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MC 2025 In-course Diagnostics for Undergraduate Mathematics MATH140 WP

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Find an equation of the sphere with center (8,-4,8) that touches the -plane.

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Suppose you start at the origin, move along the -axis a distance of 8 units in the positive direction, and then move downward a distance of 1 units. What are the coordinates of your position?

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Write an equation that represents all points on and inside a circular cylinder of radius 6 with the -axis as its axis.
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Find the midpoint of the line segment from to

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Find the midpoint of the line segment from to

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Suppose you start at the origin, move along the -axis a distance of 4 units in the positive direction, and then move downward a distance of 8 units. What are the coordinates of your position?
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Find the distance from (-10,2,-8) to the -plane.

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The equation of the polar curve given below is:

M7 Q12 pic

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The equation of the polar curve shown below is:

M7 Q11 pic

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Which of the following curves is defined by the equation

a.  M7 Q13a pic

M7 Q13b pic

M7 Q13c pic

M7 Q13d pic

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