A solid rectangular block has a square base. Find its maximum youme and the sides if the sum of its height and any one side of the base is 12 cm .

Use generating functions to solve the recurrence relation \( a_{n}-2 a_{n-1}-3 a_{n-2}=0, n \geq 2 \) wisth \( a_{0}=3, a_{1}=1 \).

Find the range os the function: \( y=x^{2}-3 x \)

What is the range of the inverse function for the function \( f(x) = \sqrt{x - 4} + 1 \)?

The population of a certain species in a protected area can be modeled by the function \( P(t) = 200 + 50 \sin(t) \), where \( t \) is measured in years. Determine the total population increase over one complete cycle (from \( t=0 \) to \( t=2\pi \)).

Question 5: (August 2023 ) The function \( G(m) \) represents the amount of gasoline consumed by a car traveling \( m \) miles. An appropriate domain for this function