(e) Using your work above and this picture of the graph of the function y(t) given below, answer these true/false questions: (Type in the word "True" or "False") 30 25 20 15 10 5 4 10 The top of the ladder is moving down the wall at a constant rate O T O F The foot of the ladder is moving along the ground at a constant rate O T O F There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is 1 ft/sec O T O F There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is 0 ft/sec O T O F There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is -100 ft/sec OT O F There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is less than -100 ft/sec O T O F
(e) Using your work above and this picture of the graph of the function y(t) given below, answer these true/false questions: (Type in the word "True" or "False") 30 25 20 15 10 5 4 10 The top of the ladder is moving down the wall at a constant rate O T O F The foot of the ladder is moving along the ground at a constant rate O T O F There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is 1 ft/sec O T O F There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is 0 ft/sec O T O F There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is -100 ft/sec OT O F There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is less than -100 ft/sec O T O F
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Hello.
I would like help with part E of the problem in the images attached. Using the information given from parts A through D, as well as the graph of function y(t), is it true that there is a time at which the average velocity of the top of the ladder on the time interval [a, 9] is the following in ft/sec: 1, 0, -100, less than -100?
![A ladder 25 feet long is leaning against the wall of a building. Initially, the foot of the ladder is 7 feet from the wall. The foot of the ladder begins to slide
at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. The location of the foot of the ladder at time t seconds is given by the
parametric equations (7+2t,0).
wall
25 ft. ladder
ground
7 ft
(a) The location of the top of the ladder will be given by parametric equations (0,y(t)). The formula for y(t)= V -412 – 281 + 576
(Put your cursor in the box, click and a palette will come up to help you enter your symbolic answer.)
(b) The domain of t values for y(t) ranges from 0
to 9
(c) Calculate the average velocity of the top of the ladder on each of these time intervals (correct to three decimal places):
time interval
ave velocity
time interval
ave velocity
[0,2]
-0.775
[2,4]
|-1.225
[6,8]
-3.225
[8,9]
-9.798
(d) Find a time interval [a,9] so that the average velocity of the top of the ladder on this time interval is -20 ft/sec i.e. a= 8.752](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdaad9a03-a8fc-4a89-87c0-a0cac7a21cee%2Fee1a0026-6028-4b80-a802-d374597f663c%2F28u4wm_processed.png&w=3840&q=75)
Transcribed Image Text:A ladder 25 feet long is leaning against the wall of a building. Initially, the foot of the ladder is 7 feet from the wall. The foot of the ladder begins to slide
at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. The location of the foot of the ladder at time t seconds is given by the
parametric equations (7+2t,0).
wall
25 ft. ladder
ground
7 ft
(a) The location of the top of the ladder will be given by parametric equations (0,y(t)). The formula for y(t)= V -412 – 281 + 576
(Put your cursor in the box, click and a palette will come up to help you enter your symbolic answer.)
(b) The domain of t values for y(t) ranges from 0
to 9
(c) Calculate the average velocity of the top of the ladder on each of these time intervals (correct to three decimal places):
time interval
ave velocity
time interval
ave velocity
[0,2]
-0.775
[2,4]
|-1.225
[6,8]
-3.225
[8,9]
-9.798
(d) Find a time interval [a,9] so that the average velocity of the top of the ladder on this time interval is -20 ft/sec i.e. a= 8.752
![(e) Using your work above and this picture of the graph of the function y(t) given below, answer these true/false questions: (Type in the word
"True" or "False")
30
25
20
15
10
5
10
The top of the ladder is moving down the wall at a constant rate
O F
The foot of the ladder is moving along the ground at a constant rate
O T
There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is 1 ft/sec
От
O F
There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is 0 ft/sec
O T
O F
There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is -100 ft/sec
От
F
There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is less than -100 ft/sec
От
O F](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdaad9a03-a8fc-4a89-87c0-a0cac7a21cee%2Fee1a0026-6028-4b80-a802-d374597f663c%2F9aokbl_processed.png&w=3840&q=75)
Transcribed Image Text:(e) Using your work above and this picture of the graph of the function y(t) given below, answer these true/false questions: (Type in the word
"True" or "False")
30
25
20
15
10
5
10
The top of the ladder is moving down the wall at a constant rate
O F
The foot of the ladder is moving along the ground at a constant rate
O T
There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is 1 ft/sec
От
O F
There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is 0 ft/sec
O T
O F
There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is -100 ft/sec
От
F
There is a time at which the average velocity of the top of the ladder on the time interval [a,9] is less than -100 ft/sec
От
O F
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