Show that both ℝ and ℝ2 may be covered by countably many open spheres.

Q: We consider two spheres in 3-space. The first sphere has radius 5 and is centered at the origin…

A: Given, the two spheres in 3-space. The first sphere has radius 5 and is centered at the origin (0,…

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: The two open disks B((1,2);2) and B((-2,1);1) has intersection. True or False

A: The two open disks B1,2: 2 and B-2,1: 1 We have to find there is any intersection between these…

Q: The two open disks B((1, 2); 2) and B((-2, 1); 2) has intersection. True False

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Q: Use the following definition of compactness: KCR is compact if every open covering B of K has a…

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Q: The distance between the centers of the following two spheres: is x²-58x+y2+36y+z²=-1164,…

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Q: Find the point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: There are only 12 such shapes that can be formed in the plane by joining five squares along their…

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Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: Verify that A + B and AB are upper triangular.

A: Given,    A=32-10-43000    and   B=6-32024003 Recall that, The square matrix is called upper…

Q: The point (1,2-1) in space is inside the ball B((1,1,1);2).

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Q: A point moves so that sum of the squares of its distances from the vertices of a triangle is always…

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Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: Find the rectangular form of 7T 3√/2e² i.e. the a + bi form. Do not include any spaces.

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Q: Ex.: Find the area of the triangle whose vertices are A(1,-1,0), B(2,1,-1) and C(-1, 1,2).

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Q: Solve the following and show your complete solution Find Maclaurin Series Expansion and Compact form…

A: We need to find the compact form of the Maclaurin series of xex

Q: Exhibit a commutative ring R and an element x E R such that Z CR and x is NOT prime but irreducible…

A: Take R = Z[i√5]  Clearly, R is commutative ring and Z ⊆ R  Also, 2,3 ∈ R are not prime but…

Q: Find d so that D= ľ 23 is diagonizable

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Q: SSx x dA; R is the portion of the disk x + ys 16 in the second quadrart

A: I use polar conversion method