he time in seconds after it is thro .5 1 1.5 2 25 82.2 92.625 100.6 106 lator to do a quadratic regression nds that have passed since the obj ers to 1 decimal place.
he time in seconds after it is thro .5 1 1.5 2 25 82.2 92.625 100.6 106 lator to do a quadratic regression nds that have passed since the obj ers to 1 decimal place.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
![### Quadratic Regression Analysis of an Object in Free Fall
#### Given Data:
The table below shows the height, \( h \), in meters, of an object that is thrown off the top of a building as a function of \( t \), the time in seconds after it is thrown.
| \( t \) (seconds) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
|-------------------|--------|------|------|------|--------|-------|
| \( h(t) \) (meters) | 69.325 | 82.2 | 92.625 | 100.6 | 106.125 | 109.2 |
#### Instructions:
Using your calculator to do a quadratic regression, express the height of the object as a function of the number of seconds that have passed since the object was thrown.
***Round all numbers to 1 decimal place.***
#### Problem-Solving:
1. **Using your quadratic regression, how high will the object be 2.8 seconds after it is thrown?**
- *Round to 3 decimal places.*
- Answer in:
- [ ] meters
- [ ] seconds
2. **Using your quadratic regression, how long will it take the object to reach 24 meters?**
- *Round to 3 decimal places.*
- Answer in:
- [ ] meters
- [ ] seconds
### Explanation of Concepts:
- **Quadratic Regression:** This is a process of finding the equation of the parabola that best fits a set of data points. It is generally used in scenarios where the relationship between a dependent variable \( y \) and an independent variable \( x \) is parabolic.
### Graphs and Diagrams:
In this task, you will use a quadratic regression calculator tool to find the quadratic equation in the form:
\[ h(t) = at^2 + bt + c \]
Where:
- \( h(t) \) is the height in meters.
- \( t \) is the time in seconds.
- \( a \), \( b \), and \( c \) are coefficients determined through regression analysis.
Once you have the equation, you can substitute \( t = 2.8 \) to find the height at 2.8 seconds and solve for \( t \) when \( h(t)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbadf131f-ca26-4f8e-953f-35e945c24016%2F11c8e8b3-944f-4c09-81f4-7efcef2c7dab%2Fu3a1kvd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Quadratic Regression Analysis of an Object in Free Fall
#### Given Data:
The table below shows the height, \( h \), in meters, of an object that is thrown off the top of a building as a function of \( t \), the time in seconds after it is thrown.
| \( t \) (seconds) | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 |
|-------------------|--------|------|------|------|--------|-------|
| \( h(t) \) (meters) | 69.325 | 82.2 | 92.625 | 100.6 | 106.125 | 109.2 |
#### Instructions:
Using your calculator to do a quadratic regression, express the height of the object as a function of the number of seconds that have passed since the object was thrown.
***Round all numbers to 1 decimal place.***
#### Problem-Solving:
1. **Using your quadratic regression, how high will the object be 2.8 seconds after it is thrown?**
- *Round to 3 decimal places.*
- Answer in:
- [ ] meters
- [ ] seconds
2. **Using your quadratic regression, how long will it take the object to reach 24 meters?**
- *Round to 3 decimal places.*
- Answer in:
- [ ] meters
- [ ] seconds
### Explanation of Concepts:
- **Quadratic Regression:** This is a process of finding the equation of the parabola that best fits a set of data points. It is generally used in scenarios where the relationship between a dependent variable \( y \) and an independent variable \( x \) is parabolic.
### Graphs and Diagrams:
In this task, you will use a quadratic regression calculator tool to find the quadratic equation in the form:
\[ h(t) = at^2 + bt + c \]
Where:
- \( h(t) \) is the height in meters.
- \( t \) is the time in seconds.
- \( a \), \( b \), and \( c \) are coefficients determined through regression analysis.
Once you have the equation, you can substitute \( t = 2.8 \) to find the height at 2.8 seconds and solve for \( t \) when \( h(t)
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