This problem set deals with the problem of non-constant acceleration. Two researchers from Fly By Night Industries conduct an experiment with a sports car on a test track. While one is driving the car, the other will look at the speedometer and record the speed of the car at one- second intervals. Now, these aren't official researchers and this isn't an official test track, so the speeds are in miles per hour using an analog speedometer. The data set they create is: {(1,5), (2, z), (3, 30), (4, 50), (5, 65), (6,70)} Z=25 They notice that the acceleration is not a constant value. They decide that a fourth-degree polynomial will be the best to describe the speed of the car as a function of time. The task here is to determine the fourth-degree polynomial that fits this data set the best. Exercises 1. Use a general fourth-degree polynomial and Fly By Night's data to construct six equations. Note that the equations are linear in the coefficients. Write the equations here: 2. Construct the least-squares problem Ax = b. A = 3. Construct the system of normal equations AT Ax = A¹b. ATA = b = ATB =
This problem set deals with the problem of non-constant acceleration. Two researchers from Fly By Night Industries conduct an experiment with a sports car on a test track. While one is driving the car, the other will look at the speedometer and record the speed of the car at one- second intervals. Now, these aren't official researchers and this isn't an official test track, so the speeds are in miles per hour using an analog speedometer. The data set they create is: {(1,5), (2, z), (3, 30), (4, 50), (5, 65), (6,70)} Z=25 They notice that the acceleration is not a constant value. They decide that a fourth-degree polynomial will be the best to describe the speed of the car as a function of time. The task here is to determine the fourth-degree polynomial that fits this data set the best. Exercises 1. Use a general fourth-degree polynomial and Fly By Night's data to construct six equations. Note that the equations are linear in the coefficients. Write the equations here: 2. Construct the least-squares problem Ax = b. A = 3. Construct the system of normal equations AT Ax = A¹b. ATA = b = ATB =
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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PLEASE: Can you write out the answers. Typing it out doesn't make sense all together
![This problem set deals with the problem of non-constant acceleration. Two researchers from Fly By Night Industries conduct an experiment with a sports car on a test track. While one is driving the car, the other will look at the speedometer and record the speed of the car at one-second intervals. Now, these aren’t official researchers and this isn’t an official test track, so the speeds are in miles per hour using an analog speedometer. The data set they create is:
\[
\{(1, 5), (2, z), (3, 30), (4, 50), (5, 65), (6, 70)\}
\]
\( z = 25 \)
They notice that the acceleration is not a constant value. They decide that a fourth-degree polynomial will be the best to describe the speed of the car as a function of time.
The task here is to determine the fourth-degree polynomial that fits this data set the best.
**Exercises**
1. Use a general fourth-degree polynomial and Fly By Night’s data to construct six equations. Note that the equations are linear in the coefficients. Write the equations here:
\[
\text{A (matrix to be filled)}
\]
2. Construct the least-squares problem \( \mathbf{A\vec{x}} = \vec{b} \).
\[
A =
\]
\[
\vec{b} =
\]
3. Construct the system of normal equations \( A^T A \vec{x} = A^T \vec{b} \).
\[
A^T A =
\]
\[
A^T \vec{b} =
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b8a4ad9-b66e-4dbe-8b3f-39bf0adb3cae%2F723bb7f6-8080-42e5-8472-425889ec49a8%2Frecrk3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:This problem set deals with the problem of non-constant acceleration. Two researchers from Fly By Night Industries conduct an experiment with a sports car on a test track. While one is driving the car, the other will look at the speedometer and record the speed of the car at one-second intervals. Now, these aren’t official researchers and this isn’t an official test track, so the speeds are in miles per hour using an analog speedometer. The data set they create is:
\[
\{(1, 5), (2, z), (3, 30), (4, 50), (5, 65), (6, 70)\}
\]
\( z = 25 \)
They notice that the acceleration is not a constant value. They decide that a fourth-degree polynomial will be the best to describe the speed of the car as a function of time.
The task here is to determine the fourth-degree polynomial that fits this data set the best.
**Exercises**
1. Use a general fourth-degree polynomial and Fly By Night’s data to construct six equations. Note that the equations are linear in the coefficients. Write the equations here:
\[
\text{A (matrix to be filled)}
\]
2. Construct the least-squares problem \( \mathbf{A\vec{x}} = \vec{b} \).
\[
A =
\]
\[
\vec{b} =
\]
3. Construct the system of normal equations \( A^T A \vec{x} = A^T \vec{b} \).
\[
A^T A =
\]
\[
A^T \vec{b} =
\]
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