) \( \frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\frac{1}{3 \cdot 4}+\ldots+\frac{1}{99 \cdot 100} \)

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 \( t=2\pi \)).

UESTION 3 he equation of a hyperbola is given by \( f(x)=\frac{3}{x-7}-4 \). Srite down the equation of the new function that is formed when \( f \) is transformed as follows: \( 1 \quad \) Shift two units to the left \( 2 \quad \) Shift 3 units up

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 \( t=2\pi \)).

UESTION 4 ketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \cdot 2^{x-1}+1 \). learly indicate all intercepts with the axes, turning point(s) and asymptote(s).

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 .