Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Parametric

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

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 … 16 17 Next →

Example Question #65 : Parametric Form

Convert the following parametric equation to rectangular form:

$x=2t, y=\ln(t)$

Possible Answers:

x=0

x=y

x=2e^y

x=e^y

Correct answer:

x=2e^y

Explanation:

To convert from parametric to rectangular coordinates, we must eliminate the parameter by finding t in terms of x or y:

We will start by taking the exponential of both sides of the equation y=ln(t) . Recall that $e^{ln(t)}=t$ .

Therefore we get,

t=e^y .

Now, replace t with the above term in the equation for x:

x=2e^y

Report an Error

Example Question #66 : Parametric Form

When $x=-\frac{1}{3}t+8$ and $y=\frac{2}{3}t+7$ , what is in terms of (rectangular form)?

Possible Answers:

y=-2x-9

y=-2x+23

y=2x-9

y=9x-2

y=-9x-2

Correct answer:

y=-2x+23

Explanation:

Given $x=-\frac{1}{3}t+8$ and $y=\frac{2}{3}t+7$ , wet's solve both equations for :

$x=-\frac{1}{3}t+8\rightarrow t=-3(x-8)$

$y=\frac{2}{3}t+7\rightarrow t=\frac{3}{2}(y-7)$

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

$\frac{3}{2}(y-7)=-3(x-8)$

$y-7=\frac{2}{3}(-3)(x-8)$

y-7=-2(x-8)

y-7=-2x+16

y=-2x+23

Report an Error

Example Question #61 : Parametric Form

Given x=7-t and y=2t+5 , what is in terms of ?

Possible Answers:

None of the above

y=19-2x

y=19x+2

y=19x-2

y=19+2x

Correct answer:

y=19-2x

Explanation:

Given x=7-t and y=2t+5 , let's solve both equations for :

$x=7-t\rightarrow t=7-x$

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

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

$\frac{y-5}{2}=7-x$

y-5=2(7-x)

y=2(7-x)+5

y=14-2x+5

y=19-2x

Report an Error

Example Question #68 : Parametric Form

Given $x=-\frac{3}{2}t$ and y=7+2t , what is in terms of ?

Possible Answers:

$y=7-\frac{4}{3}x$

None of the above

$y=7x-\frac{4}{3}$

$y=7x+\frac{4}{3}$

$y=7+\frac{4}{3}x$

Correct answer:

$y=7-\frac{4}{3}x$

Explanation:

Given $x=-\frac{3}{2}t$ and y=7+2t , let's solve both equations for :

$x=-\frac{3}{2}t\rightarrow t=-\frac{2}{3}x$

$y=7+2t\rightarrow t=\frac{y-7}{2}$

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

$\frac{y-7}{2}=-\frac{2}{3}x$

$y-7=-\frac{4}{3}x$

$y=7-\frac{4}{3}x$

Report an Error

Example Question #69 : Parametric Form

Given $x=4+\frac{1}{2}t$ and y=-6t , what is in terms of ?

Possible Answers:

y=48+12x

None of the above

y=48x+12

y=48-12x

y=48x-12

Correct answer:

y=48-12x

Explanation:

Given $x=4+\frac{1}{2}t$ and y=-6t , wlet's solve both equations for :

$x=4+\frac{1}{2}t\rightarrow t=2(x-4)$

$y=-6t\rightarrow t=-\frac{1}{6}y$

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

$-\frac{1}{6}y=2(x-4)$

y=-12(x-4)

y=48-12x

Report an Error

Example Question #70 : Parametric Form

Given x=-3t+8 and y=4t+1 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{4}{3}(x-8)-1$

$y=-\frac{4}{3}(x-8)-1$

$y=-\frac{4}{3}(x+8)-1$

$y=\frac{4}{3}(x-8)+1$

$y=-\frac{4}{3}(x-8)+1$

Correct answer:

$y=-\frac{4}{3}(x-8)+1$

Explanation:

Given x=-3t+8 and y=4t+1 , let's solve both equations for :

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

$y=4t+1\rightarrow t=\frac{y-1}{4}$

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

$\frac{y-1}{4}=-\frac{x-8}{3}$

$y-1=-4\left(\frac{x-8}{3}\right)$

$y=-\frac{4}{3}(x-8)+1$

Report an Error

Example Question #71 : Parametric Form

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

Possible Answers:

y=1+18x

y=18-x

None of the above

y=1-18x

y=18+x

Correct answer:

y=18-x

Explanation:

Given x=t+12 and y=6-t , let's solve both equations for :

$x=t+12\rightarrow t=x-12$

$y=6-t\rightarrow t=6-y$

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

6-y=x-12

-y=x-18

y=18-x

Report an Error

Example Question #72 : Parametric Form

Given x=2t-19 and y=4-8t , what is in terms of (rectangular form)?

Possible Answers:

y=-72x-4

y=-4x-72

None of the above

y=4x-72

y=72x-4

Correct answer:

y=-4x-72

Explanation:

Given x=2t-19 and y=4-8t , let's solve both equations for :

$x=2t-19\rightarrow t=\frac{x+19}{2}$

$y=4-8t\rightarrow t=-\frac{y-4}{8}$

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

$-\frac{y-4}{8}=\frac{x+19}{2}$

y-4=-4(x+19)

y=-4(x+19)+4

y=-4x-76+4

y=-4x-72

Report an Error

Example Question #73 : Parametric Form

Given $x=2t^{2}+3$ and y=5t+8 , what is in terms of (rectangular form)?

Possible Answers:

None of the above

$y=5\left(\pm \sqrt{\frac{x-3}{2}}\right)+8$

$y=5\sqrt{\frac{x+3}{2}}+8$

$y=5\sqrt{\frac{x-3}{2}}-8$

$y=5\sqrt{\frac{x+3}{2}}-8$

Correct answer:

$y=5\left(\pm \sqrt{\frac{x-3}{2}}\right)+8$

Explanation:

Given $x=2t^{2}+3$ and y=5t+8 , let's solve both equations for :

$x=2t^{2}+3\rightarrow t=\pm \sqrt{\frac{x-3}{2}}$

$y=5t+8\rightarrow t=\frac{y-8}{5}$

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

$\frac{y-8}{5}=\pm \sqrt{\frac{x-3}{2}}$

$y-8=5\left(\pm\sqrt{\frac{x-3}{2}}\right)$

$y=5\left(\pm \sqrt{\frac{x-3}{2}}\right)+8$

Report an Error

Example Question #74 : Parametric Form

Find dy/dx at the point corresponding to the given value of the parameter without eliminating the parameter:

x=3t^2-6, y=9t+5, t=3

Possible Answers:

$\frac{21}{32}$

$\frac{1}{9}$

$\frac{1}{2}$

$\frac{32}{21}$

Correct answer:

$\frac{1}{2}$

Explanation:

The formula for dy/dx for parametric equations is given as:

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$ From the problem statement:

$\frac{dy}{dt}=9,\frac{dx}{dt}=6t$

If we plug in t=3, into the above equations:

$\frac{dy}{dx}=\frac{9}{6(3)}=\frac{9}{18}=\frac{1}{2}$

This is one of the answer choices.

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 … 16 17 Next →

View Calculus 2 Tutors

Yoonsik
Certified Tutor

Seoul National University, Bachelor of Science, Physics. University of Pennsylvania, Doctor of Philosophy, Atomic and Molecul...

View Calculus 2 Tutors

Kurosh
Certified Tutor

University of tehran, Bachelor of Engineering, Electrical Engineering.

View Calculus 2 Tutors

Filiberto
Certified Tutor

University of Arizona, Bachelor of Science, Electrical Engineering.

All Calculus 2 Resources

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

Popular Subjects

Computer Science Tutors in Washington DC, ISEE Tutors in Atlanta, SAT Tutors in Phoenix, ISEE Tutors in San Francisco-Bay Area, English Tutors in Philadelphia, Spanish Tutors in Denver, Calculus Tutors in San Diego, Physics Tutors in Denver, ISEE Tutors in Boston, Spanish Tutors in Miami

Popular Courses & Classes

GRE Courses & Classes in Phoenix, LSAT Courses & Classes in Los Angeles, SSAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Houston, LSAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Boston, ACT Courses & Classes in New York City, GRE Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Phoenix

Popular Test Prep

GMAT Test Prep in Houston, GMAT Test Prep in San Francisco-Bay Area, GRE Test Prep in Boston, GMAT Test Prep in Boston, LSAT Test Prep in New York City, SAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in Houston, GRE Test Prep in Phoenix, GRE Test Prep in San Diego, SSAT Test Prep in San Francisco-Bay Area

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

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #65 : Parametric Form

Example Question #66 : Parametric Form

Example Question #61 : Parametric Form

Example Question #68 : Parametric Form

Example Question #69 : Parametric Form

Example Question #70 : Parametric Form

Example Question #71 : Parametric Form

Example Question #72 : Parametric Form

Example Question #73 : Parametric Form

Example Question #74 : Parametric Form

Find dy/dx at the point corresponding to the given value of the parameter without eliminating the parameter:

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: