Answers for Math Practice Problem Module 6


1.     C, pole
2.     A, rose
3.     A, 192Ö3
4.     B, 2.25p
5.     C, 47/13
6.     B, 10/3
7.     A, y2=x3
8.     A, -3/4
9.     B, 0,60
10.  C, 36.8 ft
11.  C, 5Ö3
12.  A, Ö29
13.  B, 5
14.  B, isosceles
15.  C, 5, 3, -5
16.  B, 60.510
17.  A, 112.390
18.  C, 2
19.  C, 4
20.  A, 20/3
21.  C, Ö29
22.  B, r2sin2q = 16
23.  B, y2=5x
24.  D, r2+z2 = 36q2
25.  B, (Ö61, 53.130, 39.810
26.  A, 4x-9y+7z-65 = 0
27.  C, 35/Ö69
28.  A, (-2/5, 3, -7/5)
29.  A, 2
30.  C, 32.420
31.  B, [-5, 11, 7]
32.  C, 2x-6y+3z+43 = 0
33.  B, 2
34.  D, an elliptic cone
35.  B, (0, 3, 50)
36.  A, (4Ö2, p/4, -2)
37.  A, (Ö6, Ö2, 2Ö2)
38.  A, increases
39.  A, quadratic
40.  C, (1, 6)
41.  B, 1.25 m
42.  D, -15
43.  A, linear
44.  D, f”92)>0
45.  C, 8.7 cm/s
46.  A, zero
47.  A, f”(a) = 0
48.  B, concave downward
49.  C, 0.3 cm2/hr
50.  C, 50 kph

