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mathematics
precalculus

Questions and Answers of Precalculus

In Problems 45–56, write each expression in rectangular form x + yi and in exponential form reiθ. (√3 – i)
In Problems 45–56, write each expression in rectangular form x + yi and in exponential form reiθ. 6 (√2-1)
In Problems 43–58, polar coordinates of a point are given. Find the rectangular coordinates of each point. (7.5, 11π 18
In Problems 39–62, identify and graph each polar equation. r = 20
In Problems 45–56, write each expression in rectangular form x + yi and in exponential form reiθ. (1 - √5i) ³
In Problems 39–62, identify and graph each polar equation. r = 3 + cos
Refer to Problem 55. Find the volume of a parallelepiped whose defining vectors are A = i + 6k, B = 2i + 3j − 8k, and C = 8i − 5j + 6k.Data from problem 55.A parallelepiped is a prism whose faces
In Problems 39–62, identify and graph each polar equation. r = 30
Problems 52 – 61. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
In Problems 39–62, identify and graph each polar equation. r = 1 - 3 cos 0
Problems 66–75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 59–70, the rectangular coordinates of a point are given. Find polar coordinates for each point. (一) 3 2 2 NIT
In Problems 43–58, polar coordinates of a point are given. Find the rectangular coordinates of each point. -3, 2
Problems 66–75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 66–75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.Use
Problems 52 – 61. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 43–58, polar coordinates of a point are given. Find the rectangular coordinates of each point. (-3.1, 91TT 90
Problems 66–75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 52 – 61. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Provean integer. reie = rei(0 +2km), k
Problems 66–75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 67–72, graph each pair of polar equations on the same polar grid. Find the polar coordinates of the point(s) of intersection and label the point(s) on the graph. r = 1 + cose; r = 3 cose
In Problems 61–66, write the vector v in the form ai + bj, given its magnitude v and the angle αit makes with the positive x-axis. ||v|| 15, a = 315° =
In Problems 73–82, graph each polar equation. 2 1 - cose (parabola)
In Problems 73–82, graph each polar equation. r = 2 1 - 2 cos0 (hyperbola)
If ||v|| = 2, what is the magnitude of −3/4 v?
Problems 52 – 61. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Approximate sin 40° and sin 80°.
Problems 52 – 61. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
If ||v|| = 4, what is the magnitude of 1/2v + 3v?
Problems 52 – 61. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 52 – 61. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 43–58, polar coordinates of a point are given. Find the rectangular coordinates of each point.(6.3, 3.8)
Problems 52 – 61. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Prove property (3).
Show that the vector 2v × 3w is orthogonal to both v and w.
In Problems 59–70, the rectangular coordinates of a point are given. Find polar coordinates for each point.(5, 5√3 )
Prove property (9).
Find the four complex fourth roots of unity, 1, and plot them.
Prove property (5).
Show that each complex nth root of a nonzero complex number w has the same magnitude.
Problems 66–75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 59–70, the rectangular coordinates of a point are given. Find polar coordinates for each point.(1.3, −2.1)
Find the six complex sixth roots of unity, 1, and plot them.
Problems 66–75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.For
In Problems 59–70, the rectangular coordinates of a point are given. Find polar coordinates for each point.(−0.8, −2.1)
In Problems 59–70, the rectangular coordinates of a point are given. Find polar coordinates for each point.(8.3, 4.2)
Prove formula (6). Z1 Z2 hjeta 120102 1e(0-0) 7/2 (6)
Use the result of Problem 67 to draw the conclusion that each complex nth root lies on a circle with center at the origin. What is the radius of this circle?Data from in problem 67Show that each
In Problems 59–70, the rectangular coordinates of a point are given. Find polar coordinates for each point.(−2.3, 0.2)
Show that eiπ+ 1 = 0.
Problems 66–75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 66–75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 73–82, graph each polar equation. r = 1 3-2 cos 0 (ellipse)
In Problems 73–82, graph each polar equation. r = 318 0 (reciprocal spiral)
In Problems 73–82, graph each polar equation. r = 1 1 - cos 0 (parabola)
In Problems 73–82, graph each polar equation. r = 0, 00 (spiral of Archimedes)
In Problems 73–82, graph each polar equation. r = csc02, 0
Problems 77 – 86. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
In Problems 73–82, graph each polar equation. r sin tane (cissoid) =
Problems 80–88. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 80–88. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
Solve ex+yi = 7.
Problems 66–75. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Solve ex+yi = 6i.
In Problems 73–82, graph each polar equation. tane,
In Problems 71–78, the letters x and y represent rectangular coordinates. Write each equation using polar coordinates (r,θ).4x2 y = 1
In Problems 73–82, graph each polar equation. r = cos NID 2
Problems 77 – 86. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 80–88. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 77 – 86. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 77 – 86. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
In Problems 71–78, the letters x and y represent rectangular coordinates. Write each equation using polar coordinates (r, θ).y = −3
Problems 77 – 86. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 77 – 86. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 77 – 86. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 80–88. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 77 – 86. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 80–88. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 77 – 86. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 80–88. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
In Problems 79–86, the letters r and θ represent polar coordinates. Write each equation using rectangular coordinates (x, y). r = 4 1 - cose
Problems 77 – 86. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.
Show that the graph of the equation r = −2a sin θ, a > 0, is a circle of radius a with center (0, −a) in rectangular coordinates.
Problems 80–88. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as calculus.The
In Problems 79–86, the letters r and θ represent polar coordinates. Write each equation using rectangular coordinates (x, y). r = 3 3- cose
Problems 80–88. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Problems 80–88. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for later sections, a final exam, or subsequent courses such as
Except for degenerate cases, the equationdefines an ellipse if ________. Ax2 + Bxy + Cy2 + Dx + Ey + F = 0
A conic has eccentricity e. Ife = If e< Ife 1, the conic is a(n) 1, the conic is a(n) 1, the conic is a(n)
To graph y = (x − 5)3 − 4, shift the graph of y = x3 to the (left/right) unit(s) and (up/down) unit(s).
To complete the square of x2 − 4x, add ______________.
To complete the square of x2 − 3x, add _______________.
Suppose x = x(t) and y = y(t) are two functions of a third variable t that are defined on the same interval I. The graph of the collection of points defined by (x, y) = (x(t), y(t)) is called a(n)
Transform the equation r = 6 cos θ from polar coordinates to rectangular coordinates.
To graph y = (x + 1)2 − 4, shift the graph of y = x2 to the (left/right) unit(s) and then (up/down) unit(s).
Find the intercepts of the graph of y2 = 9 + 4x2.
To transform the equationinto one in x' and y' without an x' y' -term, rotate the axes through an acute angle θ that satisfies the equation ______. Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 B = 0
If θ is acute, the Half-angle Formula for the sine function is sin θ/2 = _______.
Find the intercepts of the graph of y2 = 16 − 4x2.

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