The temperature \(T\) (in °C) in a greenhouse follows the pattern:
\begin{align*}
T(h)= \begin{cases}10+2 h, & \text {for }\ 0 \leqslant h<6 \\ 22, & \text {for }\ 6 \leqslant h \leqslant 18 \\ 58-2 h, & \text {for }\ 18<h \leqslant 24\end{cases}
\end{align*}
where \(h\) is the number of hours after midnight.
- Sketch the graph of \(T(h)\) for \(0 \leqslant h \leqslant 24\) (2 marks)
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- At what time(s) during the day is the temperature exactly 18 °C? (2 marks)
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Show Answers Only
a.
b. \(\text{Temperature is 18° at 4 am and 8 pm.}\)
Show Worked Solution
a.
b. \(\text{Temperature}=18^{\circ} \ \text{twice (see graph)}\)
\(10+2 h=18 \ \Rightarrow \ h=4\)
\(58-2 h=18 \ \Rightarrow \ h=20\)
\(\therefore \ \text{Temperature is 18° at 4 am and 8 pm.}\)