Math Practice Problems Module 6



1. If the equation r = (q) is unchanged when q is replaced by 180 + q of when r is replaced by –r, then the curve is symmetric with respect to
  1. normal size
  2. polar axis
  3. pole
  4. both axes
2. The curve whose general equation is r= a sin nq of r=a cos nq.
  1. rose
  2. lemniscate
  3. cardoid
  4. spiral
3. An equilateral triangle is inscribed in the parabola x2=8y with one vertex of the triangle at the origin. Find the area of the triangle.
  1. 192Ö3
  2. 192Ö3/2
  3. 192Ö3/4
  4. 192Ö3/5
4. Find the area in the second quadrant bounded by the curve x2/9 +y2/9 = 1 and the coordinates axes
  1. 6p
  2. 2.25p
  3. 3p
  4. 4p
5. If P (x, y) is such that AP/PB = 7/6 where A(2, 5) and B(5, -1), find x.
  1. 43/13
  2. 54/13
  3. 47/13
  4. 51/13
6. If the line segment AB is parallel to the line segment CD and A (4, -3), B(2, 0), C(4, 1), D(x,2), find x.
  1. 11/3
  2. 10/3
  3. 7/3
  4. 5/3
7. Which of the following curves is symmetric with respect to the x-axis?
  1. y2=x3
  2. y3=x2
  3. y=x3
  4. y=x2
8. Determine k so that the radius of the circle x2+y2+3x-2y +k =0 is equal to 2.
  1. –3/4
  2. ¾
  3. –3/5
  4. 3/5
9. Find the eccentricity of 25x2+16y2 = 400
  1. 0.55
  2. 0.66
  3. 0.65
  4. 0.70
10. A power cable hangs in parabolic arc between two poles 100 ft apart. If the poles are 40 ft and if the lowest point on the suspended cable is 35 ft above the ground, find the height of the cable at a point 20 ft from the pole.
  1. 34.8 ft
  2. 35.8 ft
  3. 36.8 ft
  4. 37.8 ft
11. Find the distance between (4, 3, 2) and (-3, -2, 1).
  1. 3Ö3
  2. 4Ö3
  3. 5Ö3
  4. 6Ö3
12. Find the distance from the origin to (4, -3, 2).
  1. Ö29
  2. Ö27
  3. Ö13
  4. Ö31
13. Find the radius of the sphere x2+y2+z2-2x+6y+2z-14 = 0.
  1. a. 4
  2. 5
  3. 6
  4. 3
14. The triangle with vertices (3, 5, -4), (-1, 1, 2) and (-5, -5, -2) is
  1. right
  2. isosceles
  3. equilateral
  4. scalene
15. Find the direction numbers of the line through P1 (-3, 2, 4) and P2 (2, 5, -2).
  1. –5, 3, 6
  2. 5, -3, 6
  3. 5, 3, -6
  4. 5, 3, 6
16. Find the angle between the line L1 with direction numbers 3, 4, 1 and the line L2 with direction numbers 5, 3, -6.
  1. 60.410
  2. 60.510
  3. 60.610
  4. 60.710
17. Find the angle A of the triangle whose vertices are A(4, 6, 1), B(6, 4, 0) and C(-2, 3, 3).
  1. 112.390
  2. 113.290
  3. 119.230
  4. 112.930
18. If the angle between two lines with direction numbers 1, 4, -8 and x, 3, -6 is arcos(62/63), find x.
  1. 4
  2. 3
  3. 2
  4. 1
19. The direction numbers of two lines are 2, -1, 4 and –3, y, 2. If the lines are perpendicular, find y.
  1. 2
  2. 3
  3. 4
  4. 5
20. Find the x-coordinate of the point which is 10 units from the origin and has direction cosines cosβ = 1/3 and cosa = -2/3.
  1. 20/3
  2. 19/3
  3. 10/3
  4. 17/3
21. A triangle has a vertices at A(2, -1, 3), B(-4, -3, 1) and C(0, 5, -1). Find the length of the median from vertex A to the side BC.
  1. Ö27
  2. Ö28
  3. Ö29
  4. Ö30
22. Transform xy = 8 to cylindrical coordinates.
  1. r2sin2q = 8
  2. r2sinq= 16
  3. rsin2q=8
  4. rsin2q=16
23. Transfrom psinÆsinqtanq=5 50 rectangular coordinates.
  1. y=5x
  2. y25x
  3. y=5x2
  4. xy=5
24. Transform p=6q to cylindrical coordinates
  1. r2+z2=q2
  2. r2+z2=6q2
  3. r2+z2=36
  4. r2+z2=360q
25. Give the equivalent spherical coordinate of (3, 4, 6).
  1. (Ö61, 53.130, 38.90)
  2. (Ö61, 53.130, 39.810)
  3. (Ö61, 51.330, 39.810)
  4. (Ö61, 53.310, 39.910)
26. Find the equation of the plane which passes through (-1, -3, 6) and which parallel to the plane 4x-9y+7z+2 = 0
  1. 4x-9y+7z-65 = 0
  2. 4x-9y+5z-60 = 0
  3. 4x-9y-7z+65 = 0
  4. 4x-9y+5z-60 = 0
27. Find the distance from 2x +7y +4z – 3 = 0 to (2,3,3).
  1. 32/Ö69
  2. 33/Ö69
  3. 35/Ö69
  4. 34/Ö69
28. Find the coordinates of thepoint which divides the line segment P1P2 where P1(2, 5, -3) and P2(-4, 0, 1) in the ratio 2:3.
  1. (-2/5, 3, -7/5)
  2. (/5, -3, -7/5)
  3. (2/5, -3, 7/5)
  4. –2/5, -3, 7/5)
29. If the angle between the planes 2x-3y+18 and 2x-y+kz = 12 is arcos(19/21), fin k.
  1. 2
  2. 3
  3. 4
  4. 5
30. Find the angle between the line with dircton numbers 1, -1, -1 and the plane 3x-4y+2z-5 = 0
  1. 30.400
  2. 31.410
  3. 32.420
  4. 33.430
31. Find the direction numbers of the line 2x-y+3z+4 =m 0 and 3x+2y-z+7 = 0
  1. [5, 11, -7]
  2. [-5, 11, 7]
  3. [5, -11, 7]
  4. [-5, -11, 7]
32. Find the equation of the plane perpendicular to the line joining (2, 5, -3) and (4, -1, 0) and which passes through (1, 4, -7).
  1. 2x-6y+3z-43 = 0
  2. 2x+6y+3z+43 = 0
  3. 2x-6y+3z+43 = 0
  4. 2x-6y-3z-43 = 0
33. If the acute angle between the planes kx-y+z = 7 and x+y+2z = 11 is 600, find k.
  1. 1
  2. 2
  3. 3
  4. 4
34. The surface described by the equation 4x2+y2+26z = 100 is
  1. an elliptic hyperboloid
  2. an elliptic paraboloid
  3. an ellipsoid
  4. an elliptic cone
35. Find the Cartesian coordinates of the point having the cylindrical coordinates (3, p/4, 5).
  1. (0, 5, 3)
  2. (0, 3, 5)
  3. 5, 0, 3)
  4. (3, 0, 5)
36. Find the cylindrical coordinates of the point having the Cartesian coordinate (4, 4, -2).
  1. (4Ö2, p/4, -2)
  2. (2Ö2, p/6, -2)
  3. (Ö3, /3, -2)
  4. (4Ö2, p/2, -2)
37. Find the Cartesian coordinates of the point having the spherical coordinates (4, p/6, p/4)
  1. (Ö6, Ö2, 2Ö2)
  2. (Ö3, Ö2, 2Ö3)
  3. (Ö6, Ö3, Ö2)
  4. (Ö3, Ö6, 2Ö2)
38. If an x = a, y”<0, then y’ decreases as x
  1. increases
  2. decreases
  3. becomes infinite
  4. becomes zero
39. If the 3rd derivative of a function in one variable is equal to zero, then the function is
  1. quadratic
  2. cubic
  3. linear
  4. quartic
40. Find the maximum point of y = 4+3x-x3.
  1. (0, 40
  2. –1, 2)
  3. (1, 6)
  4. (-2, 6)
41. A picture 2 m high is hanging on a wall with the bottom of the picture 0.6 m above the observer’s eye level. How far from the wall must be observer stand in order that the angle subtended by the picture be a maximum?
  1. 1.23 m
  2. 1.25 m
  3. 1.27 m
  4. 1.29 m


