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Chapter 2: Problem 75
When \(2 x^{2}-7 x+9\) is divided by a polynomial, the quotient is \(2 x-3\) and the remainder is \(3 .\) Find the polynomial.
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Solve each inequality using a graphing utility. $$\frac{x+2}{x-3} \leq 2$$
Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$g(x)=\frac{1}{x-2}$$
Galileo's telescope brought about revolutionary changes in astronomy. A comparable leap in our ability to observe the universe took place as a result of the Hubble Space Telescope. The space telescope was able to see stars and galaxies whose brightness is \(\frac{1}{50}\) of the faintest objects observable using ground-based telescopes. Use the fact that the brightness of a point source, such as a star, varies inversely as the square of its distance from an observer to show that the space telescope was able to see about seven times farther than a groundbased telescope.
Use a graphing utility to graph $$f(x)=\frac{x^{2}-4 x+3}{x-2} \text { and } g(x)=\frac{x^{2}-5 x+6}{x-2}$$ What differences do you observe between the graph of \(f\) and the graph of \(g\) ? How do you account for these differences?
If \(S=\frac{k A}{P},\) find the value of \(k\) using \(A=60,000, P=40,\) and \(S=12,000\).
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