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Find the area enclosed by the curve Find the area enclosed by the curve . .

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Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places. Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

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Using the arc length formula, set up, but do not evaluate, an integral equal to the total arc length of the ellipse. Using the arc length formula, set up, but do not evaluate, an integral equal to the total arc length of the ellipse.

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Write a polar equation in r and θ\theta of an ellipse with the focus at the origin, with the eccentricity Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and vertex at . A) B) C) D) E) and vertex at Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and vertex at . A) B) C) D) E) .


A) Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and vertex at . A) B) C) D) E)
B) Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and vertex at . A) B) C) D) E)
C) Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and vertex at . A) B) C) D) E)
D) Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and vertex at . A) B) C) D) E)
E) Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and vertex at . A) B) C) D) E)

F) A) and B)
G) C) and D)

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Find an equation of the parabola with focus Find an equation of the parabola with focus and directrix . A) B) C) D) E) and directrix Find an equation of the parabola with focus and directrix . A) B) C) D) E) .


A) Find an equation of the parabola with focus and directrix . A) B) C) D) E)
B) Find an equation of the parabola with focus and directrix . A) B) C) D) E)
C) Find an equation of the parabola with focus and directrix . A) B) C) D) E)
D) Find an equation of the parabola with focus and directrix . A) B) C) D) E)
E) Find an equation of the parabola with focus and directrix . A) B) C) D) E)

F) C) and E)
G) A) and B)

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Consider the polar equation Consider the polar equation . (a) Find the eccentricity and an equation of the directrix of the conic. (b) Identify the conic. (c) Sketch the curve. . (a) Find the eccentricity and an equation of the directrix of the conic. (b) Identify the conic. (c) Sketch the curve.

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a. 11ecb968_ab0e_bdbb_9b4c_c75a636fb303_TB5971_11 b. ellipse c. 11ecb968_c571_f5ac_9b4c_973604410a75_TB5971_11

Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

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The curve The curve cross itself at some point . Find the equations of both tangent lines at that point. A) B) C) D) E) cross itself at some point The curve cross itself at some point . Find the equations of both tangent lines at that point. A) B) C) D) E) . Find the equations of both tangent lines at that point.


A) The curve cross itself at some point . Find the equations of both tangent lines at that point. A) B) C) D) E)
B) The curve cross itself at some point . Find the equations of both tangent lines at that point. A) B) C) D) E)
C) The curve cross itself at some point . Find the equations of both tangent lines at that point. A) B) C) D) E)
D) The curve cross itself at some point . Find the equations of both tangent lines at that point. A) B) C) D) E)
E) The curve cross itself at some point . Find the equations of both tangent lines at that point. A) B) C) D) E)

F) B) and D)
G) A) and C)

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Find the area of the region that lies inside the first curve and outside the second curve. Find the area of the region that lies inside the first curve and outside the second curve. A) B) C) D) E)


A) Find the area of the region that lies inside the first curve and outside the second curve. A) B) C) D) E)
B) Find the area of the region that lies inside the first curve and outside the second curve. A) B) C) D) E)
C) Find the area of the region that lies inside the first curve and outside the second curve. A) B) C) D) E)
D) Find the area of the region that lies inside the first curve and outside the second curve. A) B) C) D) E)
E) Find the area of the region that lies inside the first curve and outside the second curve. A) B) C) D) E)

F) A) and E)
G) A) and D)

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The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest from the surface is called apolune. The Apollo 11 spacecraft was placed in an elliptical lunar orbit with perilune altitude The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest from the surface is called apolune. The Apollo 11 spacecraft was placed in an elliptical lunar orbit with perilune altitude km and apolune altitude km (above the moon). Find an equation of this ellipse if the radius of the moon is km and the center of the moon is at one focus. km and apolune altitude The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest from the surface is called apolune. The Apollo 11 spacecraft was placed in an elliptical lunar orbit with perilune altitude km and apolune altitude km (above the moon). Find an equation of this ellipse if the radius of the moon is km and the center of the moon is at one focus. km (above the moon). Find an equation of this ellipse if the radius of the moon is The point in a lunar orbit nearest the surface of the moon is called perilune and the point farthest from the surface is called apolune. The Apollo 11 spacecraft was placed in an elliptical lunar orbit with perilune altitude km and apolune altitude km (above the moon). Find an equation of this ellipse if the radius of the moon is km and the center of the moon is at one focus. km and the center of the moon is at one focus.

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Set up, but do not evaluate, an integral that represents the length of the parametric curve. Set up, but do not evaluate, an integral that represents the length of the parametric curve.

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Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0) , focus (0, - Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0) , focus (0, - ) A) B) C) D) E) )


A) Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0) , focus (0, - ) A) B) C) D) E)
B) Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0) , focus (0, - ) A) B) C) D) E)
C) Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0) , focus (0, - ) A) B) C) D) E)
D) Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0) , focus (0, - ) A) B) C) D) E)
E) Find an equation for the conic that satisfies the given conditions. parabola, vertex (0, 0) , focus (0, - ) A) B) C) D) E)

F) A) and E)
G) B) and E)

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Find the area of the region that is bounded by the given curve and lies in the specified sector. Find the area of the region that is bounded by the given curve and lies in the specified sector.

