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Chapter 1: Problem 25
Plot the points and find the slope of the line passing through the pair of points. $$(0,9),(6,0)$$
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The function \(F(y)=149.76 \sqrt{10} y^{5 / 2}\) estimates the force \(F\) (in tons) of water against the face of a dam, where \(y\) is the depth of the water (in feet). (a) Complete the table. What can you conclude from the table? $$\begin{array}{|l|l|l|l|l|l|}\hline y & 5 & 10 & 20 & 30 & 40 \\\\\hline F(y) & & & & & \\\\\hline\end{array}$$ (b) Use the table to approximate the depth at which the force against the dam is \(1,000,000\) tons. (c) Find the depth at which the force against the dam is \(1,000,000\) tons algebraically.
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: \(P=R-C\) ).
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) Use the fact that 13 inches is approximately the same length as 33 centimeters to find a mathematical model that relates centimeters \(y\) to inches \(x\). Then use the model to find the numbers of centimeters in 10 inches and 20 inches.
(a) use a graphing utility to graph the function and (b) state the domain and range of the function. $$k(x)=4\left(\frac{1}{2} x-\left[\left[\frac{1}{2} x\right]\right]\right)^{2}$$
Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(z\) varies jointly as \(x\) and \(y .(z=64 \text { when } x=4\) and \(y=8 .)\)
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