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mathematics
precalculus
Precalculus Concepts Through Functions A Unit Circle Approach To Trigonometry 5th Edition Michael Sullivan - Solutions
In Problems 39–62, identify and graph each polar equation. r = 1 cos
In Problems 39–62, identify and graph each polar equation. r = 4 cos (30)
In Problems 43–58, polar coordinates of a point are given. Find the rectangular coordinates of each point.(8.1, 5.2)
If v, w, u and a, b, c are vectors for whichandshow that a. v = b.w = c.u = 1
In Problems 39–62, identify and graph each polar equation. r² 2 sin (20)
In Problems 39–62, identify and graph each polar equation. r² = 9 cos(20)
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 are all parallelograms. Let A, B, and C be the vectors that define the parallelepiped shown in the
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. If f(x) = = 1 (x² +9)3/2 and g(x) = 3 tanx, show that 1 27 sec³ x (fog)(x) =
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 calculus.Find the exact value of (1/2). cos-1 с
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 calculus.Find the exact value of 临 sec(sin-1-√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 calculus.Use properties of logarithms to writeas a sum or difference of logarithms. Express powers as factors.
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.Find all asymptotes of the graph of f(x) = x22x 15' 2x²5 -
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 calculus.Iffind the exact value of sinθ/2. cos 0 = 3 T 82
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.Find the vertex and determine if the graph ofis concave up or concave down. f(x) = 2/3 12x + 10
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 calculus.Find the domain of f(x) = 3x + 4 x²16 2
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 calculus.An open-top box is made from a sheet of metal by cutting squares from each corner and folding up the
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 calculus.Establish the identity: (1 − sin2θ)(1 + tan2θ) = 1
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 calculus.Solve: 7x−1 = 3 · 2x+4
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.What is the function that is graphed after the graph of y = 3√x is shifted left 4 units and up 9
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 calculus.Find the exact value of cos80° cos70° − sin80° sin70°.
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 calculus.Find two pairs of polar coordinates (r,θ), one with r > 0 and the other with r < 0, for the
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 f (x) = 7x−1 + 5, find f−1 (x).
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 complex nth root of a nonzero complex number w has the same magnitude.
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 calculus.Find the area of the triangle for which a = 8, b = 9, and C = 60°.
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.Rationalize the numerator: √√x - 4 X X
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. Simplify: √√24x²y5
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 calculus.Find the exact value of sin 80°cos 50° − cos 80°sin 50°.
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: 3 x-2 > 5
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 calculus.Find the average rate of change of f (x) = csc−1 x from 1 to 2.
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 calculus.Find the area of the triangle with a = 8, b = 11, and C = 113°.
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 the triangle. 3 B 6 с A
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.Convert 240° to radians. Express your answer as a multiple of π.
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. Solve: log,√x + 4 = 2
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 calculus.Find an equation of the line perpendicular to the graph of f(x) = 2 تان 3 x - 5 at x = 6.
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.Determine whether f (x) = 5x2 − 12x + 4 has a maximum value or a minimum value, and then find the
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.Solve the triangle: a = 6, b = 8, c = 12
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.Given f (x) = 2x − 3 and g(x) = x2 + x −1, find (f º g)(x).
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.Write as a single logarithm: 3 loga x + 2 loga y − 5 loga z
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.Find the distance between the points P1 = (−1, −2) and P2 = (9, 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 calculus.Given f (x) = 3x2 − 4x and g (x) = 5x3, find (f º g)(x).
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.Form a polynomial function with real coefficients having degree 4 and zeros −i and 1 − 3i.
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 √16 sec² x - 16 = 4 tanx.
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 functionis one-to-one. Find its inverse. f(x) = 5 x - 8
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 calculus.Find the area of the region enclosed byand g(x) = 6 − x. f(x)=√√36x²
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.Find the average rate of change of f (x) = 3 tan(2x) from π 8 π 8
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) _______ _______. The variable t is called a(n)_________ .
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