# Multi-Step Problem

Here are 4 problems, solve each one, the plug the variables into the master equation to get your answer.

Problem 1:

If \( 2a + b = 10\)

and \( a = 2b\)

Find \( a \) and \( b \)

Problem 2:

\( \ cot (6c) = \frac { \sqrt {3} }{2} \) (In degrees)

Problem 3:

d is the only positive root of the following equation.

\( y = x^{3} - 4.5x^{2} - 11.5x -21 \)

Problem 4:

\( \log _{f} 512 = 9 \)

Master equation:

\( b × \sqrt {a^{c} (\mod d) × f} \)