proof of eulers theory:- V+F-E=2

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Colby Messinger answered 2 years ago

Proof: Let S ⊆ V be a subset of a vector space V over F. We...

Proof: Let S ⊆ V be a subset of a vector space V over F. We have that S is linearly dependent if and only if there exist vectors v1, v2, . . . , vn ∈ S such that vi is a linear combination of v1, v2, . . . , vi−1, vi+1, . . . , vn for some 1 ≤ i ≤ n.

E=1/2 CV^2 E= 1/2 (164 microF) (10^-6 F) (119 V)^2 E= 1.168 J How do you...

E=1/2 CV^2 E= 1/2 (164 microF) (10^-6 F) (119 V)^2 E= 1.168 J How do you figure out the J from the F V^2

Problem 2. Consider a graph G = (V,E) where |V|=n. 2(a) What is the total number...

Problem 2. Consider a graph G = (V,E) where |V|=n. 2(a) What is the total number of possible paths of length k ≥ 0 in G from a given starting vertex s and ending vertex t? Hint: a path of length k is a sequence of k + 1 vertices without duplicates. 2(b) What is the total number of possible paths of any length in G from a given starting vertex s and ending vertex t? 2(c) What is the...

Show that, for any events E and F, P(E ∪ F) = P(E) + P(F) −...

Show that, for any events E and F, P(E ∪ F) = P(E) + P(F) − P(E ∩ F). Only use the probability axioms and indicate which axiom you use where

E ::= E + T | T T ::= T * F | F F ::=...

E ::= E + T | T T ::= T * F | F F ::= num | (E) Num ::= 0 | 1 | 2 | 3 | 4 | 5 | . . . . . . . Question: 1 a. Show the Left-most derivation for the expression: 5 * 7 + 6 * (1 + 2). b. Show the Right-most derivation for the expression: 5 * 7 + 6 * (1 + 2).

Where n is the number of moles of electrons and F=96,500J/V⋅mol e− is the Faraday constant.

Part A Cell Potential and Free Energy of a Lithium–Chlorine Cell In thermodynamics, we determine the spontaneity of a reaction by the sign of ΔG. In electrochemistry, spontaneity is determined by the sign of E∘cell. The values of ΔG and E∘cell are related by the following formula: ΔG∘=−nFE∘cell where n is the number of moles of electrons and F=96,500J/V⋅mol e− is the Faraday constant. Part B Calculate the free energy ΔG∘ of the reaction. Express your answer in kilojoules. Part...

Use the weighted digraph for problems below: V = {a, b, c, d, e, f, g,...

Use the weighted digraph for problems below: V = {a, b, c, d, e, f, g, h} E = {(a,b,6), (a,d,3), (b,c,2), (b,e,5), (c,f,4), (d,e,9), (d,g,1), (e,f,7), (e,g,8), (e,h,2), (f,h,4), (g,h,4)} (3 pts.) What is the length of the longest path from a to h? Show the path! (2 pts.) Does the graph contain a cycle? Justify your answer! (3 pts.) Give the adjacency matrix for the graph. (4 pts.) Provide the order in which nodes would be visited in...

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proof of eulers theory:- V+F-E=2

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