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Chapter 2: Problem 51
Perform the indicated operation(s) and write the result in standard form. $$(2-3 i)(1-i)-(3-i)(3+i)$$
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The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$\frac{x-5}{10 x-2} \div \frac{x^{2}-10 x+25}{25 x^{2}-1}$$
Use a graphing utility to graph \(y=\frac{1}{x}, y=\frac{1}{x^{3}},\) and \(\frac{1}{x^{5}}\) in the same viewing rectangle. For odd values of \(n,\) how does changing \(n\) affect the graph of \(y=\frac{1}{x^{n}} ?\)
Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{x^{2}}-3$$
The illumination from a light source varies inversely as the square of the distance from the light source. If you raise a lamp from 15 inches to 30 inches over your desk, what happens to the illumination?
A company is planning to manufacture mountain bikes. The fixed monthly cost will be \(\$ 100,000\) and it will cost \(\$ 100\) to produce each bicycle. a. Write the cost function, \(C,\) of producing \(x\) mountain bikes. b. Write the average cost function, \(\bar{C},\) of producing \(x\) mountain bikes. c. Find and interpret \(\bar{C}(500), \bar{C}(1000), \bar{C}(2000),\) and \(\bar{C}(4000)\) d. What is the horizontal asymptote for the graph of the average cost function, \(\bar{C} ?\) Describe what this means in practical terms.
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