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Find the speed of a particle in a circular orbit with radius 1022m around an object of mass 1023kg. (G = 6.67 *10-11m/kgĀ·s2)


A) 1.50 *109 m/s
B) 6.67 * 10-10 m/s
C) 3.87 * 104 m/s
D) 2.58 *10-5 m/s
E) 4.91*10-5m/s

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

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Where is Where is continuous? A) B) C) D) 4 E) 0 continuous?


A) Where is continuous? A) B) C) D) 4 E) 0
B) Where is continuous? A) B) C) D) 4 E) 0
C) Where is continuous? A) B) C) D) 4 E) 0
D) 4
E) 0

F) All of the above
G) B) and D)

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Describe the graph of Describe the graph of

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Find the curvature Find the curvature for r(t) = 17i + 2t j + 3t<sup>2</sup> k at t = 0. A) B) C) 0 D) 1 E) for r(t) = 17i + 2t j + 3t2 k at t = 0.


A) Find the curvature for r(t) = 17i + 2t j + 3t<sup>2</sup> k at t = 0. A) B) C) 0 D) 1 E)
B) Find the curvature for r(t) = 17i + 2t j + 3t<sup>2</sup> k at t = 0. A) B) C) 0 D) 1 E)
C) 0
D) 1
E) Find the curvature for r(t) = 17i + 2t j + 3t<sup>2</sup> k at t = 0. A) B) C) 0 D) 1 E)

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

Correct Answer

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At t increases, the graph of At t increases, the graph of sketches A) Clockwise and up B) Counter-clockwise and up C) Clockwise and down D) Counter-clockwise and down E) In a circle sketches


A) Clockwise and up
B) Counter-clockwise and up
C) Clockwise and down
D) Counter-clockwise and down
E) In a circle

F) B) and D)
G) B) and E)

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Sketch x = 2 cos t, y = 3 sin t for 0 ā‰¤\le t ā‰¤\le 2 Ļ€\pi . Calculate the radius of curvature at Sketch x = 2 cos t, y = 3 sin t for 0 \le t \le 2 \pi . Calculate the radius of curvature at and sketch the oscillating circle. and sketch the oscillating circle.

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Find the unit tangent and unit normal vectors to r(t) = t i + ln(cos t) j at Find the unit tangent and unit normal vectors to r(t) = t i + ln(cos t) j at . .

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Find the acceleration of a particle moving along the curve r(t) = t3 i + (8 + 4t) j - t2 k at t = 1.


A) 3i + 4j - 2k
B) 6i - 2k
C) 3i + 4j + 2k
D) 0
E) 3i - 4j - 2k

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

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Let r(t) = (t + 2) i + e t j + 12 k. Find T(t) for t = 0.


A) Let r(t) = (t + 2) i + e <sup>t</sup> j + 12 k. Find T(t) for t = 0. A) B) C) D) E)
B) Let r(t) = (t + 2) i + e <sup>t</sup> j + 12 k. Find T(t) for t = 0. A) B) C) D) E)
C) Let r(t) = (t + 2) i + e <sup>t</sup> j + 12 k. Find T(t) for t = 0. A) B) C) D) E)
D) Let r(t) = (t + 2) i + e <sup>t</sup> j + 12 k. Find T(t) for t = 0. A) B) C) D) E)
E) Let r(t) = (t + 2) i + e <sup>t</sup> j + 12 k. Find T(t) for t = 0. A) B) C) D) E)

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

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Find the parametric equations that correspond to the given vector equation: Find the parametric equations that correspond to the given vector equation: . A) B) C) D) E) .


A) Find the parametric equations that correspond to the given vector equation: . A) B) C) D) E)
B) Find the parametric equations that correspond to the given vector equation: . A) B) C) D) E)
C) Find the parametric equations that correspond to the given vector equation: . A) B) C) D) E)
D) Find the parametric equations that correspond to the given vector equation: . A) B) C) D) E)
E) Find the parametric equations that correspond to the given vector equation: . A) B) C) D) E)

F) C) and E)
G) D) and E)

Correct Answer

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Let r(t) = 4 i + (t + 2) j + 4 k. Find T(t) for t = 0.


A) Let r(t) = 4 i + (t + 2) j + 4 k. Find T(t) for t = 0. A) B) C) D) E)
B) Let r(t) = 4 i + (t + 2) j + 4 k. Find T(t) for t = 0. A) B) C) D) E)
C) Let r(t) = 4 i + (t + 2) j + 4 k. Find T(t) for t = 0. A) B) C) D) E)
D) Let r(t) = 4 i + (t + 2) j + 4 k. Find T(t) for t = 0. A) B) C) D) E)
E) Let r(t) = 4 i + (t + 2) j + 4 k. Find T(t) for t = 0. A) B) C) D) E)

F) All of the above
G) C) and D)

Correct Answer

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Find the arc length parameterization of the line Find the arc length parameterization of the line that has the same orientation as the given curve and uses as a reference point. A) B) C) D) E) that has the same orientation as the given curve and uses Find the arc length parameterization of the line that has the same orientation as the given curve and uses as a reference point. A) B) C) D) E) as a reference point.


