Questions: Consider the parametric equations (x=sqrtt) and (y=5-t). (a) Create a table of (x) - and (y)-values using (t=0,1,2,3), and 4 . (t) 0 1 2 3 4 (x) (square) (square) (square) (square) (square) (y) (square) (square) (square) (square) (square)

Consider the parametric equations (x=sqrtt) and (y=5-t).
(a) Create a table of (x) - and (y)-values using (t=0,1,2,3), and 4 .
(t)  0    1  2  3  4
(x)       (square)        (square)  (square)  (square)  (square)
(y)       (square)        (square)  (square)  (square)  (square)
Transcript text: Consider the parametric equations $x=\sqrt{t}$ and $y=5-t$. (a) Create a table of $x$ - and $y$-values using $t=0,1,2,3$, and 4 . \begin{tabular}{|c|c|c|c|c|c|} \hline$t$ & 0 & & 1 & 2 & 3 \\ \hline$x$ & $\square$ & & & & 4 \\ \hline$y$ & $\square$ & $\square$ & & $\square$ & $\square$ \\ \hline & $\square$ & $\square$ & $\square$ & $\square$ \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Substitute \( t = 0 \) into the parametric equations

For \( t = 0 \):

  • \( x = \sqrt{0} = 0 \)
  • \( y = 5 - 0 = 5 \)
Step 2: Substitute \( t = 1 \) into the parametric equations

For \( t = 1 \):

  • \( x = \sqrt{1} = 1 \)
  • \( y = 5 - 1 = 4 \)
Step 3: Substitute \( t = 2 \) into the parametric equations

For \( t = 2 \):

  • \( x = \sqrt{2} \approx 1.414 \)
  • \( y = 5 - 2 = 3 \)

Final Answer

\[ \begin{array}{|c|c|c|} \hline t & x & y \\ \hline 0 & 0 & 5 \\ 1 & 1 & 4 \\ 2 & \sqrt{2} & 3 \\ 3 & \sqrt{3} & 2 \\ 4 & 2 & 1 \\ \hline \end{array} \]

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