Find the equation of the sphere which passes through (1,5,-3),(-3,0,0) which center on the 3x+y+z=0,x+2y +1 = 0.
Find the equation of the sphere which passes through (1,5,-3),(-3,0,0) which center on the 3x+y+z=0,x+2y +1 = 0.
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已知 ABCD 是边长为 1 的正方形, 绕其中一条轴 AB 旋转成一个圆柱.(1) 求该圆柱的表面积;(2) 将 DC 旋转 90° 至 C1D1, 求线 C1D 与平面 ABCD 的夹角.
在xOy平面上,四边形ABCD的四个顶点坐标依次为(0,0),(1,0),(2,1)及(0,3).求这个四边形绕x轴旋转一周所得到的几何体的体积.
Find the sum of n terms of the series whose nth term is 3(4n+4n²)-5n³.
Find the general term and the sum ofn terms of the series -3,-1,11,39,89,167.
Find the maximum value of (7-x)4 (2+x)6 when x lies between 7 and 2.
Find the maximum value of (5+x)(2+x)/(1-x).
Find all the positive angles less than 380° which satisfy the equation sinx+sin2xsin3x = 0.
A,B,C are the angles of a triangle, prove that tanA+tanB+tanC=tanAtanBtanC.