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  16.Find an equation of the hyperbola with vertices and asymptotes .   a. b. c. d. e.   17.Find an equation of the hyperbola with vertices and asymptotes .   a. b. c. d. e.   18.Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.   a. parabola b. ellipse c. circle d. hyperbola   19.Classify the graph of the equation as a circle, a parabola, an ellipse,.

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  6.Given and , find .   a. b. c. d. e.   7.Given and , find .   a. b. c. d. e.   8.Find a unit vector that is orthogonal to both and .   a. b. c. d. e.   9.Find the area of the parallelogram that has the given vectors and as adjacent sides.   a. b. c. d. e.   10.Find the area of a parallelogram that has the given vectors as adjacent.

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  16.Find the unit vector in the direction of u.     a. b. c. d. e.   17.Find a unit vector u in the direction opposite of .   a. 1/) b. (1/) c. 1/) d. (1/) e. 1/)   18.Determine all the values of c that satisfy the equation given   a. b. c. d. e.   19.Find the vector v with the magnitude and direction of .   a. b. c. d. e.   20.Given the vector v lies in the yz-plane, has magnitude.

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15.Find the length of the curve over the given interval.   a. b. c. d. e.   16.Find the length of the curve over the interval . Round your answer to two decimal places.   a. 0.58 b. 3.46 c. 2.00 d. 1.15 e. 1.73   17.Find the area of the surface formed by revolving about the polar axis the following curve over the given interval.   a. b. c. d. e.   18.Find the area of the.

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  6.Find the eccentricity of the polar equation .   a. 78 b. c. 26 d. 13 e.   7.Find the distance from the pole to the directrix for the conic .   a. b. 14 c. d. 42 e. 7   8.Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results.   a. eccentricity: distance from pole.

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  16.Find the distance between the point and the plane .   a. b. c. d. e.   17.Find the distance between the planes given below.   a. b. c. d. e.   18.Find the distance between the point and the line given by the set of parametric equations .   a. /11 b. 2 c. /11 d. 4 e. 1   19.A chute at the top of a grain elevator of a combine funnels the grain into.

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  6.Find the area of the region lying between the loops of .   a. b. c. d. e.   7.Find all points of intersection of the graphs of the equations.   a. b. c. d. e.   8.Find the points of intersection of the graphs of the equations.   a. b. c. d. e.   9.Find the points of intersection of the graphs of the equations .   a. b. c. d. e.   10.Find the area of the common interior of.

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MULTIPLE CHOICE 1.Identify the conic for the polar equation when . a. hyperbola b. parabola c. ellipse   2.Identify the graph for the polar equation .   a. d. b. e. c.   3.Identify the graph for the polar equation .   a. d. b. e. c.   4.Identify the graph for the polar equation .   a. d. b. e. c.   5.Find the eccentricity and distance from the pole to the directrix of the conic. Then sketch and identify.

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  11.Find the area of inside and outside by sketching the graph of the equations using the graphing utility.   a. b. c. d. e.   12.Find the length of the curve over the interval .   a. b. c. d. e.   13.Find the length of the curve over the given interval.   a. b. c. d. e.   14.Find the length of the curve over the given interval.   a. b. c. d. e.       .

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MULTIPLE CHOICE 1.Find .   a. b. c. d. e.   2.Find .   a. b. c. d. e.   3.Find .   a. b. c. d. e.   4.Find the second derivative of the parametric equations . Round your answer to two decimal places, if necessary.   a. 0 b. 2.00 c. d. 0.50 e.   5.Find and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 5.   a. : slope and concave up b. slope.

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  6.Find a set of parametric equations of the line that passes through the point and is parallel to the xy-plane and yz-plane.   a. b. c. d. e.   7.Determine whether any of the lines given below are parallel or identical.   a. are identical b. are identical c. are identical d. are parallel e. are parallel   8.Determine whether any of the lines given.

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  6.Determine whether u and v are orthogonal, parallel and pointing in the same direction, parallel and pointing in opposite directions, or neither.   a. Orthogonal b. Parallel, opposite direction c. Parallel, same direction d. Neither parallel nor orthogonal   7.Determine whether u and v are orthogonal, parallel or neither.   a. Parallel, same direction b. Orthogonal c. Neither parallel nor orthogonal d. Parallel, opposite direction   8.Find the direction cosines of the.

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MULTIPLE CHOICE 1.Write the corresponding rectangular equation for the curve represented by the parametric equation by eliminating the parameter.   a. b. c. d. e.   2.Sketch the curve represented by the parametric equations .   a. d. b. e. c.   3.Write the corresponding rectangular equation for the curve represented by the parametric equations by eliminating the parameter.   a. b. c. d. e.   4.Sketch the curve represented by the parametric.

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  11.Find the foci of the ellipse given by . a. b. c. d. e.   12.Find the eccentricity of the ellipse given by .   a. b. c. d. e.   13.Find the vertices of the ellipse given by .   a. b. c. d. e.   14.Find an equation of the ellipse with vertices and eccentricity .   a. b. c. d. e.   15.Find the center, foci, and vertices of the hyperbola.   a. b. c. d. e.     .

