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Chapter 1: Problem 14
Determine whether the equation represents \(y\) as a function of \(x .\) $$(x-2)^{2}+y^{2}=4$$
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The cost per unit in the production of an MP3 player is 60 dollars. The manufacturer charges 90 dollars per unit for orders of 100 or less. To encourage large orders, the manufacturer reduces the charge by 0.15 dollars per MP3 player for each unit ordered in excess of 100 (for example, there would be a charge of 87 dollars per MP3 player for an order size of 120 ). (a) The table shows the profits \(P\) (in dollars) for various numbers of units ordered, \(x .\) Use the table to estimate the maximum profit. $$\begin{array}{|l|c|c|c|c|c|}\hline \text { Units, } x & 130 & 140 & 150 & 160 & 170 \\\\\hline \text { Profit, } P & 3315 & 3360 & 3375 & 3360 & 3315 \\\\\hline\end{array}$$ (b) Plot the points \((x, P)\) from the table in part (a). Does the relation defined by the ordered pairs represent \(P\) as a function of \(x ?\) (c) Given that \(P\) is a function of \(x,\) write the function and determine its domain. (Note: \(P=R-C\) where \(R\) is revenue and \(C\) is cost.)
Sketch the graph of the function. $$g(x)=[[x]]-1$$
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(A\) varies directly as \(r^{2} .(A=9 \pi \text { when } r=3 .)\)
Decide whether the statement is true or false. Justify your answer. A. Given that \(y\) varies directly as the square of \(x\) and \(x\) is doubled, how will \(y\) change? Explain. B. Given that \(y\) varies inversely as the square of \(x\) and \(x\) is doubled, how will \(y\) change? Explain.
A company produces a product for which the variable cost is 12.30 dollars per unit and the fixed costs are 98,000 dollars. The product sells for 17.98 dollars. Let \(x\) be the number of units produced and sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost \(C\) as a function of the number of units produced. (b) Write the revenue \(R\) as a function of the number of units sold. (c) Write the profit \(P\) as a function of the number of units sold. (Note: \(P=R-C\) ).
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