Question 1

Find  at the point where  if

Accepted Answer

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Question 2

Find the approximate arc length of x = 3t + 2 , y = 4t - 6 , over the interval  .

Accepted Answer

The answer of Find the approximate arc length of x...

Question 3

Find  at the point where  if 
A) 
B) 11
C) 1
D) 
E) 0

Accepted Answer

The answer of Find  at the point where ...

Question 4

Find the equation of the tangent to the curve  and  at  .

Accepted Answer

The answer of Find the equation of the tangent to...

Question 5

Find the exact arc length of x = 6 sin t, y = 6 cos t , over the interval  .

Accepted Answer

The answer of Find the exact arc length of x...

Question 6

Find 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find 
A) 
B) 
C) 
D) 
E) ...

Question 7

For the parametric equation x = 9t² + 11 , y = 6t³ - 12 , the value of at t = 1 is A) 1 B) 9 C) -1 D) 11 E) 12

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The answer of For the parametric equation x = 9t²...

Question 8

Find  at the point where  if

Accepted Answer

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Question 9

Find  if 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The only difference between the two given codes is in the 9th digit, where one is 9 and the other is 8. Flipping the 9th digit gives us 8->9 or 9->8, so the answer option should have the same digits except for a flip in the 9th place. Option D does this, so it is the correct answer.

Question 10

Find the inverse of the parametric equation x = 6t² - 2t + 7 , y = 6t - 5

Accepted Answer

The answer of Find the inverse of the parametric equation...

Question 11

Find the arclength of the curve

Accepted Answer

The answer of Find the arclength of the curve ...

Question 12

Find the value(s) of t for which the tangents to  is/are horizontal.
A) 
B) 0
C) 
D) 
E)

Accepted Answer

For a tangent to be horizontal, the slope of the tangent must be 0. The slope of a tangent to a curve at a point is given by the derivative of the curve at that point. Therefore, to find the value(s) of t for which the tangents to the curve in question are horizontal, we need to find the value(s) of t for which the derivative of the curve is equal to 0.

Taking the derivative of the given curve, we get:

dy/dx = -(3/2)t^2 - 8t

Setting this equal to 0 and solving for t, we get:

-(3/2)t^2 - 8t = 0
t(3t + 16) = 0
t = 0 or t = -16/3

Therefore, the only value of t for which the tangents to the curve in question are horizontal is t = 0, which corresponds to choice B.

Question 13

Find  at the point where  if

Accepted Answer

The answer of Find  at the point where ...

Question 14

Find the equation of the tangent to the curve  and  at  .

Accepted Answer

The answer of Find the equation of the tangent to...

Question 15

Graph the parametric equation x =  , y = 4 sin t .

Accepted Answer

The answer of Graph the parametric equation x = ...

Question 16

Find the approximate arc length of x = 3t² , y = 4t³ + 2 , over the interval .

Accepted Answer

The answer of Find the approximate arc length of x...

Question 17

Find the equation of the tangent to the curve  and  at  .

Accepted Answer

The answer of Find the equation of the tangent to...

Question 18

For the parametric equation x = 2t + 9 , y = 8t - 3 , the value of  at t = 4 is
A) 2
B) 9
C) 4
D) 3
E) 0

Accepted Answer

The answer of For the parametric equation x = 2t...

Question 19

Graph the parametric equation x = 2t³ , y = 4t² .

Accepted Answer

The answer of Graph the parametric equation x = 2t³...

Quiz 10: Parametric and Polar Curves; Conic Sections

Find at the point where if

Find the approximate arc length of x = 3t + 2 , y = 4t - 6 , over the interval .

Find at the point where if

Find the equation of the tangent to the curve and at .

Find the exact arc length of x = 6 sin t, y = 6 cos t , over the interval .

Find

For the parametric equation x = 9t2 + 11 , y = 6t3 - 12 , the value of at t = 1 is

Find at the point where if

Find if

Find the inverse of the parametric equation x = 6t2 - 2t + 7 , y = 6t - 5

Find the arclength of the curve

Find the value(s) of t for which the tangents to is/are horizontal.

Find at the point where if

Find the equation of the tangent to the curve and at .

Graph the parametric equation x = , y = 4 sin t .

Find the approximate arc length of x = 3t2 , y = 4t3 + 2 , over the interval .

Find the equation of the tangent to the curve and at .

For the parametric equation x = 2t + 9 , y = 8t - 3 , the value of at t = 4 is

Graph the parametric equation x = 2t3 , y = 4t2 .

For the parametric equation x = 9t² + 11 , y = 6t³ - 12 , the value of at t = 1 is

Find the inverse of the parametric equation x = 6t² - 2t + 7 , y = 6t - 5

Find the approximate arc length of x = 3t² , y = 4t³ + 2 , over the interval .

Graph the parametric equation x = 2t³ , y = 4t² .