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Chapter 1: Problem 27
Plot the points and find the slope of the line passing through the pair of points. $$(-3,-2),(1,6)$$
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A balloon carrying a transmitter ascends vertically from a point 3000 feet from the receiving station. (a) Draw a diagram that gives a visual representation of the problem. Let \(h\) represent the height of the balloon and let \(d\) represent the distance between the balloon and the receiving station. (b) Write the height of the balloon as a function of \(d\) What is the domain of the function?
Find the difference quotient and simplify your Answer: $$f(x)=\sqrt{5 x}, \quad \frac{f(x)-f(5)}{x-5}, \quad x \neq 5$$
The table shows the numbers of tax returns (in millions) made through e-file from 2003 through \(2010 .\) Let \(f(t)\) represent the number of tax returns made through e-file in the year \(t .\) (Source: Internal Revenue Service) $$\begin{array}{|c|c|}\hline \text { Year } & \text { Number of Tax Returns Made Through E-File } \\\\\hline 2003 & 52.9 \\\2004 & 61.5 \\\2005 & 68.5 \\\2006 & 73.3 \\\2007 & 80.0 \\\2008 & 89.9 \\\2009 & 95.0 \\\2010 & 98.7 \\\\\hline\end{array}$$ (a) Find \(\frac{f(2010)-f(2003)}{2010-2003}\) and interpret the result in the context of the problem. (b) Make a scatter plot of the data. (c) Find a linear model for the data algebraically. Let \(N\) represent the number of tax returns made through e-file and let \(t=3\) correspond to 2003 (d) Use the model found in part (c) to complete the table. $$\begin{array}{|l|l|l|l|l|l|l|l|l|l|l|}\hline t & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\\\hline N & & & & & & & & \\ \hline\end{array}$$ (e) Compare your results from part (d) with the actual data. (f) Use a graphing utility to find a linear model for the data. Let \(x=3\) correspond to \(2003 .\) How does the model you found in part (c) compare with the model given by the graphing utility?
(a) Write the linear function \(f\) such that it has the indicated function values and (b) Sketch the graph of the function. $$f(1)=4, \quad f(0)=6$$
Decide whether the statement is true or false. Justify your answer. In the equation for the area of a circle, \(A=\pi r^{2},\) the area A varies jointly with \(\pi\) and the square of the radius \(r\)
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