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Chapter 0: Problem 15
Find the domain of the function. \(f(x)=\frac{3 x+1}{x^{2}}\)
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Verify the identity. \(\sin 3 t=3 \sin t-4 \sin ^{3} t\)
As broadband Internet grows more popular, video services such as YouTube will continue to expand. The number of online video viewers (in millions) is projected to grow according to the rule $$N(t)=52 t^{0.531} \quad 1 \leq t \leq 10$$ where \(t=1\) corresponds to 2003 . a. Sketch the graph of \(N\). b. How many online video viewers will there be in \(2010 ?\)
Phillip, the proprietor of a vineyard, estimates that if 10,000 bottles of wine are produced this season, then the profit will be $$\$ 5$$ per bottle. But if more than 10,000 bottles are produced, then the profit per bottle for the entire lot will drop by $$\$ 0.0002$$ for each bottle sold. Assume that at least 10,000 bottles of wine are produced and sold, and let \(x\) denote the number of bottles produced and sold above 10,000 . a. Find a function \(P\) giving the profit in terms of \(x\). b. What is the profit that Phillip can expect from the sale of 16,000 bottles of wine from his vineyard?
Fueled by the promotion of testosterone as an antiaging elixir, use of the hormone by middle-aged and older men grew dramatically. The total number of prescriptions for testosterone from 1999 through 2002 is given by \(N(t)=-35.8 t^{3}+202 t^{2}+87.8 t+648 \quad 0 \leq t \leq 3\) where \(N(t)\) is measured in thousands and \(t\) is measured in years with \(t=0\) corresponding to \(1999 .\) Find the total number of prescriptions for testosterone in 1999,2000 , 2001, and \(2002 .\)
Ramon wishes to have a rectangular-shaped garden in his backyard. But Ramon wants his garden to have an area of \(250 \mathrm{ft}^{2}\). Letting \(x\) denote the width of the garden, find a function \(f\) in the variable \(x\) that gives the length of the fencing required to construct the garden. What is the domain of the function?
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