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Chapter 1: Problem 12
Determine whether the equation represents \(y\) as a function of \(x .\) $$x^{2}+y=4$$
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Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(F\) is jointly proportional to \(r\) and the third power of \(s\) \((F=4158 \text { when } r=11 \text { and } s=3 .)\)
(a) use a graphing utility to graph the function and (b) state the domain and range of the function. $$k(x)=4\left(\frac{1}{2} x-\left[\left[\frac{1}{2} x\right]\right]\right)^{2}$$
During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6 hours, and at a rate of 0.5 inch per hour for the final hour. Write and graph a piecewise- defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?
Find the difference quotient and simplify your Answer: $$f(x)=\sqrt{5 x}, \quad \frac{f(x)-f(5)}{x-5}, \quad x \neq 5$$
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(P\) varies directly as \(x\) and inversely as the square of \(y .\) \(\left(P=\frac{28}{3} \text { when } x=42 \text { and } y=9 .\right)\)
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