Solve the system of normal equations. (I don't want you doing this by hand. Use a calculator or app.) 55.8 97.8 - 45.9 9.9 -.73 Use your answer in problem 4 to state the fourth-degree polynomial of best fit that relates the time (in seconds) to the speed (in miles per hour) of the car. 335 b 1845/189 -6605/144 2135/216 35/48 - - Use calculus to construct a polynomial that gives the acceleration of the car as a function of time.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Help with the last two please

**Problem 4:** Solve the system of normal equations. (I don't want you doing this by hand. Use a calculator or app.)

Given matrix equation:

\[ 
\begin{bmatrix}
335/10 \\
1845/189 \\
-6605/144 \\
2135/210 \\
-35/48
\end{bmatrix}
= X =
\begin{bmatrix}
-55.8 \\
97.8 \\
-45.9 \\
9.9 \\
-.73
\end{bmatrix}
\]

**Problem 5:** Use your answer in problem 4 to state the fourth-degree polynomial of best fit that relates the time (in seconds) to the speed (in miles per hour) of the car.

**Problem 6:** Use calculus to construct a polynomial that gives the acceleration of the car as a function of time.
Transcribed Image Text:**Problem 4:** Solve the system of normal equations. (I don't want you doing this by hand. Use a calculator or app.) Given matrix equation: \[ \begin{bmatrix} 335/10 \\ 1845/189 \\ -6605/144 \\ 2135/210 \\ -35/48 \end{bmatrix} = X = \begin{bmatrix} -55.8 \\ 97.8 \\ -45.9 \\ 9.9 \\ -.73 \end{bmatrix} \] **Problem 5:** Use your answer in problem 4 to state the fourth-degree polynomial of best fit that relates the time (in seconds) to the speed (in miles per hour) of the car. **Problem 6:** Use calculus to construct a polynomial that gives the acceleration of the car as a function of time.
Expert Solution
Step 1

The polynomial of degree 4 can be defined as: P(x)=a+bx+cx2+dx3+ex4. Here, a, b, c, d, e are constant.

The acceleration function is calculated by differentiating the speed with respect to the time.

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