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formula_sheet

formula_sheet - x= xi Ai Ai y= yi Ai Ai I = I c d 2 A Table...

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1. Rectangle 6. Circle 2. Right Triangle 7. Hollow Circle 3. Triangle 8. Parabola 4. Trapezoid 9. Parabolic Spandrel 5. Semicircle 10. General Spandrel C b h x x x y y y b h C x x x y y y b h C x x x y y y a b h C x y a C x x y, y y r d C x y r d D C r x y R Zero slope h C x b x x - y y y - b h y - C x x x - y y Zero slope b h y - C x x x - y y Zero slope A bh y h I bh x b I hb I bh I hb x y x y = = = = = = = 2 12 2 12 3 3 3 3 3 3 A bh y h I bh x b I hb I bh I hb x y x y = = = = = = = 2 3 36 3 36 12 12 3 3 3 3 A bh y h I bh x a b I bh a ab b I b x y x = = = = + = + ( ) = 2 3 36 3 36 3 2 2 ( ) h 3 12 A a b h y a b a b h I h a b a ab b x = + = + + ( ) = + + + ( ) ( ) ( ) 2 1 3 2 36 4 3 2 2 A r y r I r I I r x x y = = = ( ) = = π π π π π 2 4 4 2 4 3 8 8 9 8 A r d I I r d x y = = = = = π π π π 2 2 4 4 4 4 64 A R r D d I I R r D d x y = ( ) = ( ) = = ( ) = ( ) π π π π 2 2 2 2 4 4 4 4 4 4 64 ′ = = = = y h b x A bh x b y h 2 2 2 3 3 8 3 5 ′ = = = = y h b x A bh x b y h 2 2 3 3 4 3 10 ′ = = + = + + = + + y h b x A bh n x n n b

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formula_sheet - x= xi Ai Ai y= yi Ai Ai I = I c d 2 A Table...

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