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mathematics
precalculus

Questions and Answers of Precalculus

Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. x = 3sin t, y = 4 cos t + 2, 0 ≤ t ≤ 2π
Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. x = 2t2, y = 5 – t; - ∞ < t < ∞
Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve. x = 4t – 2, y = 1 – t; - ∞ < t < ∞
Convert each polar equation to a rectangular equation. 3 + 2 cos 6
Convert each polar equation to a rectangular equation. 8. 4 + 8 cos 0
Convert each polar equation to a rectangular equation. sin 0 2 - sin 0
Convert each polar equation to a rectangular equation. r 1 - cos 0 4.
Identify the conic that each polar equation represents and graph it. 10 5 + 20 sin 0
Identify the conic that each polar equation represents and graph it. 4 + 8 cos 0
Identify the conic that each polar equation represents and graph it. 3 + 2 cos 6
Identify the conic that each polar equation represents and graph it. 6. 2 - sin 0
Identify the conic that each polar equation represents and graph it. 1 + sin 0
Identify the conic that each polar equation represents and graph it. 4 1 - cos 0
Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. 9x2 – 24xy + 16y2 + 80x + 60y = 0
Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. 4x2 – 12xy + 9xy2 + 12x + 8y = 0
Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. x2 + 4xy + 4y2 + 16√5x – 8√5y = 0
Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. 6x2 + 4xy + 9y2 – 20 = 0
Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. 2x2 – 5xy + 2y2 – 9/2 = 0
Rotate the axes so that the new equation contains no xy-term. Analyze and graph the new equation. 2x2 + 5xy + 2y2 – 9/2 = 0
Identify each conic without completing the squares and without applying a rotation of axes. 4x2 + 12xy – 10y2 + x + y – 10 = 0
Identify each conic without completing the squares and without applying a rotation of axes. x2 – 2xy + 3y2 + 2x + 4y – 1 = 0
Identify each conic without completing the squares and without applying a rotation of axes. 4x2 – 10xy + 4y2 – 9 = 0
Identify each conic without completing the squares and without applying a rotation of axes. 4x2 + 10xy + 4y2 – 9 = 0
Identify each conic without completing the squares and without applying a rotation of axes. 4x2 + 4xy + y2 – 8√5x + 16√5y = 0
Identify each conic without completing the squares and without applying a rotation of axes. 9x2 – 12xy + 4y2 + 8x + 12y = 0
Identify each conic without completing the squares and without applying a rotation of axes. x2 – 8y2 – x – 2y = 0
Identify each conic without completing the squares and without applying a rotation of axes. x2 + 2y2 + 4x – 8y + 2 = 0
Identify each conic without completing the squares and without applying a rotation of axes. 2x2 – y + 8x =0
Identify each conic without completing the squares and without applying a rotation of axes. y2 + 4x + 3y – 8 = 0
Find an equation of the conic described. Graph the equation. Vertices at (0, 1) and (6, 1); asymptote the line 3y + 2x = 9
Find an equation of the conic described. Graph the equation. Vertices at (4, 0) and (4, 4); asymptote the line y + 2x = 10
Find an equation of the conic Find an equation of the conic described. Graph the equation. described. Graph the equation. Center at (4, -2); a = 1; c = 4; tranverse axis parallel to the
Find an equation of the conic described. Graph the equation. Center at (-1, 2); a = 3; c = 4
Find an equation of the conic described. Graph the equation. Hyperbola; vertices at (-3, 3) and (5, 3); focus at (7, 3)
Find an equation of the conic described. Graph the equation. Ellipse; foci at (-4, 2) and (-4, 8); vertex at (-4, 10)
Find an equation of the conic described. Graph the equation. Parabola; focus at (3, 6); directrix the line y = 8
Find an equation of the conic described. Graph the equation. Hyperbola; center at (-2, -3); focus at(-4, -3); vertex at (-3, -3)
Find an equation of the conic described. Graph the equation. Ellipse; center at (-1, 2) focus at (0, 2) vertex at (2, 2)
Find an equation of the conic described. Graph the equation. Parabola; vertex at (2, -3) focus at (2, -4)
Find an equation of the conic described. Graph the equation. Hyperbola; vertices at (-2, 0) and (2, 0) focus at (4, 0)
Find an equation of the conic described. Graph the equation. Ellipse; foci at (-3, 0) and (3, 0) vertex at (4, 0)
Find an equation of the conic described. Graph the equation. Parabola; vertex at (0, 0) directrix the line; y = -3
Find an equation of the conic described. Graph the equation. Hyperbola; center at (0, 0) focus at (0, 4) vertex at (0, -2)
Find an equation of the conic described. Graph the equation. Ellipse; center at (0, 0) focus at (0, 3) vertex at (0, 5)
Find an equation of the conic described. Graph the equation. Parabola; focus at (-2, 0) directrix the line ; x = 2
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
Identify the 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
