by comparing it with another number.
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