1.) To determine the appropriate function representation for the beach area in terms of the ocean's distance, we identify how the functions relate to each other. The beach area \( A \) is a function of the ocean's distance \( d \). Therefore, we want to use the function \( A(d(x)) \), which indicates that we are first calculating \( d(x) \) and then using that distance in the area function.
Hence, the correct option is: a. A*d=A(d(x))
2.) To find the area of the beach after \( x = 2 \) hours, we first need to compute \( d(2) \) using the equation for the ocean's distance:
\[ d(x) = -2^2 + 12x + 10 \]
Substituting \( x = 2 \):
\[ d(2) = -2(2)^2 + 12(2) + 10 \] \[ d(2) = -2(4) + 24 + 10 \] \[ d(2) = -8 + 24 + 10 \] \[ d(2) = 26 \]
Now that we have \( d(2) = 26 \), we can find the area of the beach \( A(26) \):
\[ A(d(2)) = A(26) = 200 \cdot 26 \] \[ A(26) = 5200 \]
Thus, the area of the beach after 2 hours is \( \boxed{5200} \) square units.