1. Prove, with justification, that this equation is an identity: x + (a + b)r + ab (x+ a)(x + b).

Q: Let x, y e Z. Prove that if 3x+7y is odd or 5x + 6y is even, then x or y is even.

A: We have given that for x,y belongs to integers. If 3x+7y is odd or 5x+6y is even then x or y is even…

Q: Let x, y E R. Prove that if 21x + 35y = 45, then x and y are not both integers.

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Q: If y = exp(-x²) show that -2xy and hence prove that, for n > 1, %3D y(n+1) + 2xy(") + 2ny("-1) = 0.…

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Q: If $ = 2xy?z + x²y, evaluate $ dr where C 3 from

A: Given, ϕ=2xy2z+x2y, We have to evaluate ∫Cϕdr where C(a) C is the curve x=t, y=t2, z=t3 from t=0 to…

Q: (c) Prove that 1, have equal roots if e= a'm +b °

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Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: Solve the following forr W=4xc for c %3D C = (Type an exact

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Q: consider this formula. z= y over x if z= 4.0 and y=6.0  express your answer to the tenths place

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Q: Solve the Auxiliary DE 75. и"" + u" — 2и 3D 0

A: Note: - “Since you have asked multiple question, we will solve the first question for you. If you…

Q: For x2 + Bx + C = (x + a) (x + b), which of the followingmust be true?(a) ab = B and a + b = C(b) a…

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Q: Answer the following question accordingly: a) Let A=|2 3 -1 3 a and B-l= where %3D 2 5 a ato and a $…

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Q: 11. What theorem is used to prove that BD 1 AC? C В. D A

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Q: у" + Зу" + Зу' +у%3D0

A: We have to solve the differential equations

Q: Given F(x, y, z) = (z, x, y) Solve for: а) divF b) curlF

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Q: y y' = x=2, y =4 x+ Vxy

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Q: Simplify the following by using De morgan's theorem: (with solution)  1. W = BC +B'C 2. X = A'B +…

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

Q: re 1 da Ji rVI- (In x)²

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Q: The approximation to a root of the equation x^2+x-1=0 in the interval [0,1] b applying the regula…

A: The given equation is x2+x-1=0  find the value of f(0) and f(1)  fx=x2+x-1f0=02+0-1=-1…

Q: Use the substitution x = et, to solve the following Cauchy-Euler equation: x²y// – 4xy/ + 4y = x³ In…

A: We will find out the required solution for given Cauchy Euler differential equation.

Q: ), then the value of r is

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Q: 1 Assume that 1 < a < b_and equation is solvable. + x = Show that this * – b'

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Q: For the missing elements to satisfy the condition A-1 + 14 = E e 2 b 3 5 -2 A 4 -2 i -3 Ly a 268 14…

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Q: 4. If A is a 4x4matrix and det A=2 , then det(34)is equal to (a) (b) 162 (c) 48

A: Given query is to find the det(3A) when matrix A is a 4 × 4 matrix.

Q: What must be the value of x to prove AB CD? H. (3x + 14)°\ K C (бх — 4)°

A: We know that two lines are parallel if the alternate angles are equal. We use this fact to find the…

Q: Given: 5x+4y= 24, x + 7y= 11; Prove: y = 1

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Q: If (x+iy) = a+ ib, Prove that + a b = 4(a -b*).

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Q: 2. Verify that each equation is an identity.  (b) sec2x = sec^2x+sex^4x/2+sec^2x+sex^4x.

A: To verify that the following equation is an identity, sec2x=sec2x+sec4x2+sec2x+sec4x

Q: Apply Method of Substitution and evaluate : 6x° 192x7 dx 4 e +C, Where C is an arbitrary constant O…

A: From the given problem: I=∫ e6x8 192x7dx....(1) Now apply the substitution method to calculate the…

Q: If y = exp(-x²) show that = -2xy and hence prove that, for n > 1, y(n+1) + 2xy(") + 2ny(n-1) = 0.…

A: Given that : y=e-x2. Therefore,  dydx=ddxe-x2=e-x2.-2x=-2xy  , as y=e-x2. Hence proved that…

Q: Is the following statement true or flase? Select one: True False 5 [ 2 (xy) dydx = chỉ xdx xdy) 0 0

A: To check whether the statement is true or not. Given information; The statement is ∫05∫02xydy…

Q: If u(x) = x3, then du = 3x2.

A:

Q: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

A: Show that ∗ : R × R → R defined by        a ∗ b = a + 2b is not commutative.

Q: 2 Given that i? is defined as being equal to -1, what is i9? F -i 1 H -1 i K -99

A: Given that : i2=-1

Q: If C = {x:x² + 11x + 30 = 0, x ∈ N}, then C is a/an ?

A:

Q: Discussion 1- Simplify this (A+B) (A+C) 2- Prove that (X+Y) (X+Y)= X

A: We have to simplify and prove Boolean equation

Q: If a + 0, the degree of ax"y" is

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Q: x²y' = 4x? + 7xy + 2y²

A: the given equation is homogeneous differential equation .

Q: Prove Equationally that A, B H A = B.

A: Given:                       A, B ⊢ A≡B To do: Prove the given statement equationally.

Q: for a>0 is defined a n(x² + a²) and sin ax = (x)"6 prove that la * fb = fa+b and ga * 8b =gmin (a,b)

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Q: B. GIVEN: 1= X2. PROVE: AB # BC. 24. E A C D.

A: We have to prove the given statement.

Q: -x+y<y. 2 If x < y, prove that x <

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Q: If A-B=0, implies that A*=B" %3D 0 صواب ylgn İhi O

A: Given A⇀-B→ = 0

Q: a b be suc b |, then t

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Q: Ex 6 Show that X -Ca,i) is HOM with y- (1,00) if X and y have the euraal Seibsipace op. af R Hint:…

A: Homeomorphism: Two topological spaces and are said to be homeomorphic if there exists a function…

Q: For what value of k, if any, is kre 2z dr = 1?

A: NOTE: Refresh your page if you can't see any equations. . use the integration by parts use the…

Q: If C(x, y) %3D 400 - 5ху + 10х?у, find ac ac and Əx ду ac Əx ac ду II

A: Explanation of the answer is as follows

Q: Let x, y e Z. Prove that if 3x + 7y is odd or 5x + 6y is even, then x or y is even.

A:

Q: Prove that (a - b) x (a + b) = 2 a x b and find the geometrical meaning of it.

A: find the explanation below

Q: The IHiplicative in verse of 2° tX -I in Zs [x] /is; mu d. nune of

A: Ring Theory.