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Deck 10: Section 3: Conics, Parametric Equations, and Polar Coordinates
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Question
Find 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find the area of the surface generated by revolving the curve about the given axis. 
(i) x-axis; (ii) y-axis
A)
B)
C)
D)
E)
(i) x-axis; (ii) y-axisA)
B)
C)
D)
E)
Question
Find the arc length of the curve on the given interval. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The path of a projectile is modeled by the parametric equations 
and 
where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.
A) 312.85 ft
B) 521.42 ft
C) 131.09 ft
D) 391.06 ft
E) 195.53 ft
and where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.A) 312.85 ft
B) 521.42 ft
C) 131.09 ft
D) 391.06 ft
E) 195.53 ft
Question
Determine the t intervals on which the curve 
is concave downward or concave upward.
A) concave downward:
; concave upward: 
B) concave downward:
; concave upward: 
C) concave downward:
D) concave upward:
E) concave downward:
is concave downward or concave upward.A) concave downward:
; concave upward: B) concave downward:
; concave upward: C) concave downward:
D) concave upward:
E) concave downward:
Question
Find the arc length of the curve on the given interval. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find 
and 
if possible, and find the slope and concavity (if possible) at the point corresponding to t = 5. 
A)
: slope 
and concave up
B)
slope -6 and concave down
C)
slope 14 and concave up
D)
: slope 6 and concave down
E)
: slope 
and concave up
and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 5. A)
: slope and concave upB)
slope -6 and concave downC)
slope 14 and concave upD)
: slope 6 and concave downE)
: slope and concave up Question
Find 
and 
if possible, and find the slope and concavity (if possible) at the point corresponding to 
. 
A)
at 
: slope 1 and concave down
B)
at 
: slope 
and concave down
C)
at 
: slope 
and concave up
D)
at 
: slope 1 and concave up
E)
at 
: slope of 
and concave down
and if possible, and find the slope and concavity (if possible) at the point corresponding to . A)
at : slope 1 and concave downB)
at : slope and concave downC)
at : slope and concave upD)
at : slope 1 and concave upE)
at : slope of and concave down Question
Find the area of the surface generated by revolving the curve 
about the x-axis on the interval 
.
A)
B)
C)
D)
E)
about the x-axis on the interval .A)
B)
C)
D)
E)
Question
The path of a projectile is modeled by the parametric equations 
and 
where x and y are measured in feet. Use the integration capabilities of a graphing utility to approximate the arc length of the path. Round your answer to one decimal place.
A) 387.2 ft
B) 595.8 ft
C) 335.0 ft
D) 269.9 ft
E) 465.4 ft
and where x and y are measured in feet. Use the integration capabilities of a graphing utility to approximate the arc length of the path. Round your answer to one decimal place.A) 387.2 ft
B) 595.8 ft
C) 335.0 ft
D) 269.9 ft
E) 465.4 ft
Question
Find the arc length of the curve on the given interval. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find all points (if any) of horizontal and vertical tangency to the curve 
.
A) horizontal tangents:
, vertical tangent: none
B) horizontal tangent: none, vertical tangents:
C) horizontal tangents:
, vertical tangent: none
D) horizontal tangent: none, vertical tangents:
E) horizontal tangent: none, vertical tangent: none
.A) horizontal tangents:
, vertical tangent: noneB) horizontal tangent: none, vertical tangents:
C) horizontal tangents:
, vertical tangent: noneD) horizontal tangent: none, vertical tangents:
E) horizontal tangent: none, vertical tangent: none
Question
Find the arc length of the curve 
on the interval 
. Round your answer to three decimal places.
A) 287.453
B) 191.635
C) 193.606
D) 66.480
E) 99.721
on the interval . Round your answer to three decimal places.A) 287.453
B) 191.635
C) 193.606
D) 66.480
E) 99.721
Question
Find an equation of the tangent line at a point 
on the curve 
.
A)
B)
C)
D)
E)
on the curve .A)
B)
C)
D)
E)
Question
Find the second derivative 
of the parametric equations 
. Round your answer to two decimal places, if necessary.
A) 0
B) 2.00
C)
D) 0.50
E)
of the parametric equations . Round your answer to two decimal places, if necessary.A) 0
B) 2.00
C)
D) 0.50
E)
Question
Find 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
Question
Find all points (if any) of horizontal and vertical tangency to the curve 
.
