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MATH 1720 Name___________________________________ Exam 3 Review Problems
Review your notes, homework, and previous quizzes when preparing for the exam.
Express the complex number in trigonometric form.
(^) - 5 i Express your answer in degrees. 1)
2 - 2 i Express your answer in radians. 2)
Express in standard notation.
- 5 2
(cos 150° (^) + i sin 150°) 3)
Find standard notation a + bi.
- 3 cos π 3 +^
i sin π 3
Multiply or Divide and leave the answer in trigonometric notation.
- 15 (cos^31 °^ +^ i sin^31 °) 3(cos 5° + i sin 5°)
- 6 cos π 4 + i sin π 4 · 7 cos π 6 + i sin π 6 6)
Find the given power. Write the answer in standard form.
- (- 3 + i)^6 7)
Convert to polar coordinates. Express the answer in radians, using the smallest possible positive angle.
- (- 7 , 7 ) 8)
Find the polar coordinates of the point. Express the angle in degrees and then in radians, using the smallest possible positive angle.
- (0, 7 ) 9)
Convert the rectangular coordinates to polar coordinates. Express the answer in degrees, using the smallest possible positive angle. Round r to the nearest tenth, if necessary, and round θ to the nearest tenth of a degree.
- (- 4 , - 3 ) 10)
Convert to rectangular coordinates.
- 3 , π 6
Convert to a polar equation.
- x^2 + y^2 - 4x = 0 13)
Given the ordered pairs for the initial and terminal points of each vector, are the two vectors equivalent?
- A(3, 1), B(0, 3), C(-4, 2), D(-1, - 1) AB , CD
Given the magnitudes of vectors u and v and the angle θ between them, find the magnitude of the sum u + v to the nearest tenth and the angle that the sum vector makes with u to the nearest degree.
- (^) ∣u∣ = 11 , (^) ∣v∣ = 11 , θ (^) = 122 ° 15)
Solve.
- Two forces, of 29.3 and 22.4 lb, forming an angle of 73.2°, act at a point in the plane. Find the magnitude of the resultant force.
- What is the minimum force required to prevent a ball weighing 19.5 lb from rolling down a ramp inclined 12.3° with the horizontal?
- A luggage wagon is being pulled with vector force V, which has a magnitude of 680 lb at an angle of elevation of 55°. Resolve the vector V into components.
Find the component form of the vector given the initial and terminal points.
- NM ; M(15, 2), N(11, 10) 19)
Find the magnitude of the vector.
- u = 7 , - 8 20)
Perform the indicated operation.
- u = - 11 , 2 , v = 4 , - 7 u + v
- u = - 8 , 8 , v = - 5 , 4 5 u (^) - 8 v
Find the dot product, u · v, for the given vectors.
- u = 2 , - 8 , v = 7 , - 11 23)
Find a unit vector that has the same direction as the given vector.
t (^) = - 3 , (^) - 5 24)
u = - 9 i + 9 j 25)
Solve.
- A railroad tunnel is shaped like a semi-ellipse. The height of the tunnel at the center is 46 ft and the vertical clearance must be 23 ft at a point 12 ft from the center. Find an equation for the ellipse.
Find the equation of the hyperbola satisfying the given conditions.
Vertices at ( 3 , 0) and (- 3 , 0); foci at ( 4 , 0) and (- 4 , 0) 42)
Vertices at (0, 10) and (0, - 10); asymptotes y = 53 x and y = - 53 x 43)
Find the vertices of the hyperbola.
- 36y^2 - 4x^2 = 144 44)
Find the foci of the given hyperbola.
- y
25 -^
x^2 100 =^
Find the asymptotes of the hyperbola.
- x
64 -^
y^2 36 =^1 46)
Graph the plane curve given by the parametric equations. Then find the equivalent rectangular equation.
- x = 2t - 1, y = t^2 + 2; - 4 ≤ t ≤ 4
-10 10
10
-10 10
10
Graph the plane curve given by the parametric equations.
- x = 7 cos t , y = 5 sin t; 0 ≤ t ≤ 2 π
-10 -8^ -6^ -4^ -2^2 4 6 8 10 x
10 y 8 6 4 2
-10 -8^ -6^ -4^ -2^2 4 6 8 10 x
10 y 8 6 4 2
Find a rectangular equation equivalent to the given pair of parametric equations.
- x (^) = 4 sin t, y (^) = 4 cos t; (^0) ≤ t (^) ≤ 2 π 49)
Solve the problem.
- A projectile is fired with an initial velocity of 600 feet per second at an angle of 45° with the horizontal. In how many seconds will the projectile strike the ground? (Round your answer to the nearest tenth of a second.) The parametric equations for the path of the projectile are x = (600 cos 45°)t, and y = (600 sin 45°)t - 16t2.
- A projectile is fired with an initial velocity of 400 feet per second at an angle of 45° with the horizontal. To the nearest foot, find the maximum altitude of the projectile. The parametric equations for the path of the projectile are x = (400 cos 45°)t, and y = (400 sin 45°)t - 16t2.
Answer Key
Testname: EXAM 3 REVIEW PROBLEMS
38) V: (- 9 , 0), ( 9 , 0);
F: (- 77 , 0), ( 77 , 0)
- x
- x
- x
192 +^
y^2 2116 =^1
- x
9 -^
y^2 7 =^
- y
y = 34 x, y = - 34 x
y = 1 4
x2^ + 1 2
x + 9 4
; - 9 ≤ x ≤ 7
-10 10
10
-10 10
10
-10 -8^ -6^ -4^ -2^2 4 6 8 10 x
10 y 8 6 4 2
-10 -8^ -6^ -4^ -2^2 4 6 8 10 x
10 y 8 6 4 2
- x^2 + y^2 = 16; (^) - (^4) ≤ x (^) ≤ 4
- 26.5 sec
- 1250 ft
