Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

Create An Account

All Calculus 2 Resources

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

Example Questions

Example Question #15 : Parametric Form

Given x=10t+7 and y=6t-9 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{3}{5}(x-7)+9$

$y=\frac{3}{5}(x+7)-9$

$y=\frac{3}{5}(x-7)-9$

None of the above

$y=\frac{3}{5}(x+7)+9$

Correct answer:

$y=\frac{3}{5}(x-7)-9$

Explanation:

We know that x=10t+7 and y=6t-9 , so we can solve both equations for :

$x=10t+7\rightarrow t=\frac{x-7}{10}$

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

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

$\frac{y+9}{6}=\frac{x-7}{10}$

$y+9=6(\frac{x-7}{10})$

$y=6(\frac{x-7}{10})-9$

$y=\frac{3}{5}(x-7)-9$

Report an Error

Example Question #21 : Parametric, Polar, And Vector

Given x=6t+13 and y=10t+16 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{3}{5}x-\frac{17}{3}$

$y=\frac{3}{5}x+\frac{17}{3}$

$y=\frac{5}{3}x+\frac{17}{3}$

None of the above.

$y=\frac{5}{3}x-\frac{17}{3}$

Correct answer:

$y=\frac{5}{3}x-\frac{17}{3}$

Explanation:

We know x=6t+13 and y=10t+16 , so we can solve both equations for :

$x=6t+13\rightarrow t=\frac{x-13}{6}$

$y=10t+16\rightarrow t=\frac{y-16}{10}$

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

$\frac{y-16}{10}=\frac{x-13}{6}$

$y-16=10\left(\frac{x-13}{6}\right)$

$y-16=5\left(\frac{x-13}{3}\right)$

$y=5\left(\frac{x-13}{3}\right)+16$

$y=\frac{5}{3}x-\frac{65}{3}+16$

$y=\frac{5}{3}x-\frac{65}{3}+\frac{48}{3}$

$y=\frac{5}{3}x-\frac{17}{3}$

Report an Error

Example Question #23 : Parametric

Given x=7t-6 and y=5t+6 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{5}{7}x+\frac{72}{7}$

$y=\frac{5}{7}x+\frac{7}{72}$

$y=\frac{7}{5}x+\frac{7}{72}$

$y=\frac{7}{5}x+\frac{72}{7}$

None of the above.

Correct answer:

$y=\frac{5}{7}x+\frac{72}{7}$

Explanation:

We know x=7t-6 and y=5t+6 , so we can solve both equations for :

$x=7t-6\rightarrow t=\frac{x+6}{7}$

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

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

$\frac{y-6}{5}=\frac{x+6}{7}$

7({y-6})=5(x+6)

$y-6=\frac{5}{7}(x+6)$

$y=\frac{5}{7}(x+6)+6$

$y=\frac{5}{7}x+\frac{30}{7}+6$

$y=\frac{5}{7}x+\frac{30}{7}+\frac{42}{7}$

$y=\frac{5}{7}x+\frac{72}{7}$

Report an Error

Example Question #22 : Parametric, Polar, And Vector

Given $x=\frac{2}{t}+6$ and $y=\frac{3}{t}-9$ , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{3}2x-18$

$y=\frac{2}3x-18$

None of the above.

$y=\frac{3}2x+18$

$y=\frac{2}3x+18$

Correct answer:

$y=\frac{3}2x-18$

Explanation:

We know $x=\frac{2}{t}+6$ and $y=\frac{3}{t}-9$ , so we can solve both equations for :

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

$y=\frac{3}{t}-9\rightarrow t=\frac{3}{y+9}$

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

$\frac{3}{y+9}=\frac{2}{x-6}$

3(x-6)={2}(y+9)

$\frac{3}2{}(x-6)=y+9$

$\frac{3}2{}(x-6)-9=y$

$y=\frac{3}2x-\frac{18}{2}-9$

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

$y=\frac{3}2x-18$

Report an Error

Example Question #23 : Parametric, Polar, And Vector

Convert the following parametric function into rectangular coordinates:

x=t^2+3, y=2t

Possible Answers:

$y= 2\sqrt{x-3}$

$y=\sqrt{x-3}$

$y=\pm 2\sqrt{x-3}$

$y=\sqrt{4x-3}$

Correct answer:

$y=\pm 2\sqrt{x-3}$

Explanation:

To eliminate the parameter, we can solve for t in terms of y easiest:

$\frac{y}{2}=t$

Next, substitute all of the t's in the equation for x with what we defined above:

$x=\frac{y^2}{4}+3$

To finish, subtract 3, multiply by 4 and take the square root of both sides. We need plus or minus because both positive and negative squared give a positive result.

Report an Error

Example Question #19 : Parametric Form

If x=4t-6 and y=12t+5 , what is in terms of (rectangular form)?

