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study help
mathematics
precalculus
Questions and Answers of
Precalculus
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + 2y = 5 x + y = 3
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 2x - y = -1 x + 1⁄2 y = 2
In Problems 15–42, solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, write, “Not applicable.” x - 2y + 3z = 0 = 3x + y - у 2z 2z =
In Problems 25 – 54, solve each system. Use any method you wish. y2 – x2 + 4 = 0 2x² + 3y² = 6
In Problems 35 – 42, graph each system of inequalities. x² + y² ≤ 25 + VI y ≤ x²-5
In Problems 25 – 54, solve each system. Use any method you wish. x² + 2y² = 16 y2 y² = 24 4x²
Problems 34–43. 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 17–50, find the partial fraction decomposition of each rational expression. 7x + 3 x3 - 2x² - 3x
In Problems 35 – 42, graph each system of inequalities. xy > 4 y > x² + 1
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x-бу = -4 5x +4y = 5
Problems 34–43. 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
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 8 = ०९/ + = 0 I
In Problems 25 – 54, solve each system. Use any method you wish. 4х2 + 3у2 = 4 2х2 - бу² = -3
In Problems 17–50, find the partial fraction decomposition of each rational expression. x 3 +1 - x4 x5
Problems 34–43. 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 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x + 3y = 3 3 ∞013 4x + 2 =
In Problems 43 – 52, graph each system of linear inequalities. State whether the graph is bounded or unbounded, and label the corner points. x > 0 y 20 2x + y ≤ 6 x + 2y ≤ 6
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 0 = د در | || 2y +
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + 2y = 4 2x + 4y = 8
In Problems 25 – 54, solve each system. Use any method you wish. 5 x2 3 12 + +3=0 1 = 7
In Problems 17–50, find the partial fraction decomposition of each rational expression. x2 x3 4x2 + 5x - 2
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x + y 2x 9 2 = 13 7 = 3y + 2z =
Problems 34–43. 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 34–43. 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 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x-y= y = 7 9x-3y = 21
In Problems 25 – 54, solve each system. Use any method you wish. 2 x2 x2 3 7 y2 -+ 1 = 0 +2=0
In Problems 43 – 52, graph each system of linear inequalities. State whether the graph is bounded or unbounded, and label the corner points. x>0 y ≥ 0 x + y 24 2x + 3y ≥ 6
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 2x + 3y = 6 x - y = 1|2
In Problems 43 – 52, graph each system of linear inequalities. State whether the graph is bounded or unbounded, and label the corner points. x ≥ 0 y ≥ 0 x + y 22 2x + y 24
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 2x + у y 3x -2y +4z = -4 0 -
In Problems 17–50, find the partial fraction decomposition of each rational expression. x3 (x²+16)* 2 3
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. x - 2y + 3z = 7 2x + y + z
In Problems 25 – 54, solve each system. Use any method you wish. || + 19 ~|B
In Problems 25 – 54, solve each system. Use any method you wish. x4 X + 1 1 1 4
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. 2x + y = -1 x +y = 3
In Problems 17–50, find the partial fraction decomposition of each rational expression. x² 2 (x² + 4)³
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. x + y = -2 x - 2y = 8
In Problems 19–56, solve each system of equations. If the system has no solution, state that it is inconsistent. For Problems 19–30, graph the lines of the system. 2x + y - 3z = 0 -2x+2y
In Problems 43 – 52, graph each system of linear inequalities. State whether the graph is bounded or unbounded, and label the corner points. x ≥ 0 y ≥ 0 3x + y ≤ 6 2x + y ≤ 2
In Problems 45–64, use the inverses found in Problems 35–44 to solve each system of equations. 3x - y = 8 -2x + y = 4
In Problems 39–74, solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent. 3x-5y=3 15x + 5y = 21
Open the “Ellipse” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.(a) Uncheck the box “Equation of
Open the “Ellipse” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.(a) Uncheck the box “Equation of
Open the “Hyperbola” interactive figure, which is available in the Video & Resource Library of MyLab Math (under Interactive Figures) or at bit.ly/3raFUGB.(a) Set the slider to a = 2. Grab
Answer Problems 11–14 using the figure shown to the right.If a > 0, the equation of the parabola is of the form (a) (y - k)² (c) (xh)² = = 4a (x - h) 4a(yk) (b) (yk)² (d) (x - h)² = -4a(x -
Prove that De Moivre’s Theorem is true for all integers n by assuming it is true for integers n ≥ 1 and then showing it is true for 0 and for negative integers.Multiply the numerator and the
(a) Grab the directrix slider so that the directrix is x = −2. Grab the point F (the focus) and move to (4, 2). Check the box “Show Point on Parabola.” Grab point P and move it around the
In Problems 27 – 34, find two different pairs of parametric equations for each rectangular equation. x = √y
In Problems 25 – 36, convert each polar equation to a rectangular equation. r(2 cos0) = 2
In Problems 25 – 36, convert each polar equation to a rectangular equation. r = 6 sec0 2 sec 0 - 1
In Problems 25 – 36, convert each polar equation to a rectangular equation. r = 3 csc 0 csc 1
In Problems 23–40, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.Vertex at (2, −3); focus at (2, −5)
In Problems 31–38, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation.4x2 − y2 = 16
In Problems 31–38, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation.4y2 − x2 = 16
In Problems 23–40, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.Vertex at (4, −2); focus at (6, −2)
Find two different pairs of parametric equations for y = −2x + 4.
