A plane begins its takeoff at 2:00 p.m. on a 2490-mile flight. After 5.1 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 100 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) = 0 5.1 = 2490 STEP 2: The Mean Value Theorem says that there exists a time to, 0 < to < 5.1 , such that the following is true. (Round your answer te two decimal places.) 2490 - 0 S (to) = v(to) = 5.1 488.24 STEP 3: Now v(0) = 19.6 , and v(5.1) = 94.9 and since v(to) = 488.24 we have 0 < 100 < v(to). Thus, we can apply the į to see that there are at least two times during the flight Intermediate Value Theorem to the velocity function on the intervals [0, to] and [to, 5.1 when the speed was 100 miles per hour.

A plane begins its takeoff at 2:00 p.m. on a 2490-mile flight. After 5.1 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 100 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) = 0 5.1 = 2490 STEP 2: The Mean Value Theorem says that there exists a time to, 0 < to < 5.1 , such that the following is true. (Round your answer te two decimal places.) 2490 - 0 S (to) = v(to) = 5.1 488.24 STEP 3: Now v(0) = 19.6 , and v(5.1) = 94.9 and since v(to) = 488.24 we have 0 < 100 < v(to). Thus, we can apply the į to see that there are at least two times during the flight Intermediate Value Theorem to the velocity function on the intervals [0, to] and [to, 5.1 when the speed was 100 miles per hour.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: 80 Height (metres) 40 Y 5 10 15 Time (minutes) 20 25 30

A: A graph of the trigonometric function is given, we have to find the equation of the graph.

Q: Jerry is driving across the country at a constant speed. Jerry enters Intersate 90 and and starts…

A: Given that Jerry is driving across the country at a constant speed. Since he start the clock, when…

Q: Jerry is driving across the country at a constant speed. Jerry enters Intersate 90 and and starts a…

A: Given that Jerry is driving across the country at a constant speed. Jerry enters Interstate 90 and…

Q: You throw a rock straight up in the air. The acceleration due to gravity is 10 meters per second per…

A: We have to find position equation .

Q: You get on a ferris wheel at the bottom that has a radius of 25 feet. 13 minutes after you get on,…

Q: The following equation represents the relationship between hours of TV watched per day (x) and the…

A: Given dataŷ = -0.944x + 24.52x is the hours of TV watched per dayŷ is the number of situpspredicting…

Q: A ball is thrown from an initial height of 5 feet with an initial upward velocity of 21 ft/s. The…

A: Given that, h = 5 + 21t - 16t2 Where h represents the height in feet and t represents the time in…

Q: If a rock is thrownin the air and has a position equation of s(t) = -2.5t2+14t. Where position is…

A: Given:position function is given as:s(t) = -2.5t2 + 14t A. Time at which the rock reaches it's…

Q: A rock is thrown straight up in the air from an initial height h., in metres, with initial velocity…

Q: If an object is dropped from a 150-foot-high building, its position (in feet above the ground) is…

A: Negative sign of the velocity is due to the downward movement of the body.

Q: – 4.9t² + 12t + 18 meters above the ground. From An object is thrown upward at time t = 0. After t…

A: y = - 4.9t2 + 12t + 18 -------Given To find : Height at t= 0

Q: A new building that costs $1,000,000 has a useful life of 100 years and a scrap value of $500,000.…

A: A new building that costs $ 1,000,000 has a useful life of 100 years and a scrap value of $500,000.…

Q: A population of owls oscillates 30 above and below an average of 110 during the year, hitting the…

A: Solution: General form :P=A cos (B(t-c)) +D

Concept explainers

Quadratic Equation

When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.

Demand and Supply Function

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.

Question

A plane begins its takeoff at 2:00 p.m. on a 2490-mile flight. After 5.1 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 100 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) = 0
s( 5.1
= 2490
STEP 2: The Mean Value Theorem says that there exists a time to, 0
< to < 5.1
, such that the following is true. (Round your answer to
two decimal places.)
2490 - 0
S (to) = v(to) =
5.1
488.24
-0
STEP 3: Now v(0) = 19.6
and v(5.1) = 94.9
and since v(to) = 488.24
we have 0 < 100 < v(to). Thus, we can apply the
i to see that there are at least two times during the flight
Intermediate Value Theorem to the velocity function on the intervals [0, to] and [to, 5.1
when the speed was 100 miles per hour.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Fundamentals of Algebraic Equations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Jerry is driving across the country at a constant speed. Jerry enters Intersate 90 and and starts a clock as he passes mile marker 52. After 5.4 hours, Jerry passes miles marker 484. Represent the time elapsed in hours using the independent variable t. Represent the mile marker passed at time t with the dependent variable x. At what speed is Jerry driving? miles per hour Write a formula to compute the mile marker x as a function of t. x= What mile marker is Jerry passing when 8.6 hours have elapsed?
4. Aden jumped off a cliff into the ocean to show his friends that he is the bravest one of the bunch. His height as a function of time could be modeled by the function h(t) = - 16t° + 16t + 480, where t is the time in seconds and h is the height in feet. a. How long did it take for Aden to reach his maximum height?
NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = – 4.9t + 325t + 346. Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? (Round to the nearest tenth.) The rocket splashes down after seconds. How high above sea-level does the rocket get at its peak? (Round to the nearest tenth.) The rocket peaks at meters above sea-level.
When there is no wind, a runner is able to run 10 000 m at an average speed of x m/s. When he runs with a tailwind, his average speed increases by 0.05 m/s and it takes him 15 s less to run the 10 000 m. The equation shown below represents this relationship. 10 000 10 000 x+0.05 X = 15, x > 0 6. When there is no wind, find the runner's average speed, to the nearest hundredth of a metre per second.
Plot the following functions y =-1 2x
Q15