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Chapter 3: Problem 46
Give the domain and the range of each quadratic function whose graph is described. The vertex is \((-3,-4)\) and the parabola opens down.
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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.
Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies inversely as \(x . y=12\) when \(x=5 .\) Find \(y\) when \(x=2\).
Whe lise a graphing utility to graph $$ f(x)=\frac{x^{2}-4 x+3}{x-2} \text { and } g(x)=\frac{x^{2}-5 x+6}{x-2} $$ What differences do you observe between the graph of \(f\) and the graph of \(g\) ? How do you account for these differences?
The water temperature of the Pacific Ocean varies inversely as the water's depth. At a depth of 1000 meters, the water temperature is \(4.4^{\circ}\) Celsius. What is the water temperature at a depth of 5000 meters?
The force of wind blowing on a window positioned at a right angle to the direction of the wind varies jointly as the area of the window and the square of the wind's speed. It is known that a wind of 30 miles per hour blowing on a window measuring 4 feet by 5 feet exerts a force of 150 pounds. During a storm with winds of 60 miles per hour, should hurricane shutters be placed on a window that measures 3 feet by 4 feet and is capable of withstanding 300 pounds of force?
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