STEP 1: Let S(t) be the position of the plane. Let t= 0 correspond to 2 p.m., and fill in the following values. S(0) = = 1830 STEP 2: The Mean Value Theorem says that there exists a time tor 1830- S '(to) = v(to) = STEP 3: Now v(0) = -0 , and v(4.2) = and since v(to) =| , such that the following is true. (Round your answer to two decimal places.) we have 0 < 300 < v(to). Thus, we can apply the Intermediate Value Theorem to the velocity function on the intervals [0, to] and [to
STEP 1: Let S(t) be the position of the plane. Let t= 0 correspond to 2 p.m., and fill in the following values. S(0) = = 1830 STEP 2: The Mean Value Theorem says that there exists a time tor 1830- S '(to) = v(to) = STEP 3: Now v(0) = -0 , and v(4.2) = and since v(to) =| , such that the following is true. (Round your answer to two decimal places.) we have 0 < 300 < v(to). Thus, we can apply the Intermediate Value Theorem to the velocity function on the intervals [0, to] and [to
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![A plane begins its takeoff at 2:00 p.m. on a 1830-mile flight. After 4.2 hours, the plane arrives at its destination. Explain why there are at least two times during the flight when the speed of the plane is 300 miles per hour.
STEP 1: Let S(t) be the position of the plane. Let t = 0 correspond to 2 p.m., and fill in the following values.
S(0)
S
=
= 1830
STEP 2: The Mean Value Theorem says that there exists a time to,
1830
S '(t) = v(to)
-0
< to
=
I
such that the following is true. (Round your answer to two decimal places.)
STEP 3: Now v(0) =
and v(4.2) =
and since v(t)=
I
we have 0 < 300 ≤ v(tỏ). Thus, we can apply the Intermediate Value Theorem to the velocity function on the intervals [0, to] and [to,
to see that there are at least two times during the flight when the speed was 300 miles per hour.
]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddbc108f-40b7-45ba-95b8-e08d8c37565c%2F33a10434-b37e-4646-89fd-e45b67185cde%2Fpdyfh6g_processed.png&w=3840&q=75)
Transcribed Image Text:A plane begins its takeoff at 2:00 p.m. on a 1830-mile flight. After 4.2 hours, the plane arrives at its destination. Explain why there are at least two times during the flight when the speed of the plane is 300 miles per hour.
STEP 1: Let S(t) be the position of the plane. Let t = 0 correspond to 2 p.m., and fill in the following values.
S(0)
S
=
= 1830
STEP 2: The Mean Value Theorem says that there exists a time to,
1830
S '(t) = v(to)
-0
< to
=
I
such that the following is true. (Round your answer to two decimal places.)
STEP 3: Now v(0) =
and v(4.2) =
and since v(t)=
I
we have 0 < 300 ≤ v(tỏ). Thus, we can apply the Intermediate Value Theorem to the velocity function on the intervals [0, to] and [to,
to see that there are at least two times during the flight when the speed was 300 miles per hour.
]
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