Possible Answers:

y=23x-3

y=3x-23

None of the above

y=23x+3

y=3x+23

Correct answer:

y=3x+23

Explanation:

Given x=4t-6 and y=12t+5 , we can find the rectangular form by solving both equations for :

$x=4t-6\rightarrow t=\frac{x+6}{4}$

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

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

$\frac{y-5}{12}=\frac{x+6}{4}$

${y-5}=12(\frac{x+6}{4})$

y-5=3(x+6)

y=3(x+6)+5

y=3x+18+5

y=3x+23

Report an Error

Example Question #24 : Parametric, Polar, And Vector

If $x=\frac{1}{t}+7$ and y=14t-3 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{x-7}{14}-3$

$y=\frac{14}{x-7}-3$

$y=\frac{14}{x-7}+3$

None of the above

$y=\frac{x-7}{14}+3$

Correct answer:

$y=\frac{14}{x-7}-3$

Explanation:

Given $x=\frac{1}{t}+7$ and y=14t-3 , we can find the rectangular form by solving both equations for :

$x=\frac{1}{t}+7\rightarrow t=\frac{1}{x-7}$

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

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

$\frac{y+3}{14}=\frac{1}{x-7}$

$y+3=\frac{14}{x-7}$

$y=\frac{14}{x-7}-3$

Report an Error

Example Question #25 : Parametric, Polar, And Vector

If x=t+4 and y=5t+12 , what is in terms of (rectangular form)?

Possible Answers:

y=8x+5

None of the above

y=5x+8

y=5x-8

y=8x-5

Correct answer:

y=5x-8

Explanation:

Given x=t+4 and y=5t+12 , we can find the rectangular form by solving both equations for :

$x=t+4\rightarrow t=x-4$

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

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

$\frac{y-12}{5}=x-4$

y-12=5(x-4)

y=5(x-4)+12

y=5x-20+12

y=5x-8

Report an Error

Example Question #26 : Parametric, Polar, And Vector

Given x=5t+12 and y=12t+5 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

$y=12\left(\frac{x+12}{5}\right)-5$

$y=12\left(\frac{x-12}{5}\right)+5$

$y=12\left(\frac{x+12}{5}\right)+5$

$y=12\left(\frac{x-12}{5}\right)-5$

Correct answer:

$y=12\left(\frac{x-12}{5}\right)+5$

Explanation:

Since we have x=5t+12 and y=12t+5 , let's solve each equation for :

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

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

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

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

$y-5=12\left(\frac{x-12}{5}\right)$

$y=12\left(\frac{x-12}{5}\right)+5$

Report an Error

Example Question #27 : Parametric, Polar, And Vector

Given x=3t-11 and y=6t-2 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

y=20x+2

y=20x-2

y=2x+20

y=2x-20

Correct answer:

y=2x+20

Explanation:

Since we have x=3t-11 and y=6t-2 , let's solve each equation for :

$x=3t-11\rightarrow t=\frac{x+11}{3}$

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

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

$\frac{y+2}{6}=\frac{x+11}{3}$

$y+2=6\left(\frac{x+11}{3}\right)$

y+2=2(x+11)

y+2=2x+22

y=2x+20

Report an Error

View Calculus 2 Tutors

Mayowa
Certified Tutor

Logan University, Bachelor of Science, Biology, General.

View Calculus 2 Tutors

Muhammad
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Mechanical Engineering.

View Calculus 2 Tutors

Dawn
Certified Tutor

University of Oregon, Bachelor in Arts, Biochemistry and Molecular Biology. Johns Hopkins University, Doctor of Philosophy, E...

All Calculus 2 Resources

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

Popular Subjects

SSAT Tutors in Philadelphia, Calculus Tutors in Los Angeles, Biology Tutors in Los Angeles, Physics Tutors in San Diego, GRE Tutors in Denver, ISEE Tutors in Atlanta, Math Tutors in San Francisco-Bay Area, French Tutors in Philadelphia, English Tutors in San Francisco-Bay Area, Calculus Tutors in San Francisco-Bay Area

Popular Courses & Classes

SAT Courses & Classes in Atlanta, SAT Courses & Classes in Philadelphia, SAT Courses & Classes in Denver, GMAT Courses & Classes in Atlanta, MCAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Denver, SSAT Courses & Classes in San Francisco-Bay Area, GMAT Courses & Classes in Philadelphia, ISEE Courses & Classes in New York City

Popular Test Prep

ACT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Denver, SAT Test Prep in Phoenix, LSAT Test Prep in Philadelphia, MCAT Test Prep in Denver, MCAT Test Prep in Los Angeles, MCAT Test Prep in Houston, GMAT Test Prep in Philadelphia, MCAT Test Prep in Seattle, SSAT Test Prep in Los Angeles

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Calculus 2 : Parametric, Polar, and Vector

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #15 : Parametric Form

Example Question #21 : Parametric, Polar, And Vector

Example Question #23 : Parametric

Example Question #22 : Parametric, Polar, And Vector

Example Question #23 : Parametric, Polar, And Vector

Example Question #19 : Parametric Form

Example Question #24 : Parametric, Polar, And Vector

Example Question #25 : Parametric, Polar, And Vector

Example Question #26 : Parametric, Polar, And Vector

Example Question #27 : Parametric, Polar, And Vector

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: