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Calculus 2 : Calculus II

Study concepts, example questions & explanations for Calculus 2

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All Calculus 2 Resources

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

Example Questions

Example Question #58 : Parametric, Polar, And Vector

Given x=5t-9 and y=2t+7 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{2}{5}(x-9)+7$

$y=\frac{2}{5}(x+9)+7$

None of the answers provided

$y=\frac{2}{5}(x-9)-7$

Correct answer:

$y=\frac{2}{5}(x+9)+7$

Explanation:

Given x=5t-9 and y=2t+7 , let's solve both equations for :

$x=5t-9\rightarrow t=\frac{x+9}{5}$

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

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

$\frac{y-7}{2}=\frac{x+9}{5}$

$y-7=2\left(\frac{x+9}{5}\right)$

$y=\frac{2}{5}(x+9)+7$

Report an Error

Example Question #59 : Parametric, Polar, And Vector

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

Possible Answers:

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

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

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

$y=\frac{1}{2}(x+1)$

None of the above

Correct answer:

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

Explanation:

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

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

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

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

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

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

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

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Example Question #60 : Parametric, Polar, And Vector

Given x=5t+11 and y=-2t-7 , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{2}{5}(x-11)-7$

$y=-\frac{2}{5}(x-11)-7$

$y=\frac{2}{5}(x-11)+7$

None of the above

$y=-\frac{2}{5}(x-11)+7$

Correct answer:

$y=-\frac{2}{5}(x-11)-7$

Explanation:

Given x=5t+11 and y=-2t-7 , let's solve both equations for :

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

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

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

$-\frac{y+7}{2}=\frac{x-11}{5}$

$y+7=-2\left(\frac{x-11}{5}\right)$

$y+7=-\frac{2}{5}(x-11)$

$y=-\frac{2}{5}(x-11)-7$

Report an Error

Example Question #61 : Parametric, Polar, And Vector

Given $x=\frac{1}{2}t-2$ and $y=\frac{1}{3}t-5$ , what is in terms of (rectangular form)?

Possible Answers:

$y=\frac{2}{3}(x+2)-5$

$y=-\frac{2}{3}(x+2)-5$

$y=\frac{2}{3}(x-2)+5$

$y=\frac{2}{3}(x+2)+5$

$y=\frac{2}{3}(x-2)-5$

Correct answer:

$y=\frac{2}{3}(x+2)-5$

Explanation:

Given $x=\frac{1}{2}t-2$ and $y=\frac{1}{3}t-5$ , let's solve both equations for :

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

$y=\frac{1}{3}t-5\rightarrow t=3(y+5)$

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

3(y+5)=2(x+2)

$y+5=\frac{2}{3}(x+2)$

$y=\frac{2}{3}(x+2)-5$

Report an Error

Example Question #62 : Parametric, Polar, And Vector

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

Possible Answers:

y=16x-3

None of the above

y=16x+3

y=16-3x

y=16+3x

Correct answer:

y=16-3x

Explanation:

Given x=6-t and y=3t-2 , let's solve both equations for :

$x=6-t\rightarrow t=6-x$

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

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

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

y+2=3(6-x)

y=3(6-x)-2

y=18-3x-2

y=16-3x

Report an Error

Example Question #571 : Calculus Ii

Convert the following equation from parametric to rectangular form:

$x=t^2, y=\sec(t)+\tan(t)$

Possible Answers:

y=x

y=0

$y=\sec(\pm \sqrt{x})+\tan(\pm \sqrt{x})$

$y=\sec(-\sqrt{x})+\tan(-\sqrt{x})$

Correct answer:

$y=\sec(\pm \sqrt{x})+\tan(\pm \sqrt{x})$

Explanation:

To convert from parametric to rectangular form, we must eliminate the parameter from one of the equations:

$t=\pm\sqrt{x}$

Now, replace all of the t's in the equation for y with the above term:

$y=\sec(\pm \sqrt{x})+\tan(\pm \sqrt{x})$

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Example Question #572 : Calculus Ii

Convert the following parametric equation to rectangular form:

x=t-1, y=8t

Possible Answers:

y=x

y=8(x-1)

y=8x

y=8(x+1)

Correct answer:

y=8(x+1)

Explanation:

To convert the equation into parametric form, we must eliminate the parameter by finding t in terms of either x or y:

t=x+1

Now, replace all of the t's in the equation for y with the above term:

y=8(x+1)

Report an Error

Example Question #573 : Calculus Ii

Convert the following parametric equation into rectangular form:

$x=2t, y=\cos(t)+2$

Possible Answers:

y=x

$y=\cos(x)-2$

$y=\cos(x)+2$

$y=\cos\left(\frac{x}{2}\right)+2$

Correct answer:

$y=\cos\left(\frac{x}{2}\right)+2$

Explanation:

To convert from parametric form to rectangular form, we must eliminate the parameter:

To do this we will first get t in terms of x.

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

Now, replace all of the t's in the equation for y:

$y=\cos\left(\frac{x}{2}\right)+2$

Report an Error

Example Question #66 : Parametric, Polar, And Vector

Given x=9-t and y=10-2t , what is in terms of (rectangular form)?

Possible Answers:

y=2x+8

y=8x+2

y=2x-8

None of the above

y=8x-2

Correct answer:

y=2x-8

Explanation:

Given x=9-t and y=10-2t , let's solve both equations for :

$x=9-t\rightarrowt=9-x$

$y=10-2t\rightarrow t=-\frac{y-10}{2}$

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

$-\frac{y-10}{2}=9-x$

y-10=-2(9-x)

y=-2(9-x)+10

y=-18+2x+10

y=2x-8

Report an Error

Example Question #61 : Parametric Form

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

Possible Answers:

y=-6x

$y=\frac{1}{6}x$

y=6x

None of the above

$y=-\frac{1}{6}x$

Correct answer:

y=-6x

Explanation:

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

$x=-\frac{1}{2}t\rightarrow t=-2x$

$y=3t\rightarrow t=\frac{y}{3}$

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

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

y=-6x

Report an Error

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Calculus 2 : Calculus II

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #58 : Parametric, Polar, And Vector

Example Question #59 : Parametric, Polar, And Vector

Example Question #60 : Parametric, Polar, And Vector

Example Question #61 : Parametric, Polar, And Vector

Example Question #62 : Parametric, Polar, And Vector

Example Question #571 : Calculus Ii

Example Question #572 : Calculus Ii

Example Question #573 : Calculus Ii

Example Question #66 : Parametric, Polar, And Vector

Example Question #61 : Parametric Form

All Calculus 2 Resources

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