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Chapter 13: Problem 5
Find the intercepts and sketch the graph of the plane. $$ 2 x-y+3 z=4 $$
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Sketch the region \(R\) whose area is given by the double integral. Then change the order of integration and show that both orders yield the same area. $$ \int_{0}^{2} \int_{x / 2}^{1} d y d x $$
Use a double integral to find the area of the region bounded by the graphs of the equations. $$ 2 x-3 y=0, x+y=5, y=0 $$
Plot the points and determine whether the data have positive, negative, or no linear correlation (see figures below). Then use a graphing utility to find the value of \(r\) and confirm your result. The number \(r\) is called the correlation coefficient. It is a measure of how well the model fits the data. Correlation coefficients vary between \(-1\) and 1, and the closer \(|r|\) is to 1, the better the model. $$ (1,7.5),(2,7),(3,7),(4,6),(5,5),(6,4.9) $$
Use a double integral to find the volume of the solid bounded by the graphs of the equations. $$ z=x+v, x^{2}+v^{2}=4 \text { (first octant) } $$
Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the given points. $$ (6,4),(1,2),(3,3),(8,6),(11,8),(13,8) $$
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