**with equations** 𝑥= 𝑡/2 and 𝑦= −√𝑡+5, 0 ≤𝑡 ≤8,  

create a table with 4 columns, list: t from 0 to 8, x, y, and (x,y) 




Here is the table with the values of \( t \), \( x \), \( y \), and the corresponding pairs \( (x, y) \):

\[
\begin{array}{|c|c|c|c|}
\hline
t & x & y & (x, y) \\
\hline
0 & 0.0 & 5.000 & (0.0, 5.0) \\
1 & 0.5 & 4.000 & (0.5, 4.0) \\
2 & 1.0 & 3.586 & (1.0, 3.5858) \\
3 & 1.5 & 3.268 & (1.5, 3.2679) \\
4 & 2.0 & 3.000 & (2.0, 3.0) \\
5 & 2.5 & 2.764 & (2.5, 2.7639) \\
6 & 3.0 & 2.551 & (3.0, 2.5505) \\
7 & 3.5 & 2.354 & (3.5, 2.3542) \\
8 & 4.0 & 2.172 & (4.0, 2.1716) \\
\hline
\end{array}
\]

Would you like any further details or explanations?

Here are some related questions you might consider:
1. How do these values change if we adjust the range of \( t \)?
2. What is the behavior of \( y \) as \( t \) approaches 0 and 8?
3. Can you plot the graph of \( (x, y) \)?
4. How can you calculate the rate of change of \( x \) and \( y \) with respect to \( t \)?
5. What is the physical meaning if these were time-based equations?

**Tip:** When working with square root functions like \( y = -\sqrt{t} + 5 \), remember that the domain of \( t \) must ensure the value inside the square root is non-negative.

With equations x = t/2 and y = -√t + 5, 0 ≤ t ≤ 8, create a table with 4 columns, list: t from 0 to 8, x, y, and (x, y).

Learn how to create a table listing values for t from 0 to 8, with corresponding x and y values using the parametric equations x = t/2 and y = -√t + 5. This problem covers key algebraic concepts, including square root functions and their domains, suitable for Grades 9-11.

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