Webb) The volume of a right circular cone is given by: V = (1/3)πr^2h Substituting the expression for r from part (i) and the expression for h from part (ii), we get: V = (1/3)π(a cos(θ))^2 (a sin(θ)) Simplifying, we get: V = (1/3)πa^3 cos^2(θ) sin(θ) Using the identity sin(2θ) = 2sin(θ)cos(θ), we can rewrite this as: V = (1/6)πa^3 sin(2θ) cos(θ) Using the … WebAnswer (1 of 2): The point of intersection is the (r,theta) combination that satisfies both equations. To find \theta, we can set the two “r” values equal to each other. sin 2\theta = …
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WebExample 2 Find the area bounded by the lemniscate of Bernoulli r2 = a2 cos 2θ. Solution [collapse collapsed] The curve is symmetrical with respect to the origin, and occurs only with values of θ from -45° to 45° (-¼ π to ¼ π). WebCos 2θ sinθ r2 cosθ. 1 r. Cos 2θ sinθ sin 2θ cosθ 1 r. The polar curves r 1 sin2θ and r sin2θ 1 have the same graph 6. The equations r 2, x2 y2 4, and rt 2 sin3t, 2 cos3t 0 t. Rsin … dcr.wv gov
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WebCalculus. Calculus questions and answers. Find the area of the region that lies inside both curves. r2 = 2 sin (2θ), r = 1. WebApr 13, 2024 · 48 南昌大学学报( 工科版) 2024 年 严重ꎬ出现平行于节点核心区主裂缝的次裂缝ꎬ主裂 缝最大宽度为 12 mmꎬ试验终止ꎮ 整个试验过程ꎬ梁 端钢筋均未达到屈服状态ꎮ 试件 CJ 现浇节点的最 终破坏模态ꎬ如图 7 所示ꎮ ( a) 试件 SPJ-1 最终破坏形态 ( b) 试件 SPJ-2 最终破坏形态 ( c) 试件 SPJ-3 最终破坏... Web1 1 3 3 a 2 ⋅ θ + 2 sin θ + sin 2θ = π a 2 = 2 4 2 2 0 则所求的最短距离 d = 2 2 2 6、 计算 ∫∫∫ ( y + z ) dv , 其中 Ω 是由 xoz 面曲线 z = 2 x 绕 x 轴旋转所得旋转体与平面 x = 2, x = 5 Ω bc addendum