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(c) x/10 + y/10 + z/15 = 1 (d) (5x 10)(5y + 10)(5z 15) = 1 (e) (x 5)2/2 + (y 5)2/2 (z 5)2/3 = 1 88 Consider the graph of the pair of parametric equations q = p /3 and r = 3t In the polar coordinate plane, the graph of this system is a (a) spiral that expands as we rotate clockwise (b) circle passing through the origin (c) circle centered at the origin (d) straight line that doesn t pass through the origin (e) straight line passing through the origin 89 The period of the graph representing the function y = 2p csc x is (a) 2p (b) p /2 (c) 2 (d) 1/2 (e) undefined 90 In two-space, a relation can always be represented as a set of (a) lines (b) circles (c) parabolas (d) closed curves (e) ordered pairs 91 Consider the two functions y = ln x and y = ln (1/x )
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When we graph the sum of these two functions in the Cartesian xy plane, we get (a) an open-ended ray corresponding to the line y = x in the first quadrant (b) an open-ended ray corresponding to the positive y axis (c) an open-ended ray corresponding to the positive x axis (d) an open-ended ray corresponding to the line y = x in the fourth quadrant (e) a circle centered at the origin and having a radius of e units 92 Which of the following relations is not a true function of x (a) y = 2x + 3 (b) x = 2y + 3 (c) y = x2 + 3 (d) x = y2 + 3 (e) y = x/2 + 3 93 Consider the following equation in three variables x, y, and z : 2x + y + 7z = 3 In Cartesian xyz space, this equation represents a (a) straight line (b) circle (c) sphere (d) hyperboloid (e) plane 94 Consider again the equation in Question 93, and the geometric figure it represents in Cartesian xyz space At what coordinates, if any, does the figure cross the z axis (a) (0,0, 3/2) (b) (0,0,1/3) (c) (0,0,3/7) (d) (0,0,1/2) (e) The figure doesn t cross the z axis anywhere 95 Which of the following types of graphs is not a conic section (a) A circular curve (b) An elliptical curve (c) A logarithmic curve (d) A parabolic curve (e) A hyperbolic curve 96 Consider the following equation in three variables x, y, and z : x 2 + y 2 + z 2 + 2z + 1 = 20
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In Cartesian xyz-space, this equation represents a (a) plane (b) cone (c) cylinder (d) hyperboloid (e) sphere 97 In two-space, a function is a relation that (a) never maps any specific value of the independent variable to more than one value of the dependent variable (b) never maps more than one value of the independent variable to any specific value of the dependent variable (c) has a domain and range that both encompass the entire set of real numbers (d) has a domain that s a proper subset of the range (e) has a range that s a proper subset of the domain 98 Consider the following three-way equation: x /3 = y /4 = z /2 In Cartesian xyz space, this equation represents a (a) straight line through the origin (b) circle centered at the origin (c) circular cone centered at the origin (d) circle centered at the point (3,4, 2) (e) circular cone whose apex is at the point (3,4, 2) 99 Consider the following system of parametric equations: x = p cos t y = p z = 2p sin t The graph of this system in Cartesian xyz space is (a) an ellipse that lies in a plane perpendicular to the y axis (b) a parabola that lies in the xz plane (c) a circle that passes through all three axes (d) a hyperbola that s centered on the y axis (e) impossible to figure out based on the information given here
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