Math Problem Statement
a dam has the shape of an isoceles trapexoid with a height of 50 m the width at the top is 80 and the width at the bottom is 50. The surface of the water is 8 m below the top of the dam. find the force on the dam due to the hydostratic pressure
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Hydrostatic Pressure
Geometry of Trapezoids
Formulas
Pressure formula: P(y) = ρgy
Width of trapezoid as a function of depth: w(y) = 50 + (3/5)y
Hydrostatic force: F = ∫_0^42 P(y) * w(y) dy
Theorems
Integration of polynomial functions
Hydrostatic pressure theory
Suitable Grade Level
Grades 11-12 or College
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