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Deck 13: Section 6: Functions of Several Variables
ملء الشاشة (f)
سؤال
The radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute. What is the rate of change of the volume when the radius is 14 inches and the height is 32 inches?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate 
at 
using the appropriate Chain Rule for 
where 
and 
. Round your answer to two decimal places.
A) 22.26
B) 22.34
C) 29.22
D) 26.94
E) 24.42
at using the appropriate Chain Rule for where and . Round your answer to two decimal places.A) 22.26
B) 22.34
C) 29.22
D) 26.94
E) 24.42
سؤال
Find 
using the appropriate Chain Rule for 
where 
and 
, and evaluate the partial derivative at 
and 
. Round your answer to two decimal places.
A) 1,209.99
B) 806.71
C) 1,210.14
D) 806.69
E) 1,209.20
using the appropriate Chain Rule for where and , and evaluate the partial derivative at and . Round your answer to two decimal places.A) 1,209.99
B) 806.71
C) 1,210.14
D) 806.69
E) 1,209.20
سؤال
Differentiate implicitly to find 
. 
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
سؤال
Find 
using the appropriate Chain Rule for 
where 
, and 
.
A)
B)
C)
D)
E)
using the appropriate Chain Rule for where , and .A)
B)
C)
D)
E)
سؤال
Differentiate implicitly to find 
, given 
.
A)
B)
C)
D)
E)
, given .A)
B)
C)
D)
E)
سؤال
Find 
using the appropriate Chain Rule for 
where 
, and 
.
A)
B)
C)
D)
E)
using the appropriate Chain Rule for where , and .A)
B)
C)
D)
E)
سؤال
Find 
using the appropriate Chain Rule for 
where 
and 
.
A)
B)
C)
D)
E)
using the appropriate Chain Rule for where and .A)
B)
C)
D)
E)
سؤال
Find 
using the appropriate Chain Rule for 
where 
and 
.
A)
B)
C)
D)
E)
using the appropriate Chain Rule for where and .A)
B)
C)
D)
E)
سؤال
The parametric equations for the paths of two projectiles are given below. At what rate is the distance between the two objects changing at 
? Round your answer to two decimal places. 
A) 0.86
B) 1.54
C) 0.58
D) -1.73
E) -0.65
? Round your answer to two decimal places. A) 0.86
B) 1.54
C) 0.58
D) -1.73
E) -0.65
سؤال
Differentiate implicitly to find 
, given 
.
A)
B)
C)
D)
E)
, given .A)
B)
C)
D)
E)
سؤال
The radius of a right circular cylinder is increasing at a rate of 9 inches per minute, and the height is decreasing at a rate of 7 inches per minute. What is the rate of change of the surface area when the radius is 12 inches and the height is 32 inches?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Let 
be the angle between equal sides of an isosceles triangle and let x be the length of these sides. x is increasing at 
meter per hour and 
is increasing at 
radian per hour. Find the rate of increase of the area when 
and 
. Round your answer to three decimal places.
A)
B)
C)
D)
E)
be the angle between equal sides of an isosceles triangle and let x be the length of these sides. x is increasing at meter per hour and is increasing at radian per hour. Find the rate of increase of the area when and . Round your answer to three decimal places.A)
B)
C)
D)
E)
سؤال
The two radii of the frustum of a right circular cone are increasing at a rate of 4 centimeters per minute, and the height is increasing at a rate of 12 centimeters per minute (see figure). Find the rate at which the volume is changing when the two radii are 15 centimeters and 30 centimeters, and the height is 10 centimeters. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Let 
, where 
and 
. Find 
.
A)
B)
C)
D)
E)
, where and . Find .A)
B)
C)
D)
E)
سؤال
Let 
, where 
, 
, and 
. Find 
.
