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Chapter 1: Problem 40
Write the equation in the slopeintercept form and then find the slope and \(y\) -intercept of the corresponding line. $$ y-2=0 $$
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The United States is not building many nuclear plants, but the ones it has are running at nearly full capacity. The output (as a percent of total capacity) of nuclear plants is described by the equation $$ y=1.9467 t+70.082 $$ where \(t\) is measured in years, with \(t=0\) corresponding to the beginning of 1990 . a. Sketch the line with the given equation. b. What are the slope and the \(y\) -intercept of the line found in part (a)? c. Give an interpretation of the slope and the \(y\) -intercept of the line found in part (a). d. If the utilization of nuclear power continues to grow at the same rate and the total capacity of nuclear plants in the United States remains constant, by what year can the plants be expected to be generating at maximum capacity?
For each supply equation, where \(x\) is the quantity supplied in units of 1000 and \(p\) is the unit price in dollars, (a) sketch the supply curve and (b) determine the number of units of the commodity the supplier will make available in the market at the given unit price. $$ p=\frac{1}{2} x+20 ; p=28 $$
The line with equation \(A x+B y+C=0(B \neq 0)\) and the line with equation \(a x+b y+c=0(b \neq 0)\) are parallel if \(A b-a B=0 .\)
The amount of corn used in the United States for the production of ethanol is expected to rise steadily as the demand for plant-based fuels continue to increase. The following table gives the projected amount of corn (in billions of bushels) used for ethanol production from 2005 through \(2010(x=1\) corresponds to 2005 ): $$ \begin{array}{lcccccc} \hline \text { Year, } \boldsymbol{x} & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Amount, } \boldsymbol{y} & 1.4 & 1.6 & 1.8 & 2.1 & 2.3 & 2.5 \\\ \hline \end{array} $$ a. Find an equation of the least-squares line for these data. b. Use the result of part (a) to estimate the amount of corn that will be used for the production of ethanol in 2011 if the trend continues.
Find an equation of the line that passes through the point \((-2,2)\) and is parallel to the line \(2 x-4 y-8=0\).
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