8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

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07/20/22 Perkins AP Calculus AB Day 12 Section 2.6

Transcript of 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

Page 1: 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

04/19/23 Perkins

AP Calculus AB

Day 12Section 2.6

Page 2: 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

ftsec4

dx

dt

1. The base of a 25-foot ladder is being pulled away from the house it leans on at a rate of 4 feet per second. At what rate is the top of the ladder moving when the base of the ladder is 7 feet from the building?

Find .dy

dt7 feetx

x

y2 2 25x y

7

24

25

25

2 2 0dx dyx ydt dt

2 7 4 2 0dy

ydt

2 7 4 2 24 0dy

dt

56

48

dy

dt

sec

7

6ft

Page 3: 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

sec4 ftdx

dt

2a. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second away from a light that is 13 feet above the ground. Find the rate at which his shadow’s length is changing when he is 10 feet from the base of the light.

13

6

d

s

10 ftx

Find .ds

dt

13 6s d

sx

d

6

13 ft

d x s

13 6 6s x s 7 6s x

7 6ds dx

dt dt

7 6 4ds

dt

sec

24

7ft

ds

dt

Page 4: 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

sec4 ftdx

dt

2b. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second away from a light that is 13 feet above the ground. Find the rate at which the position of the tip of his shadow is changing when he is 10 feet from the base of the light.

10 ftx

Find .dd

dt

d x s

sec

24

7ft

ds

dt

dd dx ds

dt dt dt

244

7 sec

52

7ft

sx

d

6

13 ft

Page 5: 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

ftsec1

dr

dt

3. A fishing line is reeled in at a rate of 1 foot per second from a bridge that is 15 feet above the water. At what rate is the angle between the line and the water changing when 25 feet of line is out?

Find .d

dt

25 feetr

x

15

15sin

r

20

15

r

115r

2cos 15d dr

rdt dt

25

2

20 151

25 25

d

dt

2

15 25

2025

d

dt

sec

3

100rad

Page 6: 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

Perkins

AP Calculus AB

Day 12Section 2.6

Page 7: 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

1. The base of a 25-foot ladder is being pulled away from the house it leans on at a rate of 4 feet per second. At what rate is the top of the ladder moving when the base of the ladder is 7 feet from the building?

Page 8: 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

2a. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second away from a light that is 13 feet above the ground. Find the rate at which his shadow’s length is changing when he is 10 feet from the base of the light.

Page 9: 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

2b. Mr. Aldridge, who is 6 feet tall, walks at a rate of 4 feet per second away from a light that is 13 feet above the ground. Find the rate at which the position of the tip of his shadow is changing when he is 10 feet from the base of the light.

Page 10: 8/15/2015 Perkins AP Calculus AB Day 12 Section 2.6.

3. A fishing line is reeled in at a rate of 1 foot per second from a bridge that is 15 feet above the water. At what rate is the angle between the line and the water changing when 25 feet of line is out?