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Chapter 0: Problem 93
Simplify each algebraic expression. $$7-4[3-(4 y-5)]$$
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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鈥檚 original price, the sale price can be modeled by original price, the sale price cafe $$(x-0.3 x)-0.3(x-0.3 x)$$
You had \(\$10,000\) to invest. You put x dollars in a safe, government-insured certificate of deposit paying 5% per year. You invested the remainder of the money in noninsured corporate bonds paying 12% per year. Your total interest earned at the end of the year is given by the algebraic expression $$0.05 x+0.12(10,000-x)$$ a. Simplify the algebraic expression. b. Use each form of the algebraic expression to determine your total interest earned at the end of the year if you invested $6000 in the safe, government-insured certificate of deposit.
Factor completely. $$(x-5)^{-\frac{1}{2}}(x+5)^{-\frac{1}{2}}-(x+5)^{\frac{1}{2}}(x-5)^{-\frac{3}{2}}$$
What does \(a^{\frac{m}{n}}\) mean?
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 47,to solve this exercise. You are moving at \(90 \%\) of the speed of light. Substitute 0.9c 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?
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