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mathematics
precalculus

Precalculus Concepts Through Functions A Unit Circle Approach To Trigonometry 5th Edition Michael Sullivan - Solutions

A 2-pound weight is attached to a 3-pound weight by a rope that passes over an ideal pulley. The smaller weight hangs vertically, while the larger weight sits on a frictionless inclined ramp with angle θ. The rope exerts a tension force T on both weights along the direction of the rope. Find the
Problems 94–103. 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 Descartes’ Rule of Signs to determine the possible number of positive or negative real zeros for
A 20-pound box sits at rest on a horizontal surface, and there is friction between the box and the surface. One side of the surface is raised slowly to create a ramp. The friction force f opposes the direction of motion and is proportional to the normal force FN exerted by the surface on the box.
Problems 94 – 103. 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: log4 (x + 3) − log4 (x − 1) = 2
A box sitting on a horizontal surface is attached to a second box sitting on an inclined ramp by a rope that passes over an ideal pulley. The rope exerts a tension force T on both weights along the direction of the rope, and the coefficient of friction between the surface and boxes is 0.6. If the
Problems 95 – 104. 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 radians to degrees. 3
Problems 94 – 103. 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 midpoint of the line segment connecting the points (−3, 7) and (1/2, 2).
Two muscles exert force on a bone at the same point. The first muscle exerts a force of 800 N at a 10° angle with the bone. The second muscle exerts a force of 710 N at a 35° angle with the bone. What are the direction and magnitude of the resulting force on the bone?
Problems 95 – 104. 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 the amplitude and period of y = −2 sin(5x) without graphing.
Problems 94–103. 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 that the point (3, 8) is on the graph of y = f (x), what is the corresponding point on the graph
Problems 95 – 104. 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 any asymptotes for the graph of R(x)= = x + 3 - x² x 12
Problems 94 – 103. 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 z = 2 − 5i and w = 4 + i, find z · w.
Problems 95 – 104. 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 remainder when 3x5 − 2x3 + 7x − 5 is divided by x − 1.
Problems 94 – 103. 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 equation: 4 sinθ cosθ= 1, 0 ≤ θ < 2π
Problems 95 – 104. 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 a triangle with sides 6, 11, and 13.
Problems 94 – 103. 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 = 65°, B = 37°, c = 10
Refer to Problem 99. The points (−3, 0), (−1, −2), (3, 1), and (1, 3) are the vertices of a parallelogram ABCD.Data from problem 99The field of computer graphics utilizes vectors to compute translations of points. For example, if the point (−3, 2), represented by vector u = (−3, 2), is to
Problems 95 – 104. 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: 32x−3 = 91−x
Problems 94 – 103. 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: 5x²3e3x e³x. 10x (5x2)2
Problems 94 – 103. 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 7π/12.
Problems 95 – 104. 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: 6x2 + 7x = 20
To drag a 500-pound boulder into place, Tyrone, Bill, and Chuck attach three ropes to the boulder as shown in the diagram. If Tyrone pulls with 240 pounds of force and Chuck pulls with 110 pounds of force, then Bill must pull with how much force in order for the boulder to move? 500
Problems 95 – 104. 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.m = f'(x) = 3x2 + 8x gives the slope of the tangent line to the graph of f (x) = x3 + 4x2 − 5 at
Problems 94 – 103. 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 sin5 x = sin x − 2 cos2 x sin x + cos4 x sin x.
See Problem 102. If Bill pulls due east with 200 pounds of force, then what direction does the boulder move?Data from problem 102To drag a 500-pound boulder into place, Tyrone, Bill, and Chuck attach three ropes to the boulder as shown in the diagram. If Tyrone pulls with 240 pounds of force and
Problems 107–116. 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: √x 2 = 3 X
Problems 95 – 104. 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 cos3 x = cos x − sin2 x cos x .
Problems 107–116. 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.109. Find the exact value of tan[cos-¹(2)].
Problems 107–116. 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.Factor −3x3 + 12x2 + 36x completely.
Problems 107–116. 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 amplitude, period, and phase shift ofGraph the function, showing at least two periods.
Problems 107–116. 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 (−5, −8) and (7, 1).
Problems 107–116. 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) = x4, find f(x) — ƒ(3) x - 3
Problems 107–116. 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 the equation of the circle in standard form: x2 + y2 − 20x + 4y + 55 = 0
Problems 107–116. 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(0) = √25-02 show that (fog)(0) and g(0) = 5 sin 0, = 5 cos0. 110110 <
Problems 107–116. 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 the intercepts of the graph of f (x) = x3 + 2x2 − 9x − 18
Problems 107–116. 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: 4(x − 5)2 + 9 = 53
The distance d from P1 = (3, −4) to P2 = (−2, 1) is d = _____________.
For f (x) = −3x2 + 5x − 2, find f(x+h)-f(x) h h = 0
The sum formula for the sine function is sin(A + B) = ______________.
The formula for the distance d from P1 = (x1, y1) to P2 = (x2 , y2) is d = ____________.
