10)
\[
\begin{array}{l}
g(t)=t-4 \\
h(t)=t-5 \\
\text { Find }(g \cdot h)(t)
\end{array}
\]

Answer

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Answer

Final Answer: \(\boxed{t^2-9t+20}\)

Steps

Step 1 ：Find the product of the functions \(h\) and \(g\) at \(t\).

Step 2 ：For \(g(t)\), substitute \(t\) into the function \(g(t)=t-4\) to get \(g(t)=t-4\).

Step 3 ：For \(h(t)\), substitute \(t\) into the function \(h(t)=t-5\) to get \(h(t)=t-5\).

Step 4 ：The product of the functions \(h\) and \(g\) evaluated at \(t\) is \((g \cdot h)(t)=g(t)*h(t)=(t-4)*(t-5)=t^2-9t+20\).

Step 5 ：So, \((g \cdot h)(t)=t^2-9t+20\).

Step 6 ：Final Answer: \(\boxed{t^2-9t+20}\)