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ABCD is a smooth horizontal fixed plane on which mass m = 0. 1 . . . - Toppr It is connected by an ideal string which is passing through a smooth hole and connects mass m, = kg at the other end as shown m, also moves in a horizontal circle of same radius of 1 m with a speed of 10 m s Ifg= 10 m s2, then the speed of m, is - (A) 10 m s (B) 10 m s (c) m's (D) None of these VIO
abstract algebra - If $G Z (G)$ is cyclic, then $G$ is abelian . . . We have that G Z(G) G Z (G) is cyclic, and so there is an element x ∈ G x ∈ G such that G Z(G) = xZ(G) G Z (G) = x Z (G) , where xZ(G) x Z (G) is the coset with representative x x Now let g ∈ G g ∈ G We know that gZ(G) = (xZ(G))m g Z (G) = (x Z (G)) m for some m m, and by definition (xZ(G))m =xmZ(G) (x Z (G)) m = x m Z (G) Now, in general, if H ≤ G H ≤ G, we have by
If $f,g$ are continuous functions, then $fg$ is continuous? Here is an alternative approach: Claim 1 If f: X → R f: X → R and g: X → R g: X → R are continuous, then f + g: X → R f + g: X → R is continuous Proof Given a point x ∈ X x ∈ X and ϵ> 0 ϵ> 0, we want to show that there exists a neighbourhood Nx N x of x x such that (f + g)(Nx) ⊆Bϵ((f + g)(x)) (f + g) (N x) ⊆ B ϵ ((f + g) (x)) By continuity of f f and g g, you can
proof verification - Mathematics Stack Exchange You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
efficient and accurate approximation of error function You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
multiplicative group of infinite fields - Mathematics Stack Exchange 8 Let F* be the multiplicative group of all nonzero elements of a field F We have seen that ifG is a finite subgroup of F*, then G is cyclic Prove that if F is an infinite field then no infinite subgroup G of F* is cyclic
Two liquids A and B form an ideal solution. At 300 K, the . . . - Toppr Two liquids A and B form ideal solutions At 300K, the vapour pressure of solution containing 1 mole of A and 3 mole of B is 550mmH g At the same temperature, if one more mole of B is added to this solution, the vapour pressure of the solution increases by 10mmH g Determine the vapour pressure of A and B in the pure states (in mm H g)
How to show that the commutator subgroup is a normal subgroup You don't need to figure out what a general element in the commutator subgroup looks like The commutator subgroup is generated by commutators Show that the property of "being a commutator" is invariant under conjuation (in fact it is invariant under all automorphisms)