Math Problem Statement
the region in the xy-plane defined by the inequalities x − 3y2 ≥ 0, 2 − x − 5|y| ≥ 0 find its area.
Solution
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Math Problem Analysis
Mathematical Concepts
Inequalities
Quadratic Equations
Absolute Value
Integration
Area under Curves
Formulas
x - 3y^2 ≥ 0 (Parabolic inequality)
2 - x - 5|y| ≥ 0 (Linear inequality with absolute value)
Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
Area formula: ∫[a,b] (f(y) - g(y)) dy
Theorems
Symmetry of regions about the x-axis
Quadratic formula for solving quadratic equations
Integration of curves to find the area between them
Suitable Grade Level
Grades 11-12 (Pre-Calculus/Calculus)
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