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Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

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9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Parametric

Given x=9t-2 and y=6t+9 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

$y= \frac{2}{3}(x+2)+9$

$y= \frac{3}{2}(x+2)+9$

$y= \frac{3}{2}(x+2)-9$

$y= \frac{2}{3}(x+2)-9$

Correct answer:

$y= \frac{2}{3}(x+2)+9$

Explanation:

Since we have x=9t-2 and y=6t+9 , let's solve each equation for :

$x=9t-2\rightarrow t=\frac{x+2}{9}$

$y=6t+9 \rightarrow t=\frac{y-9}{6}$

Since both equations equal , we can set them equal to each other and solve for :

$\frac{y-9}{6}=\frac{x+2}{9}$

$y-9= 6\left(\frac{x+2}{9}\right)$

$y-9= \frac{2}{3}(x+2)$

$y= \frac{2}{3}(x+2)+9$

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Example Question #32 : Parametric

Given x=6t-5 and y=3t+8 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

$y=\frac{x+2}{5}-8$

$y=\frac{x+2}{5}+8$

$y=\frac{x+5}{2}+8$

$y=\frac{x+5}{2}-8$

Correct answer:

$y=\frac{x+5}{2}+8$

Explanation:

Given x=6t-5 and y=3t+8 , let's solve both equations for :

$x=6t-5\rightarrow t=\frac{x+5}{6}$

$y=3t+8\rightarrow t=\frac{y-8}{3}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-8}{3}=\frac{x+5}{6}$

$y-8=3\left(\frac{x+5}{6}\right)$

$y=\frac{x+5}{2}+8$

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Example Question #33 : Parametric

Given x=t+9 and y=5t+11 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

y=5x+66

y=66+5x

y=5x-34

y=5x-66

Correct answer:

y=5x-34

Explanation:

Given x=t+9 and y=5t+11 let's solve both equations for :

$x=t+9\rightarrow t=x-9$

$y=5t+11\rightarrow t=\frac{y-11}{5}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-11}{5}=x-9$

y-11=5(x-9)

y=5(x-9)+11

y=5x-45+11

y=5x-34

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Example Question #34 : Parametric

Given x=7t-15 and y=7t+15 , what is in terms of (rectangular form)?

Possible Answers:

y=-x

y=x-30

y=x+30

y=x

None of the above

Correct answer:

y=x+30

Explanation:

Given x=7t-15 and y=7t+15 , let's solve both equations for :

$x=7t-15\rightarrow t=\frac{x+15}{7}$

$y=7t+15\rightarrow t=\frac{y-15}{7}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-15}{7}=\frac{x+15}{7}$

$\frac{y-15}{7}=7\left(\frac{x+15}{7}\right)$

y-15=x+15

y=x+30

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Example Question #35 : Parametric

If x=3t+14 and y=5t+12 , what is in terms of ?

Possible Answers:

$y=\frac{5}{3}(x+14)+12$

$y=\frac{5}{3}(x+14)-12$

$y=\frac{5}{3}(x-14)+12$

None of the above

$y=\frac{5}{3}(x-14)-12$

Correct answer:

$y=\frac{5}{3}(x-14)+12$

Explanation:

Given x=3t+14 and y=5t+12 , let's solve both equations for :

$x=3t+14\rightarrow t=\frac{x-14}{3}$

$y=5t+12\rightarrow t=\frac{y-12}{5}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-12}{5}=\frac{x-14}{3}$

$y-12=\frac{5}{3}(x-14)$

$y=\frac{5}{3}(x-14)+12$

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Example Question #36 : Parametric

If x=2t-15 and y=t+8 , what is in terms of ?

Possible Answers:

None of the above

$y=\frac{x-15}{2}+8$

$y=\frac{x-15}{2}-8$

$y=\frac{x+15}{2}-8$

$y=\frac{x+15}{2}+8$

Correct answer:

$y=\frac{x+15}{2}+8$

Explanation:

Given x=2t-15 and y=t+8 , let's solve both equations for :

$x=2t-15\rightarrow t=\frac{x+15}{2}$

$y=t+8\rightarrow t=y-8$

Since both equations equal , let's set them equal to each other and solve for :

$y-8=\frac{x+15}{2}$

$y=\frac{x+15}{2}+8$

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Example Question #37 : Parametric

If $x=\frac{2}{t}+6$ and y=12t-5 , what is in terms of ?

Possible Answers:

$y=\frac{24}{x-6}-5$

$y=\frac{24}{x+6}+6$

$y=\frac{24}{x-6}+5$

$y=\frac{24}{x+6}-5$

None of the above

Correct answer:

$y=\frac{24}{x-6}-5$

Explanation:

Given $x=\frac{2}{t}+6$ and y=12t-5 , let's solve both equations for :

$x=\frac{2}{t}+6\rightarrow t=\frac{2}{x-6}$

$y=12t-5\rightarrow t=\frac{y+5}{12}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y+5}{12}=\frac{2}{x-6}$

$y+5=\frac{24}{x-6}$

$y=\frac{24}{x-6}-5$

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Example Question #31 : Parametric Form

Convert the following function from parametric to rectangular coordinates:

x=t^2+4 , y=t+2

Possible Answers:

$y=2\pm \sqrt{x+4}$

$y=2\pm \sqrt{x-4}$

$y=2-\sqrt{x-4}$

$y=2+\sqrt{x-4}$

Correct answer:

$y=2\pm \sqrt{x-4}$

Explanation:

To convert to rectangular coordinates, eliminate the parameter by setting one of the functions equal to t:

$t=\pm \sqrt{x-4}$

To finish, substitute this into the equation for y:

$y=2\pm \sqrt{x-4}$

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Example Question #39 : Parametric

Given x=4t+14 and y=5t-2 , what is in terms (rectangular form)?

Possible Answers:

$y=\frac{5}{4}(x+14)-2$

None of the above

$y=\frac{5}{4}(x-14)+2$

$y=\frac{5}{4}(x+14)+2$

$y=\frac{5}{4}(x-14)-2$

Correct answer:

$y=\frac{5}{4}(x-14)-2$

Explanation:

Given x=4t+14 and y=5t-2 , let's solve both equations for :

$x=4t+14\rightarrow t=\frac{x-14}{4}$

$y=5t-2\rightarrow t=\frac{y+2}{5}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y+2}{5}=\frac{x-14}{4}$

$y+2=5(\frac{x-14}{4})$

$y=\frac{5}{4}(x-14)-2$

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Example Question #40 : Parametric

Given x=t-5 and y=2t+11 , what is in terms (rectangular form)?

Possible Answers:

y=2x-21

None of the above

y=2x+21

y=2x+1

y=2x-1

Correct answer:

y=2x+21

Explanation:

Given x=t-5 and y=2t+11 , let's solve both equations for :

$x=t-5\rightarrow t=x+5$

$y=2t+11\rightarrow t=\frac{y-11}{2}$

Since both equations equal , let's set them equal to each other and solve for :

$\frac{y-11}{2}=x+5$

y-11=2(x+5)

y=2(x+5)+11

y=2x+10+11

y=2x+21

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Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #31 : Parametric

Example Question #32 : Parametric

Example Question #33 : Parametric

Example Question #34 : Parametric

Example Question #35 : Parametric

Example Question #36 : Parametric

Example Question #37 : Parametric

Example Question #31 : Parametric Form

Example Question #39 : Parametric

Example Question #40 : Parametric

All Calculus 2 Resources

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