42. Evaluate

 lim x3-x2-x+10
 

x® -2   x2+3x+2
  1. 0
  2. a
  3. –5
  4. –15
43. If the first derivative of a function is a constant, then it is a, _______function.
  1. linear
  2. quadratic
  3. logarithmic
  4. exponential
44. The function y = f(x) has a minimum value at x = 2 of f92) = 0 and if
  1. f”(2) = 0
  2. f”(2) ¹ 0
  3. f”(2)<0
  4. f”(2)>0
45. How fast does the diagonal of a cube increase if each side of the cube increases at the constant rate of 5 cm/s?
  1. 6.7 cm/s
  2. 7.6 cm/s
  3. 8.7 cm/s
  4. 7.8cm/s
46. At the minimum point, the slope of the tangent line is
  1. zero
  2. positive
  3. negative
  4. infinity
47. At the inflection point where x = a,
  1. f”(a) = 0
  2. f”(a)>0
  3. f”(a)<0
  4. f”(a)¹0
48. When y” is negative, then the curve y = f(x) is
  1. concave upward
  2. concave downward
  3. horizontal
  4. vertical
49. The volume of a sphere is increasing at the rate of 6 cm3/hr. At what rate is its surface area increasing when the radius is 40 cm?
  1. 0.5 cm2/hr
  2. 0.4cm2
  3. 0.3 cm2/hr
  4. 0.2 cm2/hr
50 The paths of two planes, flying in straight line at the same altitude, intersect at an angle of 60 degrees at a point A. one of the planes is flying at 300 kph towards A while the other is flying at 400 kph away from A. if at some point, they are 100 km away from A, find the rare at which the distance between them is changing.
  1. 60 kph
  2. 70 kph
  3. 50 kph
  4. 40 kph
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