Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
First, let's analyze the chart provided:
[tex]\[ \begin{array}{|c|c|} \hline A & B \\ \hline 0 & 0 \\ \hline 4 & 2.5 \\ \hline 8 & 6 \\ \hline 12 & 8 \\ \hline 16 & 10.5 \\ \hline \end{array} \][/tex]
We will start by determining the relationship between columns [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
#### Step 1: Determine the Relationship
To find this, we can calculate the slope between any two points. The slope [tex]\((m)\)[/tex] is given by:
[tex]\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's use the points [tex]\( (0, 0) \)[/tex] and [tex]\( (16, 10.5) \)[/tex].
[tex]\[ m = \frac{10.5 - 0}{16 - 0} = \frac{10.5}{16} = 0.65625 \][/tex]
The slope we obtained is 0.65625. This slope represents the rate of change of [tex]\( B \)[/tex] with respect to [tex]\( A \)[/tex].
#### Step 2: Determine the Y-intercept
Since one of the recorded points is [tex]\( (0, 0) \)[/tex], we can see that the y-intercept [tex]\( (b) \)[/tex] is:
[tex]\[ b = 0 \][/tex]
Thus, the equation of the line is:
[tex]\[ y = 0.65625x + 0 \][/tex]
#### Step 3: Infer the Context Based on Slope and Graph
Given the slope and y-intercept, the relationship suggests a linear change, which is typical in physics for phenomena such as:
- Position as a function of time
- Velocity as a function of time under constant acceleration
#### Step 4: Analyze Possible Titles
The plausible titles for columns need to match the context of a linear relationship where the slope suggests a steady increase over time.
1. Column A should be "Time," and Column B should be "Position.": Time versus position graphs usually exhibit a linear relationship, especially under constant velocity.
2. Column A should be "Position," and Column B should be "Time.": This would imply time changes with position, less intuitive for this data.
3. Column A should be "Velocity," and Column B should be "Speed.": This doesn't align well with the linear relationship and absolute values given.
4. Column A should be "Speed," and Column B should be "Velocity": Similar to above, this doesn't match the provided data context.
Thus, the best fit titles are:
Column A should be "Time," and Column B should be "Position."
This matches well with the slope and intercept obtained, indicating a typical position change over time relationship.
[tex]\[ \begin{array}{|c|c|} \hline A & B \\ \hline 0 & 0 \\ \hline 4 & 2.5 \\ \hline 8 & 6 \\ \hline 12 & 8 \\ \hline 16 & 10.5 \\ \hline \end{array} \][/tex]
We will start by determining the relationship between columns [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
#### Step 1: Determine the Relationship
To find this, we can calculate the slope between any two points. The slope [tex]\((m)\)[/tex] is given by:
[tex]\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Let's use the points [tex]\( (0, 0) \)[/tex] and [tex]\( (16, 10.5) \)[/tex].
[tex]\[ m = \frac{10.5 - 0}{16 - 0} = \frac{10.5}{16} = 0.65625 \][/tex]
The slope we obtained is 0.65625. This slope represents the rate of change of [tex]\( B \)[/tex] with respect to [tex]\( A \)[/tex].
#### Step 2: Determine the Y-intercept
Since one of the recorded points is [tex]\( (0, 0) \)[/tex], we can see that the y-intercept [tex]\( (b) \)[/tex] is:
[tex]\[ b = 0 \][/tex]
Thus, the equation of the line is:
[tex]\[ y = 0.65625x + 0 \][/tex]
#### Step 3: Infer the Context Based on Slope and Graph
Given the slope and y-intercept, the relationship suggests a linear change, which is typical in physics for phenomena such as:
- Position as a function of time
- Velocity as a function of time under constant acceleration
#### Step 4: Analyze Possible Titles
The plausible titles for columns need to match the context of a linear relationship where the slope suggests a steady increase over time.
1. Column A should be "Time," and Column B should be "Position.": Time versus position graphs usually exhibit a linear relationship, especially under constant velocity.
2. Column A should be "Position," and Column B should be "Time.": This would imply time changes with position, less intuitive for this data.
3. Column A should be "Velocity," and Column B should be "Speed.": This doesn't align well with the linear relationship and absolute values given.
4. Column A should be "Speed," and Column B should be "Velocity": Similar to above, this doesn't match the provided data context.
Thus, the best fit titles are:
Column A should be "Time," and Column B should be "Position."
This matches well with the slope and intercept obtained, indicating a typical position change over time relationship.
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.