A) horizontal tangents:
, vertical tangents: 
B) horizontal tangents:
, vertical tangents: 
C) horizontal tangent:
, vertical tangent: 
D) horizontal tangents:
, vertical tangents: 
E) horizontal tangent:
, vertical tangent: 
.A) horizontal tangents:
, vertical tangents: B) horizontal tangents:
, vertical tangents: C) horizontal tangent:
, vertical tangent: D) horizontal tangents:
, vertical tangents: E) horizontal tangent:
, vertical tangent: Question
Determine the t intervals on which the curve 
is concave downward or concave upward.
A) concave downward:
; concave upward: 
B) concave downward:
; concave upward: 
C) concave downward:
; concave upward: 
D) concave downward:
; concave upward: 
E) concave downward:
; concave upward: 
is concave downward or concave upward.A) concave downward:
; concave upward: B) concave downward:
; concave upward: C) concave downward:
; concave upward: D) concave downward:
; concave upward: E) concave downward:
; concave upward: Question
Find the second derivative 
of the parametric equations 
.
A)
B)
C)
D)
E)
of the parametric equations .A)
B)
C)
D)
E)
Question
Find the area of the surface generated by revolving the curve 
about the y-axis on the interval 
. Round your answer to two decimal places.
A) 1427.12
B) 1178.96
C) 1049.37
D) 589.48
E) 1898.04
about the y-axis on the interval . Round your answer to two decimal places.A) 1427.12
B) 1178.96
C) 1049.37
D) 589.48
E) 1898.04
Question
Find the area of the surface generated by revolving the curve about the given axis. 
(i) x-axis; (ii) y-axis
A)
B)
C)
D)
E)
(i) x-axis; (ii) y-axisA)
B)
C)
D)
E)
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Deck 10: Section 3: Conics, Parametric Equations, and Polar Coordinates
1
Find .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
2
Find the area of the surface generated by revolving the curve about the given axis. (i) x-axis; (ii) y-axis
A)
B)
C)
D)
E)
(i) x-axis; (ii) y-axisA)
B)
C)
D)
E)
3
Find the arc length of the curve on the given interval.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
4
The path of a projectile is modeled by the parametric equations and where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.
A) 312.85 ft
B) 521.42 ft
C) 131.09 ft
D) 391.06 ft
E) 195.53 ft
and where x and y are measured in feet. Use a graphing utility to approximate the range of the projectile. Round your answer to two decimal places.A) 312.85 ft
B) 521.42 ft
C) 131.09 ft
D) 391.06 ft
E) 195.53 ft
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5
Determine the t intervals on which the curve is concave downward or concave upward.
A) concave downward: ; concave upward:
B) concave downward: ; concave upward:
C) concave downward:
D) concave upward:
E) concave downward:
is concave downward or concave upward.A) concave downward:
; concave upward: B) concave downward:
; concave upward: C) concave downward:
D) concave upward:
E) concave downward:
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6
Find the arc length of the curve on the given interval.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 22 flashcards in this deck.
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7
Find and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 5.
A) : slope and concave up
B) slope -6 and concave down
C) slope 14 and concave up
D) : slope 6 and concave down
E) : slope and concave up
and if possible, and find the slope and concavity (if possible) at the point corresponding to t = 5. A)
: slope and concave upB)
slope -6 and concave downC)
slope 14 and concave upD)
: slope 6 and concave downE)
: slope and concave up Unlock Deck
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8
Find and if possible, and find the slope and concavity (if possible) at the point corresponding to .
A) at : slope 1 and concave down
B) at : slope and concave down
C) at : slope and concave up
D) at : slope 1 and concave up
E) at : slope of and concave down
and if possible, and find the slope and concavity (if possible) at the point corresponding to . A)
at : slope 1 and concave downB)
at : slope and concave downC)
at : slope and concave upD)
at : slope 1 and concave upE)
at : slope of and concave down Unlock Deck
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9
Find the area of the surface generated by revolving the curve about the x-axis on the interval .
A)
B)
C)
D)
E)
about the x-axis on the interval .A)
B)
C)
D)
E)
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k this deck
10
The path of a projectile is modeled by the parametric equations and where x and y are measured in feet. Use the integration capabilities of a graphing utility to approximate the arc length of the path. Round your answer to one decimal place.
