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mathematics
precalculus

Questions and Answers of Precalculus

Decompose v into its vertical and horizontal components.P1 = (3√2, 7√2) and P2 = (8√2, 2√2)
P1 = (3√2, 7√2) and P2 = (8√2, 2√2)Find the angle between v and i.
P1 = (3√2, 7√2) and P2 = (8√2, 2√2)Find the unit vector in the direction of v.
P1 = (3√2, 7√2) and P2 = (8√2, 2√2)Find |v|.
P1 = (3√2, 7√2) and P2 = (8√2, 2√2)Find the position vector equal to P1P2(vector).
Find all the complex cube roots of -8 +8√3i. Then plot them in rectangular coordinates.
Perform the given operation, where z = 2(cos 85° + i sin 85°) and w = 3(cos 22° + i sin 22°). Write your answer in polar form. w5
Perform the given operation, where z = 2(cos 85° + i sin 85°) and w = 3(cos 22° + i sin 22°). Write your answer in polar form. w/z
Perform the given operation, where z = 2(cos 85° + i sin 85°) and w = 3(cos 22° + i sin 22°). Write your answer in polar form.z • w
Test the polar equation for symmetry with respect to the pole, the polar axis, and the line θ = π/2.r = 5sin θ cos2 θ
Test the polar equation for symmetry with respect to the pole, the polar axis, and the line θ = π/2. r2cos θ = 5
Convert the polar equation to a rectangular equation. Graph the equation. rsin2 θ + 8sin θ = r
Convert the polar equation to a rectangular equation. Graph the equation. tanθ = 3
Convert the polar equation to a rectangular equation. Graph the equation. r = 7
Convert (2,2,√3) from rectangular coordinates to polar coordinates (r,θ), where r > 0 and 0 ≤ < 2π.
Plot each point given in polar coordinates. (-4,π/3)
Plot each point given in polar coordinates. (3,-π/6)
Plot each point given in polar coordinates. (2,3π/4)
A moving van with a gross weight of 8000 pounds is parked on a street with a 5° grade. Find the magnitude of the force required to keep the van from rolling down the hill. What is the magnitude of
Find the work done by a force of 5 pounds acting in the direction 60° to the horizontal in moving an object 20 feet from (0,0) to (20,0).
A weight of 2000 pounds is suspended from two cables, as shown in the figure. What are the tensions in each cable? 40° 30° 2000 pounds
An airplane has an airspeed of 500 kilometers per hour (k/hr) in a northerly direction. The wind velocity is 60 (k/hr) in a southeasterly direction. Find the actual speed and direction of the plane
A swimmer can maintain a constant speed of 5 miles per hour. If the swimmer heads directly across a river that has a current moving at the rate of 2 miles per hour, what is the actual speed of the
Suppose u x v = 3v what is u x v?
If u x v 2i - 3j + k what v x u?
Find the area of the parallelogram with vertices P1 = (2,-1,1), P2 = (5,4,1), P3 = (0,1,1), P4 = (3,3,5)
Find the area of the parallelogram with vertices P1 = (1,1,1), P2 = (2,3,4), P3 = (6,5,2), P4 = (7,7,5)
Find the direction angles of the vector v = i - j + 2k.
Find the direction angles of the vector v = 3i - 4j +2k.
Decompose v into two vectors, one parallel to w and the other orthogonal to w.v = -i + 2j; w = 3i - j
Decompose v into two vectors, one parallel to w and the other orthogonal to w.v = 2i + 3j 104. ; w = 3i + j
Decompose v into two vectors, one parallel to w and the other orthogonal to w.v = -3i + 2j; w = -2i + j
Decompose v into two vectors, one parallel to w and the other orthogonal to w.v = 2i + j; w = -4i + 3j
Determine whether v and w are parallel, orthogonal, or neither.v = -4i + 2j; w = 2i + 4j
Determine whether v and w are parallel, orthogonal, or neither.v = 3i - 2j; w = 4i + 6j
Determine whether v and w are parallel, orthogonal, or neither.v = -2i + 2j; w = -3i + 2j
Determine whether v and w are parallel, orthogonal, or neither.v = 3i - 4j; w = -3i + 4j
Determine whether v and w are parallel, orthogonal, or neither.v = -2i - j; w = 2i + j
Determine whether v and w are parallel, orthogonal, or neither.v = 2i + 3j; w = -4i - 6j
Find the dot product v • w and the angle between v and w.v = -i - 2j + 3k, w = 5i + j + k
Find the dot product v • w and the angle between v and w.v = 4i - j + 2k, w = i - 2j - 3k
Find the dot product v • w and the angle between v and w.v = i - j + k, w = 2i + j + k
Find the dot product v • w and the angle between v and w.v = i + j + k, w = i - j + k
Find the dot product v • w and the angle between v and w.v = i + 4j, w = 3i - 2j
Find the dot product v • w and the angle between v and w.v = i - 3j, w = -i + j
