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study help
mathematics
precalculus
Questions and Answers of
Precalculus
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
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.
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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.
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
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
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
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
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
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.
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
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.
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
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
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
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 <
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 <
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
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
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
In Problems 21 – 26, opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box.(−2, −3, 0);
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. rcsco -2
In Problems 15 – 30, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. r sece = -4
Find a vector of magnitude 15 that is parallel to 4i − 3j.
In Problems 21 – 34, plot each point given in polar coordinates. (-1, 7 3
In Problems 25 – 36, write each complex number in rectangular form. Tein
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