# Augmented matrices word problem - tiny issue

• IrinaK.
In summary: Let's say "x" for the number of hours after 9 PM, so we have x1=0, x2=3, x3=6. In this case, the coldest temperature of the night was 50F and it occurred at x=3 hours after 9 PM. In summary, the problem from Stitz-Zeager Pre-calculus book asks for a quadratic function to be fitted to temperature data collected at 9 PM, midnight, and 6 AM. The temperature, T, is the dependent variable and the number of hours after 9 PM, t, is the independent variable. By using the technique in Example 8.2.3, the coldest temperature of the night was found
IrinaK.

## Homework Statement

Hello!
Here is the problem from Stitz-Zeager Pre-calculus book:

At 9 PM, the temperature was 60F; at midnight, the temperature was 50F; and at 6 AM,

the temperature was 70F . Use the technique in Example 8.2.3 to t a quadratic function

to these data with the temperature, T, measured in degrees Fahrenheit, as the dependent

variable, and the number of hours after 9 PM, t, measured in hours, as the independent

variable. What was the coldest temperature of the night? When did it occur?

2. Homework Equations

## The Attempt at a Solution

[/B]
My question is about the number of hours as undependable variable:

do you think authors mean x1=9, x2=3, x3=9 by saying "the number of hours after 9PM"? Or do you think it should be x1=9, x2=0, x3=6, or x1=9, x2=12, x3=6?
I am confused :)

Thank you!

IrinaK. said:

## Homework Statement

Hello!
Here is the problem from Stitz-Zeager Pre-calculus book:

At 9 PM, the temperature was 60F; at midnight, the temperature was 50F; and at 6 AM,

the temperature was 70F . Use the technique in Example 8.2.3 to t a quadratic function

to these data with the temperature, T, measured in degrees Fahrenheit, as the dependent

variable, and the number of hours after 9 PM, t, measured in hours, as the independent

variable. What was the coldest temperature of the night? When did it occur?

2. Homework Equations

## The Attempt at a Solution

[/B]
My question is about the number of hours as undependable variable:

do you think authors mean x1=9, x2=3, x3=9 by saying "the number of hours after 9PM"? Or do you think it should be x1=9, x2=0, x3=6, or x1=9, x2=12, x3=6?
I am confused :)

Thank you!

FWIW, 'undependable variable' = independent variable, in English. 'undependable' also means 'unreliable'.

I'm afraid the wording of the problem is rather clear: the times are supposed to be taken as hours after 9 pm. You seem to want to impose your own time scale on the problem, using midnight as the origin of the time axis. So, for the reading taken at 9 pm, t = 0 hours, and the for reading taken at midnight, t = 3 hours. Eazy, peazy.

SteamKing said:
FWIW, 'undependable variable' = independent variable, in English. 'undependable' also means 'unreliable'.

I'm afraid the wording of the problem is rather clear: the times are supposed to be taken as hours after 9 pm. You seem to want to impose your own time scale on the problem, using midnight as the origin of the time axis. So, for the reading taken at 9 pm, t = 0 hours, and the for reading taken at midnight, t = 3 hours. Eazy, peazy.

Right! :) Thank you, SteamKing! And sorry for the typo - I can't find the way to edit that now; of course, it is "independent".

## 1. What is an augmented matrix?

An augmented matrix is a representation of a system of linear equations in matrix form, where the coefficients and constants are arranged in a rectangular array with a vertical line separating the coefficient matrix and the constant matrix.

## 2. How are augmented matrices used to solve word problems?

Augmented matrices are used to organize and solve systems of linear equations in real-world situations or word problems. They allow us to easily manipulate and solve for the variables in the equations.

## 3. Can you provide an example of solving a word problem using augmented matrices?

Sure, let's say we have a word problem that involves the cost of tickets to a concert. We know that 2 adults and 3 children's tickets cost $150, and 3 adults and 2 children's tickets cost$180. We can set up the system of equations as follows:2x + 3y = 1503x + 2y = 180We can then create the augmented matrix [2 3 | 150; 3 2 | 180] and use row operations to solve for x and y.

## 4. What is the significance of the vertical line in an augmented matrix?

The vertical line in an augmented matrix separates the coefficient matrix (the left side) from the constant matrix (the right side). This allows us to easily keep track of the coefficients and constants as we manipulate the matrix to solve for the variables.

## 5. Are augmented matrices only used for word problems?

No, augmented matrices are also used in other areas of mathematics and science, such as computer graphics, quantum mechanics, and optimization problems. They provide a convenient way to represent and solve systems of linear equations in many different contexts.

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