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Sagot :
To solve this problem, we need to evaluate the elevation [tex]\(e\)[/tex] using the given equation [tex]\(e = 300 - 10t\)[/tex] for the specified time points [tex]\(t = -2\)[/tex], [tex]\(t = 3.5\)[/tex], and [tex]\(t = 30\)[/tex].
1. Calculate [tex]\( e \)[/tex] when [tex]\( t = -2 \)[/tex]:
- Substitute [tex]\( t = -2 \)[/tex] into the equation [tex]\(e = 300 - 10t\)[/tex]:
[tex]\[ e = 300 - 10(-2) \][/tex]
- Simplify the expression:
[tex]\[ e = 300 + 20 \][/tex]
- Thus, the elevation [tex]\(e\)[/tex] when [tex]\( t = -2 \)[/tex] is:
[tex]\[ e = 320 \][/tex]
2. Calculate [tex]\( e \)[/tex] when [tex]\( t = 3.5 \)[/tex]:
- Substitute [tex]\( t = 3.5 \)[/tex] into the equation [tex]\(e = 300 - 10t\)[/tex]:
[tex]\[ e = 300 - 10(3.5) \][/tex]
- Simplify the expression:
[tex]\[ e = 300 - 35 \][/tex]
- Thus, the elevation [tex]\(e\)[/tex] when [tex]\( t = 3.5 \)[/tex] is:
[tex]\[ e = 265.0 \][/tex]
3. Calculate [tex]\( e \)[/tex] when [tex]\( t = 30 \)[/tex]:
- Substitute [tex]\( t = 30 \)[/tex] into the equation [tex]\(e = 300 - 10t\)[/tex]:
[tex]\[ e = 300 - 10(30) \][/tex]
- Simplify the expression:
[tex]\[ e = 300 - 300 \][/tex]
- Thus, the elevation [tex]\(e\)[/tex] when [tex]\( t = 30 \)[/tex] is:
[tex]\[ e = 0 \][/tex]
Now, we populate the table with the calculated values:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time } (t) & \text{Elevation } (e) \\ \hline -2 & 320 \\ \hline 3.5 & 265.0 \\ \hline 30 & 0 \\ \hline \end{array} \][/tex]
Thus, the values in the table are:
[tex]\[ a = 320 \checkmark \\ b = 265.0 \checkmark \\ c = 0 \][/tex]
1. Calculate [tex]\( e \)[/tex] when [tex]\( t = -2 \)[/tex]:
- Substitute [tex]\( t = -2 \)[/tex] into the equation [tex]\(e = 300 - 10t\)[/tex]:
[tex]\[ e = 300 - 10(-2) \][/tex]
- Simplify the expression:
[tex]\[ e = 300 + 20 \][/tex]
- Thus, the elevation [tex]\(e\)[/tex] when [tex]\( t = -2 \)[/tex] is:
[tex]\[ e = 320 \][/tex]
2. Calculate [tex]\( e \)[/tex] when [tex]\( t = 3.5 \)[/tex]:
- Substitute [tex]\( t = 3.5 \)[/tex] into the equation [tex]\(e = 300 - 10t\)[/tex]:
[tex]\[ e = 300 - 10(3.5) \][/tex]
- Simplify the expression:
[tex]\[ e = 300 - 35 \][/tex]
- Thus, the elevation [tex]\(e\)[/tex] when [tex]\( t = 3.5 \)[/tex] is:
[tex]\[ e = 265.0 \][/tex]
3. Calculate [tex]\( e \)[/tex] when [tex]\( t = 30 \)[/tex]:
- Substitute [tex]\( t = 30 \)[/tex] into the equation [tex]\(e = 300 - 10t\)[/tex]:
[tex]\[ e = 300 - 10(30) \][/tex]
- Simplify the expression:
[tex]\[ e = 300 - 300 \][/tex]
- Thus, the elevation [tex]\(e\)[/tex] when [tex]\( t = 30 \)[/tex] is:
[tex]\[ e = 0 \][/tex]
Now, we populate the table with the calculated values:
[tex]\[ \begin{array}{|c|c|} \hline \text{Time } (t) & \text{Elevation } (e) \\ \hline -2 & 320 \\ \hline 3.5 & 265.0 \\ \hline 30 & 0 \\ \hline \end{array} \][/tex]
Thus, the values in the table are:
[tex]\[ a = 320 \checkmark \\ b = 265.0 \checkmark \\ c = 0 \][/tex]
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