A) Find the arc length parameterization of the line that has the same orientation as the given curve and uses as a reference point. A) B) C) D) E)
B) Find the arc length parameterization of the line that has the same orientation as the given curve and uses as a reference point. A) B) C) D) E)
C) Find the arc length parameterization of the line that has the same orientation as the given curve and uses as a reference point. A) B) C) D) E)
D) Find the arc length parameterization of the line that has the same orientation as the given curve and uses as a reference point. A) B) C) D) E)
E) Find the arc length parameterization of the line that has the same orientation as the given curve and uses as a reference point. A) B) C) D) E)

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

Correct Answer

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Let r(t) = (-9 + t) i + t2 j + t3 k. Find T(t) when t = 0.


A) i
B) Let r(t) = (-9 + t) i + t<sup>2</sup> j + t<sup>3</sup> k. Find T(t) when t = 0. A) i B) C) D) E)
C) Let r(t) = (-9 + t) i + t<sup>2</sup> j + t<sup>3</sup> k. Find T(t) when t = 0. A) i B) C) D) E)
D) Let r(t) = (-9 + t) i + t<sup>2</sup> j + t<sup>3</sup> k. Find T(t) when t = 0. A) i B) C) D) E)
E) Let r(t) = (-9 + t) i + t<sup>2</sup> j + t<sup>3</sup> k. Find T(t) when t = 0. A) i B) C) D) E)

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

Correct Answer

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Find the arc length of the graph of Find the arc length of the graph of A) B) C) 0 D) 1 E) 4


A) Find the arc length of the graph of A) B) C) 0 D) 1 E) 4
B) Find the arc length of the graph of A) B) C) 0 D) 1 E) 4
C) 0
D) 1
E) 4

F) All of the above
G) A) and D)

Correct Answer

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Let r(t) = (t2 + 2) i + e t j + (9 + e t ) k. Find T(t) for t = 0.


A) Let r(t) = (t<sup>2</sup> + 2) i + e <sup>t</sup> j + (9 + e <sup>t</sup> ) k. Find T(t) for t = 0. A) B) C) D) E)
B) Let r(t) = (t<sup>2</sup> + 2) i + e <sup>t</sup> j + (9 + e <sup>t</sup> ) k. Find T(t) for t = 0. A) B) C) D) E)
C) Let r(t) = (t<sup>2</sup> + 2) i + e <sup>t</sup> j + (9 + e <sup>t</sup> ) k. Find T(t) for t = 0. A) B) C) D) E)
D) Let r(t) = (t<sup>2</sup> + 2) i + e <sup>t</sup> j + (9 + e <sup>t</sup> ) k. Find T(t) for t = 0. A) B) C) D) E)
E) Let r(t) = (t<sup>2</sup> + 2) i + e <sup>t</sup> j + (9 + e <sup>t</sup> ) k. Find T(t) for t = 0. A) B) C) D) E)

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

Correct Answer

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Find the unit tangent and unit normal vectors to the curve r(t) = 2 sin t i + 3 cos t j at Find the unit tangent and unit normal vectors to the curve r(t) = 2 sin t i + 3 cos t j at . Sketch a portion of the curve showing the point of tangency. . Sketch a portion of the curve showing the point of tangency.

Correct Answer

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Find the speed of a particle moving along the curve r(t) = (13 + t3) i + 4t j - t2 k at t = 1.


A) Find the speed of a particle moving along the curve r(t) = (13 + t<sup>3</sup>) i + 4t j - t<sup>2</sup> k at t = 1. A) B) C) D) E)
B) Find the speed of a particle moving along the curve r(t) = (13 + t<sup>3</sup>) i + 4t j - t<sup>2</sup> k at t = 1. A) B) C) D) E)
C) Find the speed of a particle moving along the curve r(t) = (13 + t<sup>3</sup>) i + 4t j - t<sup>2</sup> k at t = 1. A) B) C) D) E)
D) Find the speed of a particle moving along the curve r(t) = (13 + t<sup>3</sup>) i + 4t j - t<sup>2</sup> k at t = 1. A) B) C) D) E)
E) Find the speed of a particle moving along the curve r(t) = (13 + t<sup>3</sup>) i + 4t j - t<sup>2</sup> k at t = 1. A) B) C) D) E)

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

Correct Answer

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If If find A) B) C) D) E) find If find A) B) C) D) E)


A) If find A) B) C) D) E)
B) If find A) B) C) D) E)
C) If find A) B) C) D) E)
D) If find A) B) C) D) E)
E) If find A) B) C) D) E)

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

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If If , find k(s) . A) B) C) 2 D) 4 E) 0 , find k(s) .


A) If , find k(s) . A) B) C) 2 D) 4 E) 0
B) If , find k(s) . A) B) C) 2 D) 4 E) 0
C) 2
D) 4
E) 0

F) D) and E)
G) B) and D)

Correct Answer

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Describe the graph of Describe the graph of

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