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Questions and Answers of College Algebra

Solve the problem.A one-way road passes under an overpass in the shape of half an ellipse, 15 ft high at the center and 20 ft wide. Assuming a truck is 12 ft wide, what is the tallest truck that can
How can the method of Exercise 45 be modified to draw a circle?Exercise 45Draftspeople often use the method shown in the sketch to draw an ellipse. Why does this method work?
Draftspeople often use the method shown in the sketch to draw an ellipse. Why does this method work?
Find the eccentricity e of each ellipse. Round to the nearest hundredth as needed.x2 + 25y2 = 25
Find the eccentricity e of each ellipse. Round to the nearest hundredth as needed.4x2 + 7y2 = 28
Find the eccentricity e of each ellipse. Round to the nearest hundredth as needed. ,2 = 1 8
Find the eccentricity e of each ellipse. Round to the nearest hundredth as needed. x2 y2 3 4
Determine the two equations necessary to graph each ellipse using a graphing calculator, and graph it in the viewing window indicated. (y + 4)2 13; x? 36 4 [-9.9, 9.9] by [-8.2, 8.2]
Determine the two equations necessary to graph each ellipse using a graphing calculator, and graph it in the viewing window indicated. (х — 3)? у? y2 1; 9. 25 [-9.9, 9.9] by [-8.2, 8.2]
Determine the two equations necessary to graph each ellipse using a graphing calculator, and graph it in the viewing window indicated. y2 1; 25 4 [-6.6, 6.6] by [-5.2, 5.2]
Determine the two equations necessary to graph each ellipse using a graphing calculator, and graph it in the viewing window indicated. x2 y2 1; 16 4 [-6.6, 6.6] by [-4.1, 4.1]
Graph the equation. Give the domain and range. Identify any that are functions. x2 y = 100
Graph the equation. Give the domain and range. Identify any that are functions. y2 х‑ 64
Graph the equation. Give the domain and range. Identify any that are functions. х 4 9.
Graph the equation. Give the domain and range. Identify any that are functions. x2 2 25
Write an equation for the ellipse.e = 2/3 ; foci at (0, -9), (0, 9)
Write an equation for the ellipse.e = 3/4 ; foci at (0, -2), (0, 2)
Write an equation for the ellipse.e = 1/2 ; vertices at (-4, 0), (4, 0)
Write an equation for the ellipse.e = 4/5 ; vertices at (-5, 0), (5, 0)
Write an equation for the ellipse.Foci at (-3, -3), (7, -3); the point (2, -7) on ellipse
Write an equation for the ellipse.Foci at (0, -3), (0, 3); the point (8, 3) on ellipse
Write an equation for each ellipse.Foci at (-4, 0), (4, 0); sum of distances from foci to point on ellipse is 9
Write an equation for each ellipse.Foci at (0, 4), (0, -4); sum of distances from foci to point on ellipse is 10
Write an equation for the ellipse.Center at (-2, 7); major axis vertical, with length 10; c = 2
Write an equation for the ellipse.Center at (3, 1); minor axis vertical, with length 8; c = 3
Write an equation for the ellipse.Minor axis with length 4; foci at (-5, 0), (5, 0)
Write an equation for the ellipse.Major axis with length 6; foci at (0, 2), (0, -2)
Write an equation for the ellipse.x-intercepts (±√15, 0) ; y-intercepts (0, ±4)
Write an equation for the ellipse.x-intercepts (±5, 0); y-intercepts (0, ±4)
Graph the ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci. |(x – 1)2, (y + 3)² 25 9.
Graph the ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci. (х + 3)? (у — 2)? 16 36
Graph the ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci. (x + 2)² (y+ 1)² 16 9.
Graph each ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci. |(x – 2)2 (y – 1)? 25 1)? -= 1
Graph each ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci.4x2 = 16 - y2
Graph each ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci.4x2 = 100 - 25y2
Graph each ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci.4x2 + 16y2 = 64
Graph each ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci.9x2 + y2 = 81
Graph each ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci. х2 y? 36 16
Graph each ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci. + y? = 1
Graph each ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci. x2 y2 16 25
Graph each ellipse. Give the domain, range, center, vertices, endpoints of the minor axis, and foci. x? y? х 25
For each ellipse, give the domain, range, center, vertices, and foci. y ( ² , (y–2)² _I (x+3)2 9, -4
For each ellipse, give the domain, range, center, vertices, and foci. (x–2)² , (y–1)² 25 -3 -2-
For each ellipse, give the domain, range, center, vertices, and foci. %3D 16 36 -4 14
For each ellipse, give the domain, range, center, vertices, and foci. y = 1 16 to -4 -3 4, 3.
Determine whether or not each equation is that of an ellipse. If it is not, state the kind of graph the equation has. (b) x² + y? = 4 (a) x² + 4y2 = 4 (c) x² + y = 4 х (d) 4 25
Match each equation of an ellipse in Column I with the appropriate intercepts in Column II. П (а) 36х? + 9y2 — 324 (b) 9х2 + 36у2 3 324 y2 A. (-3,0). (3, 0). (0, -6), (0, 6) B. (-4,0), (4, 0),
Given three noncollinear points, we can find an equation of the form x = ay2 + by + c of the horizontal parabola joining them by solving a system of equations. Work Exercises in order, to find the
Given three noncollinear points, we can find an equation of the form x = ay2 + by + c of the horizontal parabola joining them by solving a system of equations. Work Exercises in order, to find the
Given three noncollinear points, we can find an equation of the form x = ay2 + by + c of the horizontal parabola joining them by solving a system of equations. Work Exercises in order, to find the
Given three noncollinear points, we can find an equation of the form x = ay2 + by + c of the horizontal parabola joining them by solving a system of equations. Work Exercises in order, to find the
Prove that the parabola with focus (p, 0) and directrix x = -p has the equation y2 = 4px.
