The cost of manufacturing $x$ clocks is given by $C(x)=44+37 x-x^{2}$. Also, it is known that in $t$ hours the number of clocks that can be produced is given by $x=6 t$, where $1 \leq t \leq 12$. Express $C$ as a function of $\mathrm{t}$
Answer
Final Answer: The cost function $C$ as a function of $t$ is \(\boxed{-36t^{2} + 222t + 44}\).
Step 1 ：The cost of manufacturing $x$ clocks is given by $C(x)=44+37 x-x^{2}$.
Step 2 ：The number of clocks that can be produced in $t$ hours is given by $x=6 t$, where $1 \leq t \leq 12$.
Step 3 ：We are asked to express the cost function $C(x)$ in terms of $t$.
Step 4 ：We can substitute $x$ in the cost function with $6t$ to get the cost function in terms of $t$.
Step 5 ：So, $C(t) = 44+37(6t)-(6t)^{2}$.
Step 6 ：Simplifying this, we get $C(t) = -36t^{2} + 222t + 44$.
Step 7 ：Final Answer: The cost function $C$ as a function of $t$ is \(\boxed{-36t^{2} + 222t + 44}\).
