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mathematics
precalculus

Questions and Answers of Precalculus

Write each complex number in the standard form and plot each in the complex plane.0.1(cos 350° + i sin 350°)
Write each complex number in the standard form and plot each in the complex plane. Зт Зп cos 4 + i sin 4. 4,
Write each complex number in the standard form and plot each in the complex plane. + i sin 2т 3 3 cos 3 3.
Write each complex number in the standard form and plot each in the complex plane.3(cos 60° + i sin 60°)
Write each complex number in the standard form and plot each in the complex plane.2(cos 150° + i sin 150°)
Write each complex number in polar form. Express each argument in degrees. 3 - 2i
Write each complex number in polar form. Express each argument in degrees. 4 - 3i
Write each complex number in polar form. Express each argument in degrees. -√3 + i
Write each complex number in polar form. Express each argument in degrees. -1 - i
Sketch the graph of each polar equation. Be sure to test for symmetry.r = 2 + cosθ
Sketch the graph of each polar equation. Be sure to test for symmetry.r = 1 -2 cosθ
Sketch the graph of each polar equation. Be sure to test for symmetry.r = 4 - cosθ
Sketch the graph of each polar equation. Be sure to test for symmetry.r = 3 -3sinθ
Sketch the graph of each polar equation. Be sure to test for symmetry.r = 3sinθ
Sketch the graph of each polar equation. Be sure to test for symmetry.r = 4 cosθ
The variables r and θ represent polar coordinates. (a) Write each polar equation as an equation in rectangular coordinates (x,y).(b) Identify the equation and graph it.r2 + 4rsin θ – 8r
The variables r and θ represent polar coordinates. (a) Write each polar equation as an equation in rectangular coordinates (x,y).(b) Identify the equation and graph it.r cosθ + 3rsinθ = 6
The variables r and θ represent polar coordinates. (a) Write each polar equation as an equation in rectangular coordinates (x,y).(b) Identify the equation and graph it.θ = π/4
The variables r and θ represent polar coordinates. (a) Write each polar equation as an equation in rectangular coordinates (x,y).(b) Identify the equation and graph it.r = 5
The variables r and θ represent polar coordinates. (a) Write each polar equation as an equation in rectangular coordinates (x,y).(b) Identify the equation and graph it.3r = sinθ
The variables r and θ represent polar coordinates. (a) Write each polar equation as an equation in rectangular coordinates (x,y).(b) Identify the equation and graph it.r = 2sinθ
The rectangular coordinates of a point are given. Find two pairs of polar coordinates (r,θ) for each point, one with r > 0 and the other with r < 0 Express in radians.(-5, 12)
The rectangular coordinates of a point are given. Find two pairs of polar coordinates (r,θ) for each point, one with r > 0 and the other with r < 0 Express in radians.(3, 4)
The rectangular coordinates of a point are given. Find two pairs of polar coordinates (r,θ) for each point, one with r > 0 and the other with r < 0 Express in radians.(0,-2)
The rectangular coordinates of a point are given. Find two pairs of polar coordinates (r,θ) for each point, one with r > 0 and the other with r < 0 Express in radians.(2, 0)
The rectangular coordinates of a point are given. Find two pairs of polar coordinates (r,θ) for each point, one with r > 0 and the other with r < 0 Express in radians.(1,-1)
The rectangular coordinates of a point are given. Find two pairs of polar coordinates (r,θ) for each point, one with r > 0 and the other with r < 0 Express in radians.(-3,3)
Plot each point given in polar coordinates, and find its rectangular coordinates. (-4,-π/4)
Plot each point given in polar coordinates, and find its rectangular coordinates. (-3,-π/2)
Plot each point given in polar coordinates, and find its rectangular coordinates. (-1,5π/4)
Plot each point given in polar coordinates, and find its rectangular coordinates. (-2,4π/3)
Plot each point given in polar coordinates, and find its rectangular coordinates. (4,2π/3)
Plot each point given in polar coordinates, and find its rectangular coordinates. (3,π/6)
If u•v = 0 and , u x v = 0 what, if anything, can you conclude about u and v?
Prove property (9). u x v|| = ||u| |sin 0, where 0 is the angle between u and v. (9)
Prove property (5). u x (v + w) = (u X v) + (u X w) (5)
Prove property (3). u X v = -(v x u) (3)
Show that if u and v are orthogonal unit vectors then u x v is also a unit vector
Show that if u and v are orthogonal then |u x v|= |u||v|
Prove for vectors u and v that |u x v|2 = |u|2|v|2 – (u • v)2Proceed as in the proof of property (4), computing first the left side and then the right side.
Refer to Problem 55. Find the volume of a parallelepiped whose defining vectors are A = (1,0,6), B = (2,3,8) and C = (8,-5,6).Problem 55A parallelepiped is a prism whose faces are all parallelograms.
A parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the vectors that define the parallelepiped shown in the figure. The volume V of the parallelepiped is given by the
Find a unit vector normal to the plane containing v = 2i + 3j - k and w = -2i - 4j -3k.
Find a unit vector normal to the plane containing v = i + 3j - 2k and w = -2i + j +3k.
Find the area of the parallelogram with vertices P1, P2, P3 and P4.P1 = (-1,1,1), P2 = (-1,2,2), P3 = (-2,3,-5), P4 = (-3,5,-4)
Find the area of the parallelogram with vertices P1, P2, P3 and P4.P1 = (1,2,-1), P2 = (4,2,-3), P3 = (6,-5,2), P4 = (9,-5,0)
Find the area of the parallelogram with vertices P1, P2, P3 and P4.P1 = (2,1,1), P2 = (2,3,1), P3 = (-2,4,1), P4 = (-2,6,1)
Find the area of the parallelogram with vertices P1, P2, P3 and P4.P1 = (1,1,2), P2 = (1,2,3), P3 = (-2,3,0), P4 = (-2,4,1)
Find the area of the parallelogram with one corner at and adjacent sides and P1P2 (vector) and P1P3 (vector).P1 = (-2,0,2), P2 = (2,1,-1), P3 = (2,-1,2)
Find the area of the parallelogram with one corner at and adjacent sides and P1P2 (vector) and P1P3 (vector).P1 = (1,2,0), P2 = (-2,3,4), P3 = (0,-2,3)
Find the area of the parallelogram with one corner at and adjacent sides and P1P2 (vector) and P1P3 (vector).P1 = (0,0,0), P2 = (2,3,1), P3 = (-2,4,1)
Find the area of the parallelogram with one corner at and adjacent sides and P1P2 (vector) and P1P3 (vector).P1 = (0,0,0), P2 = (1,2,3), P3 = (-2,3,0)
Find a vector orthogonal to both u and j + k.
Find a vector orthogonal to both u and i + j.
Find a vector orthogonal to both u and w.
Find a vector orthogonal to both u and v.
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.(w • w) • v
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.u • (v • v)
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.(v x u) • w
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.v • (u x w)
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.(u x v) • w
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.u • (v x w)
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.v • (v x w)
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.u • (u x v)
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.(-3v) x w
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.u x (2v)
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.v x (4w)
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.(3u) x v
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.w x w
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.v x v
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.w x v
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.v x u
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.v x w
Use the given vectors u, v, and w to find each expression. u = 2i - 3j + k, v = -3i + 3j + 2k, w = i + j + 3k.u x v
Find (a) v x w, (b) w x v, (c) w x w, (d) v x v. v = 2i - 3j w = 3j - 2k
Find (a) v x w, (b) w x v, (c) w x w,(d) v x v. v = i - j - k w = 4i - 3k
Find (a) v x w, (b) w x v, (c) w x w,(d) v x v. v = 3i + j + 3k w = i - k
Find (a) v x w, (b) w x v, (c) w x w,(d) v x v. v = 2i - j + 2k w = j - k
Find (a) v x w, (b) w x v, (c) w x w,(d) v x v. v = i - 4j + 2k w = 3i + 2j + k
Find (a) v x w, (b) w x v, (c) w x w,(d) v x v. v = i + j w = 2i + j + k
Find (a) v x w, (b) w x v, (c) w x w,(d) v x v. v = -i + 3j + 2k w = 3i - 2j - k
Find (a) v x w, (b) w x v, (c) w x w,(d) v x v. v = 2i - 3j + k w = 3i - 2j - k
Find the value of each determinant. C| -2 -3 2 -2| B
Find the value of each determinant. A B -1 3 5 0 -2 5
Find the value of each determinant. | A B C 3 3 2.
Find the value of each determinant. A B C 2 4 3
Find the value of each determinant. 0 5 3 -4
Find the value of each determinant. 5| -2 -1
Find the value of each determinant. -2 5 2 -3
Find the value of each determinant. 1 3.
True or False.The area of the parallelogram having u and v as adjacent sides is the magnitude of the cross product of u and v.
True or False. |u x v| = |u| |v| cosθ, where θ is the angle between u and v.
True or False.u x v is a vector that is parallel to both u and v.
True or False.If u and v are vectors, then u x v + v x u = 0.
True or False.For any vector v, v x v = 0.
True or False. If u and v are parallel vectors, then u x v = 0.
The work W done by a constant force F in moving an object from a point A in space to a point B in space is defined as W = F.AB(vector). Use this definition in given Problem. Find the work done
The work W done by a constant force F in moving an object from a point A in space to a point B in space is defined as W = F.AB(vector). Use this definition in given Problem. Find the work done
The work W done by a constant force F in moving an object from a point A in space to a point B in space is defined as W = F.AB(vector). Use this definition in given Problem. Find the work done
Find the radius and center of each sphere. 3x2 + 3y2 + 3z2 + 6x – 6y = 3

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