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Find the eccentricity of the conic. Find the eccentricity of the conic. A) B) C) D) E)


A) Find the eccentricity of the conic. A) B) C) D) E)
B) Find the eccentricity of the conic. A) B) C) D) E)
C) Find the eccentricity of the conic. A) B) C) D) E)
D) Find the eccentricity of the conic. A) B) C) D) E)
E) Find the eccentricity of the conic. A) B) C) D) E)

F) B) and C)
G) C) and E)

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Find an equation of the hyperbola with vertices Find an equation of the hyperbola with vertices and asymptotes . A) B) C) D) E) and asymptotes Find an equation of the hyperbola with vertices and asymptotes . A) B) C) D) E) .


A) Find an equation of the hyperbola with vertices and asymptotes . A) B) C) D) E)
B) Find an equation of the hyperbola with vertices and asymptotes . A) B) C) D) E)
C) Find an equation of the hyperbola with vertices and asymptotes . A) B) C) D) E)
D) Find an equation of the hyperbola with vertices and asymptotes . A) B) C) D) E)
E) Find an equation of the hyperbola with vertices and asymptotes . A) B) C) D) E)

F) B) and C)
G) B) and D)

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A

The graph of the following curve is given. Find the area that it encloses. The graph of the following curve is given. Find the area that it encloses. A) A= B) C) D) E) The graph of the following curve is given. Find the area that it encloses. A) A= B) C) D) E)


A) A=The graph of the following curve is given. Find the area that it encloses. A) A= B) C) D) E)
B) The graph of the following curve is given. Find the area that it encloses. A) A= B) C) D) E)
C) The graph of the following curve is given. Find the area that it encloses. A) A= B) C) D) E)
D) The graph of the following curve is given. Find the area that it encloses. A) A= B) C) D) E)
E) The graph of the following curve is given. Find the area that it encloses. A) A= B) C) D) E)

F) B) and D)
G) A) and D)

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Write a polar equation in r and θ\theta of an ellipse with the focus at the origin, with the eccentricity Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and directrix . A) B) C) D) E) and directrix Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and directrix . A) B) C) D) E) .


A) Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and directrix . A) B) C) D) E)
B) Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and directrix . A) B) C) D) E)
C) Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and directrix . A) B) C) D) E)
D) Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and directrix . A) B) C) D) E)
E) Write a polar equation in r and \theta of an ellipse with the focus at the origin, with the eccentricity and directrix . A) B) C) D) E)

F) None of the above
G) A) and D)

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Find the surface area generated by rotating the lemniscate Find the surface area generated by rotating the lemniscate about the line . A) B) C) D) E) about the line Find the surface area generated by rotating the lemniscate about the line . A) B) C) D) E) .


A) Find the surface area generated by rotating the lemniscate about the line . A) B) C) D) E)
B) Find the surface area generated by rotating the lemniscate about the line . A) B) C) D) E)
C) Find the surface area generated by rotating the lemniscate about the line . A) B) C) D) E)
D) Find the surface area generated by rotating the lemniscate about the line . A) B) C) D) E)
E) Find the surface area generated by rotating the lemniscate about the line . A) B) C) D) E)

F) A) and D)
G) B) and D)

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B

Find a Cartesian equation for the curve described by the given polar equation. Find a Cartesian equation for the curve described by the given polar equation.

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Suppose a planet is discovered that revolves around its sun in an elliptical orbit with the sun at one focus. Its perihelion distance (minimum distance from the planet to the sun) is approximately 1.3 Suppose a planet is discovered that revolves around its sun in an elliptical orbit with the sun at one focus. Its perihelion distance (minimum distance from the planet to the sun) is approximately 1.3 km, and its aphelion distance (maximum distance from the planet to the sun) is approximately 6.9 km. Approximate the eccentricity of the planet's orbit. Round to three decimal places. A) 0.683 B) 1.464 C) 5.308 D) 0.188 km, and its aphelion distance (maximum distance from the planet to the sun) is approximately 6.9 Suppose a planet is discovered that revolves around its sun in an elliptical orbit with the sun at one focus. Its perihelion distance (minimum distance from the planet to the sun) is approximately 1.3 km, and its aphelion distance (maximum distance from the planet to the sun) is approximately 6.9 km. Approximate the eccentricity of the planet's orbit. Round to three decimal places. A) 0.683 B) 1.464 C) 5.308 D) 0.188 km. Approximate the eccentricity of the planet's orbit. Round to three decimal places.


A) 0.683
B) 1.464
C) 5.308
D) 0.188

E) All of the above
F) A) and B)

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