Find the dot product v • w and the angle between v and w.v = 3i - j, w = i + j
Find the dot product v • w and the angle between v and w.v = -2i + j, w = 4i - 3j
Find a unit vector orthogonal to both v and w.
Find a unit vector in the same direction as v and then in the opposite direction of v.
Use the vectors v = 3i + j - 2k and w = -3i + 2j - k to find each expression. |v - w|
Use the vectors v = 3i + j - 2k and w = -3i + 2j - k to find each expression. v • (v x w)
Use the vectors v = 3i + j - 2k and w = -3i + 2j - k to find each expression. v x w
Use the vectors v = 3i + j - 2k and w = -3i + 2j - k to find each expression. |v| + |w|
Use the vectors v = 3i + j - 2k and w = -3i + 2j - k to find each expression. |v| - |w|
Use the vectors v = 3i + j - 2k and w = -3i + 2j - k to find each expression. |v + w|
Use the vectors v = 3i + j - 2k and w = -3i + 2j - k to find each expression. -v + 2w
Use the vectors v = 3i + j - 2k and w = -3i + 2j - k to find each expression. 4v - 3w
A vector v has initial point P = (0,-4,3) and terminal point Write Q = (6, -5, -1). Write v in the from v = ai + bj + ck.
A vector v has initial point P = (1,3,-2) and terminal point Write Q = (4, -2, 1). Write v in the from v = ai + bj + ck.
Find the distance from to P1 = (0,-4,3) to P2 = (6,-5,-1).
Find the distance from to P1 = (1,3,-2) to P2 = (4, -2, 1).
Find the direction angle between i and v = 2i - 6j.
Find the direction angle between i and v = -i + √3j.
Find the vector v in the xy-plane with magnitude 5 if the angle between v and i is 150°.
Find the vector v in the xy-plane with magnitude 3 if the angle between v and i is 60°.
Find a unit vector in the opposite direction of w.
Find a unit vector in the same direction as v.
Use the vectors v = -2i + j and w = 4i - 3j to find.|2v| - 3|w|
Use the vectors v = -2i + j and w = 4i - 3j to find.|v + w|
Use the vectors v = -2i + j and w = 4i - 3j to find.|v + w|
Use the vectors v = -2i + j and w = 4i - 3j to find.|v|
Use the vectors v = -2i + j and w = 4i - 3j to find.-v + 2w
Use the vectors v = -2i + j and w = 4i - 3j to find.4v - 3w
Use the vectors v = -2i + j and w = 4i - 3j to find.v - w
Use the vectors v = -2i + j and w = 4i - 3j to find.v + w
The vector v is represented by the directed line segment PQ (vector). Write v in the form and ai + bj find |v|.P = (3, -4); Q = (-2, 0)
The vector v is represented by the directed line segment PQ (vector). Write v in the form and ai + bj find |v|.P = (0, -2); Q = (-1, 1)
The vector v is represented by the directed line segment PQ (vector). Write v in the form and ai + bj find |v|.P = (-3, 1); Q = (4, -2)
The vector v is represented by the directed line segment PQ (vector). Write v in the form and ai + bj find |v|.P = (1, -2); Q = (3, -6)
Use the figure to graph each of the following: 5v - 2w V u W
Use the figure to graph each of the following: 2u + 3v V u W
Use the figure to graph each of the following: v + w V u W
Use the figure to graph each of the following: u + v V u W
Find all the complex fourth roots of -16.
Find all the complex cube roots of 27.
Write each expression in the standard form a + bi.( 1 – 2i)4
Write each expression in the standard form a + bi.(3 + 4i)4
Write each expression in the standard form a + bi.(2 – 2i)8
Write each expression in the standard form a + bi.(1 – √3i)6
Write each expression in the standard form a + bi. 5 5 16 + i sin 21 cos cos 16
Write each expression in the standard form a + bi. 14 [v=(co 5п Cos + i sin 8.
Write each expression in the standard form a + bi.[2(cos 50° + i sin 50°)]3
Write each expression in the standard form a + bi. [3(cos 20° + i sin 20°)]3
Find z and z/w. Leave your answers in polar form.z = 4(cos 50° + i sin 50°) w = cos 340° + i sin 340°
Find z and z/w. Leave your answers in polar form.z = 5(cos 10° + i sin 10°) w = cos 355° + i sin 355°
Find z and z/w. Leave your answers in polar form. - 2(c* 5т 5т z = 2 cos = + i sin 3 3 * + i sin 3 3 cos s 3
Find z and z/w. Leave your answers in polar form. 97 + i sin 5 9т z = 3| cos 5 = 2(« + i sin cos 5
Find z and z/w. Leave your answers in polar form.z = cos 205° + i sin 205° w = cos 85° + i sin 85°
Find z and z/w. Leave your answers in polar form.z = cos 80° + i sin 80° w = cos 50° + i sin 50°
Write each complex number in the standard form and plot each in the complex plane.0.5(cos 160° + i sin 160°)

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