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## Polynomial Inequalities

When does revenue exceed cost? When will one race car pass another? Model these values with polynomials and use polynomial inequalities to solve questions like these and more.

# Problem Solving

If $$x+y=20$$, what is the maximum value of $$2xy$$?

A rectangular wall for a chicken coop is to be made out of a $$44 \mbox{ m}$$ wire mesh. Let $$x$$ be the shorter side of the rectangle in meters. If the area of the rectangle, $$A$$, is $$120 \mbox{ m}^2 < A < 121 \mbox{ m}^2$$, then $$x$$ must satisfy $$a < x < b$$. What is the value of $$a+b$$?

If $$x$$ and $$y$$ are positive numbers, what is the minimum value of $$(3x + 4y)\left(\frac{27}{x} + \frac{4}{y} \right)$$?

Which is larger?

Hint: Let $$x = 2 ^ {2015}$$.

What is the maximum value of $$x$$ that satisfies the inequality $$(x - 6)(x^2 - 4x + 9) \leq 0$$?

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