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Chapter 6: Problem 34
Find the inclination \(\theta\) (in radians and degrees) of the line. \(4 x+5 y-9=0\)
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The revenue \(R\) (in dollars) generated by the sale of \(x\) units of a patio furniture set is given by \((x-106)^{2}=-\frac{4}{5}(R-14,045)\) Use a graphing utility to graph the function and approximate the number of sales that will maximize revenue.
The first artificial satellite to orbit Earth was Sputnik I (launched by the former Soviet Union in 1957 ). Its highest point above Earth's surface was 947 kilometers, and its lowest point was 228 kilometers (see figure). The center of Earth was at one focus of the elliptical orbit, and the radius of Earth is 6378 kilometers. Find the eccentricity of the orbit.
The equations of a parabola and a tangent line to the parabola are given. Use a graphing utility to graph both equations in the same viewing window. Determine the coordinates of the point of tangency. \(y^{2}-8 x=0 \quad x-y+2=0\)
Find the equation of an ellipse such that for any point on the ellipse, the sum of the distances from the point (2,2) and (10,2) is 36 .
Find the eccentricity of the ellipse. \(x^{2}+9 y^{2}-10 x+36 y+52=0\)
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