A) 387.2 ft
B) 595.8 ft
C) 335.0 ft
D) 269.9 ft
E) 465.4 ft
and where x and y are measured in feet. Use the integration capabilities of a graphing utility to approximate the arc length of the path. Round your answer to one decimal place.A) 387.2 ft
B) 595.8 ft
C) 335.0 ft
D) 269.9 ft
E) 465.4 ft
Unlock Deck
Unlock for access to all 22 flashcards in this deck.
Unlock Deck
k this deck
11
Find the arc length of the curve on the given interval.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 22 flashcards in this deck.
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k this deck
12
Find .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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13
Find all points (if any) of horizontal and vertical tangency to the curve .
A) horizontal tangents: , vertical tangent: none
B) horizontal tangent: none, vertical tangents:
C) horizontal tangents: , vertical tangent: none
D) horizontal tangent: none, vertical tangents:
E) horizontal tangent: none, vertical tangent: none
.A) horizontal tangents:
, vertical tangent: noneB) horizontal tangent: none, vertical tangents:
C) horizontal tangents:
, vertical tangent: noneD) horizontal tangent: none, vertical tangents:
E) horizontal tangent: none, vertical tangent: none
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Unlock for access to all 22 flashcards in this deck.
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k this deck
14
Find the arc length of the curve on the interval . Round your answer to three decimal places.
A) 287.453
B) 191.635
C) 193.606
D) 66.480
E) 99.721
on the interval . Round your answer to three decimal places.A) 287.453
B) 191.635
C) 193.606
D) 66.480
E) 99.721
Unlock Deck
Unlock for access to all 22 flashcards in this deck.
Unlock Deck
k this deck
15
Find an equation of the tangent line at a point on the curve .
A)
B)
C)
D)
E)
on the curve .A)
B)
C)
D)
E)
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Unlock for access to all 22 flashcards in this deck.
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k this deck
16
Find the second derivative of the parametric equations . Round your answer to two decimal places, if necessary.
A) 0
B) 2.00
C)
D) 0.50
E)
of the parametric equations . Round your answer to two decimal places, if necessary.A) 0
B) 2.00
C)
D) 0.50
E)
Unlock Deck
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k this deck
17
Find .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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k this deck
18
Find all points (if any) of horizontal and vertical tangency to the curve .
A) horizontal tangents: , vertical tangents:
B) horizontal tangents: , vertical tangents:
C) horizontal tangent: , vertical tangent:
D) horizontal tangents: , vertical tangents:
E) horizontal tangent: , vertical tangent:
.A) horizontal tangents:
, vertical tangents: B) horizontal tangents:
, vertical tangents: C) horizontal tangent:
, vertical tangent: D) horizontal tangents:
, vertical tangents: E) horizontal tangent:
, vertical tangent: Unlock Deck
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19
Determine the t intervals on which the curve is concave downward or concave upward.
A) concave downward: ; concave upward:
B) concave downward: ; concave upward:
C) concave downward: ; concave upward:
D) concave downward: ; concave upward:
E) concave downward: ; concave upward:
is concave downward or concave upward.A) concave downward:
; concave upward: B) concave downward:
; concave upward: C) concave downward:
; concave upward: D) concave downward:
; concave upward: E) concave downward:
; concave upward: Unlock Deck
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20
Find the second derivative of the parametric equations .
A)
B)
C)
D)
E)
of the parametric equations .A)
B)
C)
D)
E)
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21
Find the area of the surface generated by revolving the curve about the y-axis on the interval . Round your answer to two decimal places.
A) 1427.12
B) 1178.96
C) 1049.37
D) 589.48
E) 1898.04
about the y-axis on the interval . Round your answer to two decimal places.A) 1427.12
B) 1178.96
C) 1049.37
D) 589.48
E) 1898.04
Unlock Deck
Unlock for access to all 22 flashcards in this deck.
Unlock Deck
k this deck
22
Find the area of the surface generated by revolving the curve about the given axis. (i) x-axis; (ii) y-axis
A)
B)
C)
D)
E)
(i) x-axis; (ii) y-axisA)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 22 flashcards in this deck.
Unlock Deck
k this deck
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Unlock for access to all 22 flashcards in this deck.