Suppose the two balls are now thrown upward at a 60° angle on Mars and the moon. If their initial velocity is 60 mph, then their paths in feet can be modeled by the following equation.(a) Graph on
When a projected object moves under the influence of a constant force (without air resistance), its path is parabolic. This occurs when a ball is thrown near the surface of a planet or other
The physicist Galileo observed that certain projectiles follow a parabolic path. For instance, if a cannon fires a shell at a 45° angle with a speed of v feet per second, then the path of the shell
The cable in the center portion of a bridge is supported as shown in the figure to form a parabola. The center vertical cable is 10 ft high, the supports are 210 ft high, and the distance between the
An arch in the shape of a parabola has the dimensions shown in the figure. How wide is the arch 9 ft up? |12 ft 12 ft
Suppose the telescope in Exercise 51 had diameter 400 ft and maximum depth 50 ft.(a) Write an equation of this parabola.(b) The receiver must be placed at the focus of the parabola. How far from the
Solve each problem.The U.S. Naval Research Laboratory designed a giant radio telescope that had diameter 300 ft and maximum depth 44 ft.(a) Write an equation of a parabola that models the cross
Determine the two equations necessary to graph each horizontal parabola using a graphing calculator, and graph it in the viewing window indicated.x - 5 = 2(y - 2)2; [-2, 12] by [-2, 6]
Determine the two equations necessary to graph each horizontal parabola using a graphing calculator, and graph it in the viewing window indicated.x + 2 = -(y + 1)2; [-10, 2] by [-4, 4]
Determine the two equations necessary to graph each horizontal parabola using a graphing calculator, and graph it in the viewing window indicated.x = -2y2 + 4y + 3; [-10, 6.5] by [-4, 4]
Determine the two equations necessary to graph each horizontal parabola using a graphing calculator, and graph it in the viewing window indicated.x = 3y2 + 6y - 4; [-10, 2] by [-4, 4]
Write an equation for each parabola.Vertex (1, 2), directrix x = 4
Write an equation for each parabola.Vertex (-5, 6), directrix x = -12
Write an equation for each parabola.Vertex (-2, 1), focus (-2, -3)
Write an equation for each parabola.Vertex (4, 3), focus (4, 5)
Write an equation for each parabola with vertex at the origin.Through the point (2, -4), symmetric with respect to the y-axis
Write an equation for each parabola with vertex at the origin.Through the point (3, 2), symmetric with respect to the x-axis
Write an equation for each parabola with vertex at the origin.Through the point (-2, -2√2), opens left
Write an equation for each parabola with vertex at the origin.Through the point (√3, 3), opens up
Write an equation for each parabola with vertex at the origin.Directrix y = 1/3
Write an equation for each parabola with vertex at the origin.Directrix y = -1/4
Write an equation for each parabola with vertex at the origin.Focus (-1/2, 0)
Write an equation for each parabola with vertex at the origin.Focus (5, 0)
Graph each horizontal parabola, and give the domain and range.(x + 2)2 = 20(y - )2
Graph each horizontal parabola, and give the domain and range.(x - 7)2 = 16(y + 5)
Graph each horizontal parabola, and give the domain and range.(y - 2)2 = 24(x - 3)
Graph each horizontal parabola, and give the domain and range.(y - 3)2 = 12(x - 1)
Graph each horizontal parabola, and give the domain and range.x = -16y2
Graph each horizontal parabola, and give the domain and range.x = -32y2
Graph each horizontal parabola, and give the domain and range.y2 = 16x
Graph each horizontal parabola, and give the domain and range.y2 = -4x
Graph each horizontal parabola, and give the domain and range. y-- 9.
Graph each horizontal parabola, and give the domain and range.y = -4x2
Graph each horizontal parabola, and give the domain and range. 00
Graph each horizontal parabola, and give the domain and range.x2 = 24y
Graph each horizontal parabola, and give the domain and range.-x = 2y2 + 4y - 1
Graph each horizontal parabola, and give the domain and range.-x = 3y2 + 6y + 2
Graph each horizontal parabola, and give the domain and range.x + 3y2 + 18y + 22 = 0
Graph each horizontal parabola, and give the domain and range.2x - y2 + 4y - 6 = 0
Graph each horizontal parabola, and give the domain and range.x = -2y2 + 2y - 3
Graph each horizontal parabola, and give the domain and range.x = -4y2 - 4y + 3
Graph each horizontal parabola, and give the domain and range.x = 2y2 - 4y + 6
Graph each horizontal parabola, and give the domain and range.x = y2 + 4y + 2
Graph each horizontal parabola, and give the domain and range. (y – 2)² 3
Graph each horizontal parabola, and give the domain and range. (y + 3)?
Graph each horizontal parabola, and give the domain and range. x- 4 =;(y– 1)²
Graph each horizontal parabola, and give the domain and range.x - 2 = -3(y - 1)2
Graph each horizontal parabola, and give the domain and range.x + 1 = (y + 2)2

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