1 If x is a real number, then is x² + x4 equal to а. V1 + x² b. 1 xV1+ x? c. xV1+x² d. æ|/1+ x² 1 е. |x|V1+x? O f. 1 xVx + x²

Q: Q1-let A = 6a B - ; ) [2 3 & B = Verify that (AB)" = B" A"

A: Explanation of the solution is given below....

Q: then 7(1 - а)М? + 6(1 - а) Мт %3D ВM?, 7(1 - а)т? + 6(1 — а)Мт %3D Вт?, Subtracting we obtain Y(1 –…

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Q: (b) Prove or disprove: Z10 ~ Z5 x Z₂.

A: We shall solve first question only as you have asked more than one unrelated question. For others…

Q: 3/4 Given: 4 2x+ 35 Prove: x= 4

A: Given: 42x+34=35

Q: |=1|+ |= 2 | |- |- | 3. If z3 + z,, show that VI +

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Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: If -1 1- provethat K? K2I

A: The given matrix is: k=1-1-1-11-1-1-11 Now, find the square of this matrix.…

Q: Compute E(X|Y = y), when y is any fixed positive real number. ) Compute E(X²|Y = y), when y is any…

A: We have to calculate the conditional expectation and conditional variance for given conditional…

Q: 2- Show that: (-1)m (2m + 1)! NIE

A: Solution:     Definition of Bessel's function:

Q: How many non-negative integer solutions are there of the equation: x + y + z + w = 15, such that…

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Q: 4. What is the coefficient of x? a) in (1 + 2x)117 b) in (2 – x)13? c) in (5 – 2x + y)'1, where y is…

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Q: Let a2 + y2 + z2 = 3ryz, then which of the following is 一

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Q: 22. Differentiate the following with respect to the variable x, giving your answer in a implified…

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Q: In(1+ 5.x?) 2 – 3x Differentiate with respect to x.

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Q: (b) Show that o = 2[Rx(0) - Rxx(0)] XX

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Q: A Moving to another question will save this respons Quèstion 1 If y = u - 4 and u = 3x2 + 10 , find…

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Q: 5. Show that b, is always positive, by establishing the equation (Qn-1,Qn-1) (Qn-2,Qn-2) b,

A: We will apply the properties of inner-product to prove the given statement.

Q: 6. Show that Vz eC i) z-7 is a real number. ii) (z-2) is a real number.

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Q: Given that 32a × 11º = 274x × 332× express a in terms of x?

A: Find your answer below

Q: If x is any real number, then cosh x Σ n=0 n! + 198 Σ n=0 (-x)" n!

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Q: 2. Find x in b = ax if a=23 and b=368. Reply in this format: 1. q = r = 2. x =

A: The given expression is: b=axwhere:a=23        and       b=368

Q: 4. Find all values of x satisfying In[(2x + 1)(x +2)] = 2 In(x+2). Verify the values of x you found…

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Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

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Q: For which values of a does ax = 1 have a solution in Z5?

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Q: If A= B = verify that A(B + C) = AB+ AC. :) 1 If A = 2 and B show that (AB)" =B'AT 4 -1

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Q: (16) Show that AB=BA for 0 0 0 3 0 0 0 1 A = and B = 0 3 1 2

A: A=-100030001 and B=500030002

Q: 1. Show that (a) exp(2±3лi) = -e²; (c) exp(z+лi) = - expz. πί p ( ² + 7² ) = √ = (1 + i); 4 (b) exp

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Q: Prove that if b+ 6 < 0, then x + bx + 5= 0 has at least one real solution.

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Q: 1. If x=27-3k and y = 7+57-4k, express each of the following in terms of i, j, k a) 5x-2y

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Q: Show that if u is an odd integer ,then the equation x2 +x−u=0 has no solution that is an integer.

A: The objective is to prove that x2+x-u=0 has no solution that is an integer. Suppose that there…

Q: 2. [ID # ending in 4 or 7] 2 av Determine (+) ax if v csch y = e*x² . дх ду ду

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Q: м/с How many solutions are there to the equation X1+X2 + X3 + X 4 + X5 = 25 where each Xj is and…

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Q: 3. Prove that if m is a positive integer and x is a real number, then 1 2 m 1 [mx] = [x] + \x + = |…

A: The greatest integer function is one of the most important real valued number theoretic function.…

Q: Show that e 12-1/31 2+3az| 2re?

A: The given inequality is                                           ∮|z-1|=1ezz+3dz≤2πe2 To prove the…

Q: 11| Q1) If A--2 -1,B 3 3 4 -5 -1 -1 13 -1 Find (–1 x A) + (B + C)

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Q: Q2/ prove [A] [A] = [I] if [2 4 -5 [A]= 2 7 1 3 4

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Q: Show that if 0 <y<1, and Y ~ N(0,1), we have that 9 6 3 P\Y + %(x² – 1) < =] × + (V +1). -

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: how many integer solutions are there to the equation  X + y + z = 10 for which  a. x,y and z + 10…

A: The positive integers are all the numbers that are greater than 0. The negative integers are the…

Q: B. Prove the following by contradiction: 1. If 3x + 2 is odd, then x is odd. 2. If there are two…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Given: 5(2x – 8) = 30; Prove: x = 7 -

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Q: b) Prove or disprove: Z10 ~ Z5 x Z₂.

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Q: 7. How many non-negative integer solutions are there to the equation X1 + X2 + X3 + 4 = 16 such that…

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Q: & B= Q1-Let A = 2 4 Verify that (AB)" = B" A"

A: As per our guideline we are supposed to do 1 question at a time. Please post other questions next…

Q: 11. How many solutions are there to the equation x₁ + X₂ + X3 + X₁ + X5 + x6 = 29, nonnegative…

A: We have given equation: x1+x2+x3+x4+x5+x6=29

Q: Prove they are equal 4 = 7(2x+ 1) - 5x -3(3x + 1)

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Q: 11. Answer by TRUE of FALSE each of the statements: (i) 4x³ + x² ln x¹ = O(x³). (ii) x³ + 4x + 15 =…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Prove x = 6 if 2x + 5 = 17 Statement Reason 1) 2x + 5 = 17 1) Given 2) 2x = 12 2) Subtract 5 from…

A: Please see the answer in Step 2

Q: I find B such that AB = C. If 5 0 3 A = 2 01 9. C = 3 5 c- (* :)

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Q: 4. Show that: do Tb/(a? – b²) - a+bcos0 а b2 Where a>b>0 such that * -1+ 1. < 1 - a²

A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…

Q: How many non-negative integer solutions are there for the following equation such that 0 < x1 < 10?…

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