Question

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\\(g(t) = \

$$\begin{cases} -2t(t + 1) &, \\ t < 6 \\\\ \\dfrac{5t}{6} &, \\ 6 \\leq t \\leq 12 \\\\ 2t^2 + 3t &, \\ t > 12 \\end{cases}$$

\\)
\\(g(12) = \square\\)
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Explanation:

Step1: Determine the applicable function

Since \( t = 12 \), we check the piecewise function's domains. The domain \( 6\leq t\leq12 \) includes \( t = 12 \), so we use the function \( \frac{5t}{6} \).

Step2: Substitute \( t = 12 \) into the function

Substitute \( t = 12 \) into \( \frac{5t}{6} \): \( \frac{5\times12}{6} \)

Step3: Simplify the expression

Simplify \( \frac{5\times12}{6} \). First, \( 5\times12 = 60 \), then \( \frac{60}{6}=10 \).

Answer:

\( 10 \)