The distance d from P1 = (2, −5) to P2 = (4, −2) is d = _________________.
In Problems 1 – 10, identify each equation. If it is a parabola, give its vertex, focus, and directrix; if it is an ellipse, give its center, vertices, and foci; if it is a hyperbola, give its center, vertices, foci, and asymptotes.y2 = −16x
In Problems 35–42, find ∣∣v∣∣. v = −5i + 12j
In Problems 35–42, plot each point given in polar coordinates, and find other polar coordinates (r,θ) of the point for which: (a) r> 0, -2π ≤ 0 < 0 (b) r < 0, 0≤ 0 < 2π (c) r> 0, 2π ≤ 0 < 4T
In Problems 35–42, plot each point given in polar coordinates, and find other polar coordinates (r,θ) of the point for which: (a) r> 0, -2π ≤ 0 < 0 (b) r < 0, 0≤ 0 < 2π (c) r> 0, 2π ≤ 0 < 4T
Derive formula (3). sin a cos 3 = 2 si sin (a + 3) + sin(a - 3)
Derive formula (7). sina sin 3 = 2 sina COS a - B 2 a + ß 2
For Problems 59–62, the lines that bisect each angle of a triangle meet in a single point O, and the perpendicular distance r from O to each side of the triangle is the same. The circle with center at O and radius r is called the inscribed circle of the triangle (see the figure).Use the result of
Derive formula (9). cos a - a + B sin- 2 cos 3 = -2 sin- a - B 2
Derive formula (8). a + ß 2 cosa+cos3 = 2 cos- COS a - ß 2
In Problems 7 – 14, find the value of each determinant. А 1 0 В -2 с -3 2-2
In polar coordinates, the points (r, θ) and (−r, θ) are symmetric with respect to which of the following? (a) the polar axis (or x-axis) (c) the line = (or y-axis) π (b) the pole (or origin) π (d) the line 9 4 (or y = x)
Every nonzero complex number has exactly _________ distinct complex cube roots.
To test whether the graph of a polar equation may be symmetric with respect to the line θ = π/2, replace θ by ____.
True or False In the polar coordinates (r, θ), r can be negative.
In Problems 14–18,Find ||v||. P₁ = (3√2, 7√2) and P₂ = (8√2, 2√2).
In Problems 13 – 20, match each point in polar coordinates with either A, B, C, or D on the graph. -4- B -+----+ C D 1/60 -+-
In Problems 11–18, use the vectors in the figure at the right to graph each of the following vectors.v − w W V ▬▬▬▬
In Problems 15 – 22, find(a) v × w,(b) w × v,(c) w × w,(d) v × v. v = 2i - j + 2k w =j-k
In Problems 19–21, find zw and z/w. Write your answers in polar form and in exponential form. Z = W 9π COS + i sin- 5 3(cos 9T 5 = 2(cos+isin)
In Problems 15 – 22, find(a) v × w,(b) w × v,(c) w × w,(d) v × v. v = 3i + j + 3k w = i-k W
In Problems 13 – 24, plot each complex number in the complex plane and write it in polar form and in exponential form. 9√3 +9i
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r cose = 4
In Problems 19–21, find zw and z/w. Write your answers in polar form and in exponential form. Z = 5 ( cos π w = cos. 18 71TT 36 + i sin + i sin π 18. 71п 36
In Problems 22–25, write each expression in rectangular form x + yi and in exponential form reiθ. 3 [3(cos+ i sin)]²
In Problems 21 – 34, plot each point given in polar coordinates. (3, T
In Problems 15 – 22, find(a) v × w,(b) w × v,(c) w × w,(d) v × v. v=i-j-k W w = 4i - 3k
In Problems 13 – 24, plot each complex number in the complex plane and write it in polar form and in exponential form. 2 + √3i
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r cos 0 = -2
Find b so that the vectors v = i + j and w = i + bj are orthogonal.
In Problems 21 – 34, plot each point given in polar coordinates. (4, Зп 2 /
In Problems 15 – 20, find the distance from P1 to P2.P1 = (2, −3, −3) and P2 = (4, 1, −1)
In Problems 19–22, v1 = 4i + 6j, v2 = −3i − 6j, v3 = −8i + 4j, and v4 = 10i + 15j.Which two vectors are parallel?
In Problems 22–25, write each expression in rectangular form x + yi and in exponential form reiθ. 52 (cossa 8 + i sin 5п 8 4
In Problems 15 – 22, find(a) v × w,(b) w × v,(c) w × w,(d) v × v. v = 2i - 3j w = 3j - 2k W
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r = 2 cos0
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r sin 0 -2
In Problems 22–25, write each expression in rectangular form x + yi and in exponential form reiθ. 6 (1 - √3i)*
In Problems 21 – 34, plot each point given in polar coordinates. (-3, π)
In Problems 21 – 34, plot each point given in polar coordinates. (-2, 0)
In Problems 19–22, v1 = 4i + 6j, v2 = −3i − 6j, v3 = −8i + 4j, and v4 = 10i + 15j.Which two vectors are orthogonal?
In Problems 22–25, write each expression in rectangular form x + yi and in exponential form reiθ. (3 + 4i)4
In Problems 21 – 34, plot each point given in polar coordinates. (6, π
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r = 2 sin0
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r = -4 sin 0
In Problems 19–22, v1 = 4i + 6j, v2 = −3i − 6j, v3 = −8i + 4j, and v4 = 10i + 15j.Find the angle between the vectors v1 and v2.
In Problems 25 – 36, write each complex number in rectangular form. 2π 2(cos+ i sin 3 3
In Problems 21 – 34, plot each point given in polar coordinates. -2, Зп 4
In Problems 21 – 34, plot each point given in polar coordinates. (5, T 57 3
In Problems 25 – 36, write each complex number in rectangular form. 3(co COS 7п 6 7п 6 + i sin.
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r sec0 = 4
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r = -4 cos 0
In Problems 21 – 34, plot each point given in polar coordinates. (-3, 2T 3
In Problems 13 – 24, plot each complex number in the complex plane and write it in polar form and in exponential form.√5 − i
In Problems 25 – 36, write each complex number in rectangular form. 4e¹- 7/4
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r csc 0 = 8
In Problems 21 – 34, plot each point given in polar coordinates. (2-4)
In Problems 25 – 36, write each complex number in rectangular form. 2e².5π/6
In Problems 25 – 36, write each complex number in rectangular form. 4(cos $0 + i sin
In Problems 21 – 34, plot each point given in polar coordinates. (4₁ 2п 3

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