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Mathematic Methods HW Solutions 48

# Mathematic Methods HW Solutions 48 - Chapter 9 6.1 6.4...

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Chapter 9 48 6.1 catenary 6.2 circle 6.3 circular cylinder 6.4 catenary 6.5 circle 6.6 circle 8.2 I = integraldisplay x 2 y prime 2 radicalbig 1 + y prime 2 dx , x 2 (2 y prime + y prime 3 ) = K (1 + y prime 2 ) 3 / 2 8.3 I = integraldisplay ydy radicalbig x prime 2 + 1 , x prime 2 y 2 = C 2 (1 + x prime 2 ) 3 8.4 I = integraldisplay radicalbig r 2 + r 4 θ prime 2 dr , dr = Kr r 4 - K 2 8.5 y = ae bx 8.6 ( x - a ) 2 + ( y + 1) 2 = C 2 8.7 ( y - b ) 2 = 4 a 2 ( x + 1 - a 2 ) 8.8 Intersection of r = 1 + cos θ with z = a + b sin( θ/ 2) 8.9 Intersection of the cone with r cos( θ sin α + C ) = K 8.10 Intersection of y = x 2 with az = b [2 x 4 x 2 + 1 + sinh - 1 2 x ] + c 8.11 r = K sec 2 θ + c 2 8.12 e y cos( x - a ) = K 8.13 ( x + 3 2 ) 2 + ( y - b ) 2 = c 2 8.14 ( x - a ) 2 = 4 K 2 ( y + 2 - K 2 ) 8.15 y + c = 3 2 K bracketleftBig x 1 / 3 x 2 / 3 - K 2 + K 2 cosh - 1 ( x 1 / 3 /K ) bracketrightBig 8.16 Hyperbola: r 2 cos(2 θ + α ) = K or ( x 2 - y 2 ) cos α - 2 xy sin α = K 8.17 K ln r = cosh( + C ) 8.18 Parabola: ( x - y - C ) 2 = 4 K 2 ( x + y - K 2 ) 8.19 m r - r ˙ θ 2 ) + kr = 0, r 2 ˙ θ = const. 8.20 m r - r ˙ θ 2 ) + K/r 2 = 0,
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