A)
B)
C)
D)
E)
, where , , and . Find .A)
B)
C)
D)
E)
سؤال
The two radii of the frustum of a right circular cone are increasing at a rate of 7 centimeters per minute, and the height is increasing at a rate of 11 centimeters per minute (see figure). Find the rate at which the surface area is changing when the two radii are 16 centimeters and 26 centimeters, and the height is 13 centimeters. [Note: The surface area does not include the top and bottom circles.] Round your answer to two decimal places. ![<strong>The two radii of the frustum of a right circular cone are increasing at a rate of 7 centimeters per minute, and the height is increasing at a rate of 11 centimeters per minute (see figure). Find the rate at which the surface area is changing when the two radii are 16 centimeters and 26 centimeters, and the height is 13 centimeters. [Note: The surface area does not include the top and bottom circles.] Round your answer to two decimal places. </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6313_bfae_a696_fb6f6081c68c_TB4584_00_TB4584_00.jpg)
A)![<strong>The two radii of the frustum of a right circular cone are increasing at a rate of 7 centimeters per minute, and the height is increasing at a rate of 11 centimeters per minute (see figure). Find the rate at which the surface area is changing when the two radii are 16 centimeters and 26 centimeters, and the height is 13 centimeters. [Note: The surface area does not include the top and bottom circles.] Round your answer to two decimal places. </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6313_bfaf_a696_5ff71cf78a6a_TB4584_11_TB4584_11.jpg)
B)![<strong>The two radii of the frustum of a right circular cone are increasing at a rate of 7 centimeters per minute, and the height is increasing at a rate of 11 centimeters per minute (see figure). Find the rate at which the surface area is changing when the two radii are 16 centimeters and 26 centimeters, and the height is 13 centimeters. [Note: The surface area does not include the top and bottom circles.] Round your answer to two decimal places. </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6314_0dd0_a696_83ebe0fe0caf_TB4584_11_TB4584_11.jpg)
C)![<strong>The two radii of the frustum of a right circular cone are increasing at a rate of 7 centimeters per minute, and the height is increasing at a rate of 11 centimeters per minute (see figure). Find the rate at which the surface area is changing when the two radii are 16 centimeters and 26 centimeters, and the height is 13 centimeters. [Note: The surface area does not include the top and bottom circles.] Round your answer to two decimal places. </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6314_34e1_a696_4174efe1e710_TB4584_11_TB4584_11.jpg)
D)![<strong>The two radii of the frustum of a right circular cone are increasing at a rate of 7 centimeters per minute, and the height is increasing at a rate of 11 centimeters per minute (see figure). Find the rate at which the surface area is changing when the two radii are 16 centimeters and 26 centimeters, and the height is 13 centimeters. [Note: The surface area does not include the top and bottom circles.] Round your answer to two decimal places. </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6314_5bf2_a696_0748c1b8ed09_TB4584_11_TB4584_11.jpg)
E)![<strong>The two radii of the frustum of a right circular cone are increasing at a rate of 7 centimeters per minute, and the height is increasing at a rate of 11 centimeters per minute (see figure). Find the rate at which the surface area is changing when the two radii are 16 centimeters and 26 centimeters, and the height is 13 centimeters. [Note: The surface area does not include the top and bottom circles.] Round your answer to two decimal places. </strong> A) B) C) D) E) <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB4584/11eaa595_6314_8303_a696_49c0e6846d75_TB4584_11_TB4584_11.jpg)
A)
B)
C)
D)
E)
سؤال
Find 
using the appropriate Chain Rule for 
where 
.
A) 116t
B) 58t
C) 104t
D) 32t
E) 174t
using the appropriate Chain Rule for where .A) 116t
B) 58t
C) 104t
D) 32t
E) 174t
سؤال
Let 
, where 
and 
. Find 
.
A)
B)
C)
D)
E)
, where and . Find .A)
B)
C)
D)
E)
سؤال
Find 
using the appropriate Chain Rule for 
where 
and 
, and evaluate the partial derivative at 
and 
. Round your answer to two decimal places.
A) -8.83
B) -5.89
C) -6.62
D)
2.72
E) -8.09
using the appropriate Chain Rule for where and , and evaluate the partial derivative at and . Round your answer to two decimal places.A) -8.83
B) -5.89
C) -6.62
D)
2.72E) -8.09
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العب
ملء الشاشة (f)
Deck 13: Section 6: Functions of Several Variables
1
The radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute. What is the rate of change of the volume when the radius is 14 inches and the height is 32 inches?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Evaluate at using the appropriate Chain Rule for where and . Round your answer to two decimal places.
A) 22.26
B) 22.34
C) 29.22
D) 26.94
E) 24.42
at using the appropriate Chain Rule for where and . Round your answer to two decimal places.A) 22.26
B) 22.34
C) 29.22
D) 26.94
E) 24.42
26.94
3
Find using the appropriate Chain Rule for where and , and evaluate the partial derivative at and . Round your answer to two decimal places.