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  11.Given ,  find .   a. b. c. d. e.   12.Given , sketch the graph of  .   a. b. c. d. e.   13.Find the vector  , ,   a. b. c. d. e.   14.Find a point such that the points and are collinear.   a. b. c. d. e.   15.Find the magnitude of the vector given below.     a. b. c. d. e.     .

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MULTIPLE CHOICE 1.Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent. u: (6,5),  (9,11)     v: (3,–5),  (6,1)   a. b. c. d. e.   2.Find the vector v whose initial and terminal points are given below. (5,5), (7,2)   a. b. c. d. e.   3.Find the vector v whose initial and terminal points are given below. (5.5,2.1), (9.5, 6.1)   a. b. c. d. e.   4.Given.

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  11.Find an equation of a plane passing through the given point and perpendicular to the given vector. Point:        Vector:     a. b. c. d. e.   12.Find an equation of a plane passing through the following three points.   a. b. c. d. e.   13.Find an equation of a plane passing through the points and perpendicular to the plane .   a. b. c. d. e.   14.Determine whether the following planes are parallel,.

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MULTIPLE CHOICE 1.Find the coordinates of the point that is located 4 units behind the yz-plane, 6 units to the left of xz-plane, and 4 units above the xy-plane.   a. (–4,–6,–4) b. (–4,6,4) c. (4,–6,4) d. (–4,6,–4) e. (–4,–6,4)   2.Find the distance between the points given below. (–4, 2, –3 ), ( 0, 5, 1 )   a. or 6.4031 to four decimal places. b. or.

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  11.Given and , find the projection of u onto v.   a. b. c. d. e.   12.Given and , find the vector component of u orthogonal to v.   a. b. c. d. e.   13.Suppose the vector gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively, sold at a fast-food restaurant in one week. The vector gives the prices.

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MULTIPLE CHOICE 1.Given and find .   a. –8 b. –4 c. 4 d. 7 e. –1   2.Given , find .   a. –6 b. 12 c. –8 d. –2 e. 20   3.Given and find .   a. b. c. d. e.   4.Find the angle between the vectors for u and v given below.   a. b. c. d. e.   5.Find the angle between the vectors for u and v.   a. 8.13 b. 89.77 c. 81.87 d. 8.05 e. 12.33     .

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15.Both the magnitude and the direction of the force on a crankshaft change as the crankshaft rotates. Find the torque on the crankshaft using the position and data shown in the figure. Round your answer to two decimal places.   a. 2,598.08 ft-lb b. 259.81 ft-lb c. 212.13 ft-lb d. 519.62 ft-lb e. 150.00 ft-lb   16.Find the triple scalar product .   a. b. c. d. e.   17.Use the.

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  11.Following are the vertices of the parallelogram. Find the coordinates of the fourth vertex.   a. b. c. d. e.   12.Find the area of the parallelogram with the vertices , and . Round your answer to two decimal places.   a. 35.00 b. 3.00 c. 5.92 d. 7.00 e. 2.65   13.Find the area of the triangle with the vertices and . Round your answer to two decimal places.   a. 20.00 b. 8.00 c. 6.00 d. 2.24 e. 4.47   14.A.

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  6.Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter.   a. d. b. e. none of the above c.   7.Sketch the curve represented by the parametric equations, and write the corresponding rectangular equation by eliminating the parameter.   a. d. b. e. c.   8.Use the result, "the set of parametric equations for the line passing through.

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  11.Find a set of parametric equations for the rectangular equation .   a. b. c. d. e.   12.Find a set of parametric equations for the rectangular equation that satisfies the condition at the point .   a. b. c. d. e.   13.Find a set of parametric equations for the rectangular equation that satisfies the condition at the point .   a. b. c. d. e.   14.Identify any.

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  6.Given and , find .   a. b. c. d. e.   7.The vector v and its initial point is given. Find the terminal point. ,   initial point   a. b. c. d. e.   8.Find the magnitude of the vector given below. Round  your answer to four decimal places.   a. b. c. d. e.   9.Find the unit vector in the direction of u.   a. b. c. d. e.   10.Find the vector v with the given magnitude.

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  11.Convert the rectangular equation to polar form. x = 5   a. b. c. d. e.   12.Convert the rectangular equation to polar form.   a. b. c. d. e.   13.Convert the polar equation to rectangular form.   a. b. c. d. e.   14.Convert the polar equation to rectangular form.   a. b. c. d. e.   15.Convert the polar equation to rectangular form.   a. b. c. d. e.         .

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MULTIPLE CHOICE 1.For the given point in polar coordinates, find the corresponding rectangular coordinates for the point. .   a. b. c. d. e.   2.Find the corresponding rectangular coordinates for the point . Round your answer to three decimal places.   a. b. c. d. e.   3.Find two sets of polar coordinates for the point for .   a. (,)(,) b. (242,)(242,) c. (484,)(484,) d. (,)(,) e. (,)(,)   4.Find two sets of polar coordinates for the.

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