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 $b$

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Problem 2:

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

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Problem 3:

d is the only positive root of the following equation.

$y = x^{3} - 4.5x^{2} - 11.5x -21$

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Problem 4:

$\log _{f} 512 = 9$

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Master equation:

$b × \sqrt {a^{c} (\mod d) × f}$