Prove: le* a. ſ csch x = In - |+c lex+1

Q: Let R be a commutative ring. Then R is an integral domain if and only if ab= ac implies that b = c,…

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Q: Which of the following is the derivative of f (g(h(x)))?

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Q: Determine mine a conditioN ON | x-4) that will that | 7x²-2 | 4.01

A: We have to determine the condition on  that will assure that

Q: Show that

A: Our Aim is to Prove that:-111abca2b2c2=a-bb-cc-a   -(i)

Q: rank(AB) = rank(A) – dim(N(B") R(AT)) -

A: Let A∈Mm×n,B∈Mm×n The mapping A:Fn→Fm,B:Fm→Fn RankA+Nullity A=nRank B+Nullity B=qRank AB+Nullity…

Q: 4. A stone is thrown vertically upward with an initial velocity, and its height above the ground is…

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Q: Show that

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Q: Show that

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Q: Show that /I +x 0.

A: Mean value theorem: Let f be a function satisfying the following properties: 1. f is continuous on…

Q: - Ca-8)" a b a of

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Q: sin e cos (cos a cosec 0) de (1-cos a). 2 ||

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Q: Show that

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Q: 1 Ita Į = ab

A: The objective is to show that, 11111+a1111+b=ab

Q: 1 34 268 ".95 A=

A: We find the determinant of given matrix A by determinant expansion.

Q: x : x is a natural number less than 10​}

A: Write in explicit form

Q: Show that

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Q: Find IAI A= 2 3

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Q: Number of Voters 4. 1 3 3 4 3 4 1 4 1 Show the results in each of the head-to-head contests below,…

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Q: X 5 km 13 km

A: Pythagoras theorem: The longest side of the triangle is called the "hypotenuse", so the formal…

Q: The mean of the sampling distribution of means, µã =µ i.e., E(X)=u

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Q: if f) = (1-;),0<x< 1,then f(x)is p.d.f. true O flase

A: In the given problem,

Q: Let 43^(55) + 55^(43)= 7q+r, where q and r are two integers such that 0<=q<7. Then r is equal to?

A: Let 43^(55) + 55^(43) = 7q +r, where q and r are two integers such that 0&lt;=q&lt;7. Then find the…

Q: (2.00-x) Vq₂ = ±xV|q₁|

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Q: The marks obtained by 10 students in a test, scored out of 60, are shown below. 29 38 26 42 38 45 35…

A: The given data .The aim is to find the value of range, median, and mean.

Q: 1. Determine an equation in factored form for the polynomial function represented by the graph. ya 2…

A: The given graph is We have to find polynomials by the given graph.

Q: Question 14 The current share price of a resources company is $6.85. (a) A shareholder owns 880…

A: Since you have posted multiple questions with multiple sub-parts, we will solve the first three…

Q: Theorem 8.3.3 If X ~ t(k), then E(X2r + 1) = 0 and µz, = k"- (2r – 1)(2r – 3) ... .1_ (k– 2)(k – 4).…

A: Answer: For the given theorem, The proof is:

Q: If x is a random variable and a and b are constants then E ( ax + b ) = aE ( x ) + b

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Q: if G-H-F such that and H-F <R-k So...... R-k =G-H

A: Draw a diagram representing this scenario. Use the diagram to deduce a conclusion.

Q: d csc z = -csc z cot z dz

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