Write the equation for question 9 showing all your work. This image contains a data table with two columns labeled "x" and "y". Below is the transcribed content:| x | y ||----|----|| -2 | 14 || -1 | -1 || 0 | -6 || 1 | -1 || 2 | 14 || 3 | 39 |The table shows pairs of values where the variable "x" is an integer, and the corresponding "y" value varies across the row. This table could be used to observe the relationship between "x" and "y" for educational purposes, such as interpreting data trends or exploring mathematical functions.

The equation is y=a+bx+cx2 and the normal equations…

Answered: X -2 -1 TOHN 3 0 1 2 y 14 -1 -6 -1 14…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Write the equation for question 9 showing all your work.

This image contains a data table with two columns labeled "x" and "y". Below is the transcribed content:

| x | y |
|----|----|
| -2 | 14 |
| -1 | -1 |
| 0 | -6 |
| 1 | -1 |
| 2 | 14 |
| 3 | 39 |

The table shows pairs of values where the variable "x" is an integer, and the corresponding "y" value varies across the row. This table could be used to observe the relationship between "x" and "y" for educational purposes, such as interpreting data trends or exploring mathematical functions.

Expert Solution

Step 1

The equation is y=a+bx+cx² and the normal equations are

∑y=an+b∑x+c∑x²

∑xy=a∑x+b∑x²+c∑x³

∑x²y=a∑x²+b∑x³+c∑x⁴

The values are calculated using the following table

x	y	x²	x³	x⁴	x⋅y	x²⋅y
-2	14	4	-8	16	-28	56
-1	-1	1	-1	1	1	-1
0	-6	0	0	0	0	0
1	-1	1	1	1	-1	-1
2	14	4	8	16	28	56
3	39	9	27	81	117	351
---	---	---	---	---	---	---
∑x=3	∑y=59	∑x²=19	∑x³=27	∑x⁴=115	∑x⋅y=117	∑x²⋅y=461

Substituting these values in the normal equations
6a+3b+19c=59

3a+19b+27c=117

19a+27b+115c=461

Solving these 3 equations,
Total Equations are 3

6a+3b+19c=59→(1)

3a+19b+27c=117→(2)

19a+27b+115c=461→(3)