In Problems 39–42, find an equation for each hyperbola. -3 YA 3 -3 35 2 y = x 3x y=-x
In Problems 39–42, find an equation for each hyperbola. у=-2х у 5 -5 II IN I 1 -5 y=2x Л 5 х
In Problems 41–44, find an equation for each ellipse. -3 УА 3 (-1,-1)" -3 3 x
In Problems 39–42, find an equation for each hyperbola. y = -2x -5 УА 10 -10 y= 2x 5 x
In Problems 43 parametric equations of four plane curves are given. Graph each of them, indicating the orientation. C₁: x(t) = t, y(t) = 1²; -4 ≤ t ≤ 4 C₂: x(t) = cost, y(t) = 1 sin²t; 0
In Problems 31–38, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation.y2 − 9x2 = 9
In Problems 45–56, analyze each equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. (x - 3)² (y + 1)² + 4 9 = 1
In Problems 41–44, find an equation for each ellipse. (-1, 1) -3 УА 3 -3 3 x
In Problems 41–44, find an equation for each ellipse. -3 YA 3 -3 (1, 0) 3 x
In Problems 23–40, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.Vertex at (−1, −2); focus at (0, −2)
In Problems 31–38, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation.x2 − y2 = 4
In Problems 31–38, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation.y2 − x2 = 25
In Problems 23–40, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.Focus at (−3, 4); directrix the line y = 2
In Problems 31–38, find the center, transverse axis, vertices, foci, and asymptotes. Graph each equation.2x2 − y2 = 4
In Problems 29–40, find an equation for each ellipse. Graph the equation.Vertices at (±4, 0); y-intercepts are ±1
In Problems 45–56, analyze each equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation. (x+4)² (y + 2)² + 9 4 = 1
In Problems 23–40, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.Focus at (−3, −2); directrix the line x = 1
In Problems 45–48, use a graphing utility to graph the plane curve defined by the given parametric equations. x(t) = 4 sint 2 sin (2t) - y(t) = 4 cost 2 cos(2t)
In Problems 23–40, find the equation of the parabola described. Find the two points that define the latus rectum, and graph the equation.Focus at (−4, 4); directrix the line y = −2
A crate is placed at the center of a 5-meter board that is supported only at its ends. The weight of the crate causes a deflection of the board at its center. If the shape of the deflected board is a
Patrick Mahomes throws a football with an initial speed of 80 feet per second at an angle of 35° to the horizontal. The ball leaves his hand at a height of 6 feet.(a) Find parametric equations that
Suppose that a conic has an equation of the formIf the polar coordinates of two points on the graph areshow that r ep 1 e sino
A tank is punctured on its side, and water begins to stream out in a parabolic path. If the path of the water is given byand the water hits the ground 4 inches away from the base of the tank, what is
Halley’s comet travels around the Sun in an elliptical orbit given approximately bywhere the Sun is at the pole and r is measured in AU (astronomical units). Find the distance from Halley’s comet
In Problems 45–48, use a graphing utility to graph the plane curve defined by the given parametric equations. x(t) = 4 sint + 2 sin(2t) y(t) = 4 cost + 2 cos(2t)
In Problems 45–48, use a graphing utility to graph the plane curve defined by the given parametric equations.x(t) = t sin t, y(t) = t cost, t > 0
In Problems 43–52, identify the graph of each equation without applying a rotation of axes.x2 − 7xy + 3y2 − y − 10 = 0
In Problems 45–56, analyze each equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation.(x + 5)2 + 4( y − 4)2 = 16
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 45–48, use a graphing utility to graph the plane curve defined by the given parametric equations.x(t) = sint + cost, y = sint − cost
From physics, the equation for the free-flight trajectory of a satellite launched a distance r0 from the center of the earth is given by the polar equationwhere Me is the mass of the earth, G is the
A parabolic satellite receiver is initially positioned so its axis of symmetry is parallel to the x-axis. A motor allows the receiver to rotate and track the satellite signal. If the rotated receiver
In Problems 55 – 58, apply the rotation formulas (5) toto obtain the equationShow that A + C = A'+ C', which proves that A + C is invariant ; that is, its value does not change under a rotation of
In Problems 45–56, analyze each equation; that is, find the center, foci, and vertices of each ellipse. Graph each equation.9( x − 3)2 + ( y + 2)2 = 18
A runner on an elliptical trainer inclines the machine to increase the difficulty of her workout. If the initial elliptic path of the pedals had a horizontal major axis, and the inclined path has the
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 59–66, write an equation for each parabola. -2 УА 2 -2 (1,2) (2,1) 2 X
In Problems 59–66, write an equation for each parabola. -2 У 2 (0, 1) -2 (1, 2) X
Billy hit a baseball with an initial speed of 125 feet per second at an angle of 40° to the horizontal. The ball was hit at a height of 3 feet above the ground.(a) Find parametric equations that
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
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.For
In Problems 59–66, write an equation for each parabola. -2 У 2 -2 L (2, 1) (1,0) X
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