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Chapter 9: Problem 20
Let \(f(x)=-3 x+4\) and \(g(x)=-x^{2}+4 x+1\) \(g(k)\)
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Solve each problem. The maximum load that a cylindrical column with a circular cross section can hold varies directly as the fourth power of the diameter of the cross section and inversely as the square of the height. A \(9-\mathrm{m}\) column \(1 \mathrm{~m}\) in diameter will support 8 metric tons. How many metric tons can be supported by a column \(12 \mathrm{~m}\) high and \(\frac{2}{3} \mathrm{~m}\) in diameter?
Determine whether each relation defines y as a function of \(x .\) (Solve for y first if necessary.) Give the domain. $$ x y=1 $$
Determine whether each relation defines y as a function of \(x .\) (Solve for y first if necessary.) Give the domain. $$ y=6 x+8 $$
For each pair of functions, find \(\left(\frac{f}{g}\right)(x)\) and give any \(x\) -values that are not in the domain of the quotient function. $$ f(x)=2 x^{2}-x-3, \quad g(x)=x+1 $$
Solve each problem. The number of long-distance phone calls between two cities during a certain period varies jointly as the populations of the cities, \(p_{1}\) and \(p_{2}\), and inversely as the distance between them, in miles. If 80,000 calls are made between two cities \(400 \mathrm{mi}\) apart, with populations of 70,000 and 100,000 , how many calls (to the nearest hundred) are made between cities with populations of 50,000 and 75,000 that are \(250 \mathrm{mi}\) apart?
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