The hypocycloid is a curve defined by the parametric equations x(t) = cos3t, y(t) = sin3 t, 0 ≤ t ≤ 2π(a) Graph the hypocycloid using a graphing utility. (b) Find a rectangular
Show that the parametric equations for a line passing through the points (x1, y1) and (x2, y2) are What is the orientation of this line? х%D (х, — х,)t + x1 у %3D (У2 — У1)r + У,
The position of a projectile fired with an initial velocity v0 feet per second and at an angle to the horizontal at the end of t seconds is given by the parametric equations See the
The left field wall at Fenway Park is 310 feet from home plate; the wall itself (affectionately named the Green Monster) is 37 feet high. A batted ball must clear the wall to be a home run. Suppose a
A Cessna (heading south at 120 mph) and a Boeing 747 (heading west at 600 mph) are flying toward the same point at the same altitude. The Cessna is 100 miles from the point where the flight patterns
A Toyota Camry (traveling east at 40 mph) and a Chevy Impala (traveling north at 30 mph) are heading toward the same intersection. The Camry is 5 miles from the intersection when the Impala is 4
Suppose that Karla hits a golf ball off a cliff 300 meters high with an initial speed of 40 meters per second at an angle of 45° to the horizontal on the Moon (gravity on the Moon is one-sixth of
Suppose that Adam hits a golf ball off a cliff 300 meters high with an initial speed of 40 meters per second at an angle of 45° to the horizontal. (a) Find parametric equations that model the
Mark Texeira 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 off the ground. (a) Find parametric
Ichiro throws a baseball with an initial speed of 145 feet per second at an angle of 20° to the horizontal. The ball leaves Ichiro’s hand at a height of 5 feet. (a) Find parametric equations
Jodi’s bus leaves at 5:30 PM and accelerates at the rate of 3 meters per second per second. Jodi, who can run 5 meters per second, arrives at the bus station 2 seconds after the bus has left and
Bill’s train leaves at 8:06 AM and accelerates at the rate of 2 meters per second per second. Bill, who can run 5 meters per second, arrives at the train station 5 seconds after the train has left
Alice throws a ball straight up with an initial speed of 40 feet per second from a height of 5 feet. (a) Find parametric equations that model the motion of the ball as a function of
Bob throws a ball straight up with an initial speed of 50 feet per second from a height of 6 feet. (a) Find parametric equations that model the motion of the ball as a function of time. (b)
Use a graphing utility to graph the curve defined by the given parametric equations.x = 4 sin t + 2 sin(2t) y = 4 cos t + 2 cos(2t)
Use a graphing utility to graph the curve defined by the given parametric equations.x = 4 sin t - 2 sin(2t)y = 4 cos t - 2 cos(2t)
Use a graphing utility to graph the curve defined by the given parametric equations.x = sin t + cos t y = sin t - cos t
Use a graphing utility to graph the curve defined by the given parametric equations.x = t sin t, y = t cos t, t >7 0
The parametric equations of the four curves are given. Graph each of them, indicating the orientation. C: x = t, y = V1 - ť; -1 st< 1 |C2: x = sin t, y= cos t; 0
The parametric equations of the four curves are given. Graph each of them, indicating the orientation.
Find parametric equations for an object that moves along the ellipse x2/4 + y2/9 = 1 with the motion described. The motion begins at (2, 0) is counterclockwise, and requires 3 seconds for a
Find parametric equations for an object that moves along the ellipse x2/4 + y2/9 = 1 with the motion described. The motion begins at (0, 3) is clockwise, and requires 1 second for a complete
Find parametric equations for an object that moves along the ellipse x2/4 + y2/9 = 1 with the motion described.The motion begins at (0, 3) is counterclockwise, and requires 1 second for a complete
Find parametric equations for an object that moves along the ellipse x2/4 + y2/9 = 1 with the motion described. The motion begins at (2, 0) is clockwise, and requires 2 seconds for a complete
Find parametric equations that define the curve shown. (0, 4) -2 х -2- (0, -4) 2.
Find parametric equations that define the curve shown. y. 2 1 2 3х -1 -3-2 -1 -21
Find parametric equations that define the curve shown. (-1,2) 2 -2 -1 2 3 x -2- (3, -2) -3-
Find parametric equations that define the curve shown. (7, 5) 6 4 2E2. 0) 2 4 6
Find two different parametric equations for each rectangular equation. x = √y
Find two different parametric equations for each rectangular equation. x = y3/2
Find two different parametric equations for each rectangular equation. y = x4 + 1
Find two different parametric equations for each rectangular equation. y = x3
Find two different parametric equations for each rectangular equation. y = 2x2 + 1
Find two different parametric equations for each rectangular equation. y = x2 + 1
Find two different parametric equations for each rectangular equation. y = -8x + 3

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