Unit 14 Mastery Check

What changes when $t$ is replaced by -t?

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What changes when $t$ is replaced by -t?

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State the defining idea behind parametric equations and orientation in one precise sentence.

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For parametric equations and orientation, what condition or domain restriction must remain visible in the solution?

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Eliminate $t$ from $x=t^2,y=t$ for $-1\le t\le 2$.

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Eliminate $t$ from $x=t^2,y=t$ for $-1\le t\le 2$.

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State the defining idea behind eliminating a parameter in one precise sentence.

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For eliminating a parameter, what condition or domain restriction must remain visible in the solution?

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Find average velocity for $r(t)=<cos$ t,sin $t>$ from $0$ to pi.

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Find average velocity for $r(t)=<cos$ t,sin $t>$ from $0$ to pi.

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State the defining idea behind parametric motion and vector-valued position in one precise sentence.

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For parametric motion and vector-valued position, what condition or domain restriction must remain visible in the solution?

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Can two particles' paths intersect without the particles colliding?

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Can two particles' paths intersect without the particles colliding?

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State the defining idea behind intersections, repeated points, and multiple parameter values in one precise sentence.

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For intersections, repeated points, and multiple parameter values, what condition or domain restriction must remain visible in the solution?

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Give a positive-radius form equivalent to $(-3,\frac{pi}{4})$.

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Give a positive-radius form equivalent to $(-3,\frac{pi}{4})$.

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State the defining idea behind polar coordinates and nonuniqueness in one precise sentence.

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For polar coordinates and nonuniqueness, what condition or domain restriction must remain visible in the solution?

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Convert $r=4sin$ theta to Cartesian form.

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Convert $r=4sin$ theta to Cartesian form.

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State the defining idea behind cartesian and polar conversion in one precise sentence.

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For cartesian and polar conversion, what condition or domain restriction must remain visible in the solution?

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Where does $r=3cos$ theta pass through the pole?

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Where does $r=3cos$ theta pass through the pole?

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State the defining idea behind graphing polar equations in one precise sentence.

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For graphing polar equations, what condition or domain restriction must remain visible in the solution?

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Which substitution tests symmetry about the polar axis?

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Which substitution tests symmetry about the polar axis?

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State the defining idea behind polar symmetry and repeated tracing in one precise sentence.

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For polar symmetry and repeated tracing, what condition or domain restriction must remain visible in the solution?

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How many petals does $r=sin(4theta)$ have?

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How many petals does $r=sin(4theta)$ have?

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State the defining idea behind common polar families and polar conics in one precise sentence.

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For common polar families and polar conics, what condition or domain restriction must remain visible in the solution?

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