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Chapter 1: Problem 41
Find the maximum or minimum value of the function. State whether this value is a maximum or a minimum. $$f(x)=-\frac{1}{2} x^{2}+6 x+17$$
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Solve \(3 x-5 y=15\) for \(y\)
A manufacturer produces a product at a cost of \(\$ 22.80\) per unit. The manufacturer has a fixed cost of \(\$ 400.00\) per day. Each unit retails for \(\$ 37.00\) Let \(x\) represent the number of units produced in a 5 -day period. a. Write the total cost \(C\) as a function of \(x\) b. Write the revenue \(R\) as a function of \(x\) c. Write the profit \(P\) as a function of \(x .\) [Hint: The profit function is given by \(P(x)=R(x)-C(x) .]\)
A business finds that the number of feet \(f\) of pipe it can sell per week is a function of the price \(p\) in cents per foot as given by $$f(p)=\frac{320,000}{p+25}, \quad 40 \leq p \leq 90$$ Complete the following table by evaluating \(f\) (to the nearest hundred feet) for the indicated values of \(p\) $$\begin{array}{|c|c|c|c|c|c|}\hline p & 40 & 50 & 60 & 75 & 90 \\\\\hline f(p) & & & & & \\ \hline\end{array}$$
The sum \(S\) of the first \(n\) natural numbers \(1,2,3, \ldots, n\) is given by the formula $$S=\frac{n}{2}(n+1)$$ How many consecutive natural numbers starting with 1 produce a sum of 253?
Solve each quadratic inequality. Use interval notation to write each solution set. $$x^{2}+7 x>0$$
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