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Chapter 1: Problem 7
Find the coordinates of the point. The point is located three units to the left of the \(y\) -axis and four units above the \(x\) -axis.
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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.)
Write the area \(A\) of a circle as a function of its circumference \(C\).
The height \(y\) (in feet) of a baseball thrown by a child is $$y=-\frac{1}{10} x^{2}+3 x+6$$ where \(x\) is the horizontal distance (in feet) from where the ball was thrown. Will the ball fly over the head of another child 30 feet away trying to catch the ball? (Assume that the child who is trying to catch the ball holds a baseball glove at a height of 5 feet.)
An oceanographer took readings of the water temperatures \(C\) (in degrees Celsius) at several depths \(d\) (in meters). The data collected are shown as ordered pairs \((d, C)\) (Spreadsheet at LarsonPrecalculus.com) $$\begin{aligned} &(1000,4.2) \quad(4000,1.2)\\\ &(2000,1.9) \quad(5000,0.9)\\\ &(3000,1.4) \end{aligned}$$ A.Sketch a scatter plot of the data. B. Does it appear that the data can be modeled by the inverse variation model \(C=k / d ?\) If so, find \(k\) for each pair of coordinates. C. Determine the mean value of \(k\) from part (b) to find the inverse variation model \(C=k / d\) D. Use a graphing utility to plot the data points and the inverse model from part (c). E. Use the model to approximate the depth at which the water temperature is \(3^{\circ} \mathrm{C}\)
Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$g(x)=|x|-5$$
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