A) 1,209.99
B) 806.71
C) 1,210.14
D) 806.69
E) 1,209.20
using the appropriate Chain Rule for where and , and evaluate the partial derivative at and . Round your answer to two decimal places.A) 1,209.99
B) 806.71
C) 1,210.14
D) 806.69
E) 1,209.20
1,210.14
4
Differentiate implicitly to find .
A)
B)
C)
D)
E)
. A)
B)
C)
D)
E)
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5
Find using the appropriate Chain Rule for where , and .
A)
B)
C)
D)
E)
using the appropriate Chain Rule for where , and .A)
B)
C)
D)
E)
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6
Differentiate implicitly to find , given .
A)
B)
C)
D)
E)
, given .A)
B)
C)
D)
E)
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7
Find using the appropriate Chain Rule for where , and .
A)
B)
C)
D)
E)
using the appropriate Chain Rule for where , and .A)
B)
C)
D)
E)
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8
Find using the appropriate Chain Rule for where and .
A)
B)
C)
D)
E)
using the appropriate Chain Rule for where and .A)
B)
C)
D)
E)
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9
Find using the appropriate Chain Rule for where and .
A)
B)
C)
D)
E)
using the appropriate Chain Rule for where and .A)
B)
C)
D)
E)
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10
The parametric equations for the paths of two projectiles are given below. At what rate is the distance between the two objects changing at ? Round your answer to two decimal places.
A) 0.86
B) 1.54
C) 0.58
D) -1.73
E) -0.65
? Round your answer to two decimal places. A) 0.86
B) 1.54
C) 0.58
D) -1.73
E) -0.65
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11
Differentiate implicitly to find , given .
A)
B)
C)
D)
E)
, given .A)
B)
C)
D)
E)
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12
The radius of a right circular cylinder is increasing at a rate of 9 inches per minute, and the height is decreasing at a rate of 7 inches per minute. What is the rate of change of the surface area when the radius is 12 inches and the height is 32 inches?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
Let be the angle between equal sides of an isosceles triangle and let x be the length of these sides. x is increasing at meter per hour and is increasing at radian per hour. Find the rate of increase of the area when and . Round your answer to three decimal places.
A)
B)
C)
D)
E)
be the angle between equal sides of an isosceles triangle and let x be the length of these sides. x is increasing at meter per hour and is increasing at radian per hour. Find the rate of increase of the area when and . Round your answer to three decimal places.A)
B)
C)
D)
E)
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14
The two radii of the frustum of a right circular cone are increasing at a rate of 4 centimeters per minute, and the height is increasing at a rate of 12 centimeters per minute (see figure). Find the rate at which the volume is changing when the two radii are 15 centimeters and 30 centimeters, and the height is 10 centimeters.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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15
Let , where and . Find .
A)
B)
C)
D)
E)
, where and . Find .A)
B)
C)
D)
E)
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16
Let , where , , and . Find .
A)
B)
C)
D)
E)
, where , , and . Find .A)
B)
C)
D)
E)
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17
The two radii of the frustum of a right circular cone are increasing at a rate of 7 centimeters per minute, and the height is increasing at a rate of 11 centimeters per minute (see figure). Find the rate at which the surface area is changing when the two radii are 16 centimeters and 26 centimeters, and the height is 13 centimeters. [Note: The surface area does not include the top and bottom circles.] Round your answer to two decimal places.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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18
Find using the appropriate Chain Rule for where .
A) 116t
B) 58t
C) 104t
D) 32t
E) 174t
using the appropriate Chain Rule for where .A) 116t
B) 58t
C) 104t
D) 32t
E) 174t
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19
Let , where and . Find .
A)
B)
C)
D)
E)
, where and . Find .A)
B)
C)
D)
E)
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20
Find using the appropriate Chain Rule for where and , and evaluate the partial derivative at and . Round your answer to two decimal places.
A) -8.83
B) -5.89
C) -6.62
D) 2.72
E) -8.09
using the appropriate Chain Rule for where and , and evaluate the partial derivative at and . Round your answer to two decimal places.A) -8.83
B) -5.89
C) -6.62
D)
2.72E) -8.09
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