If x is a rational number and y is irrational, prove that x +y and x y are irrational.

Q: Simplify the expression log(x-x-6)–log(x²-5x+6) restrictions on the variable. as a single logarithm....

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Q: ANSWER THE FOLLOWING TRUE OR FALSE 7 14 3 s 3 2 3 15) The product of is 1 and 16) The reciprocal of ...

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Q: Exercise 6. Let ECR such that E is nonempty and bounded. Prove that the set -E= {-x : x E E} satisfi...

A: NOTE:Kindly repost the other questions as a separate question. 

Q: Let G be a graph with exactly 10 vertices and 27 edges. Suppose that each vertex has degree 3, 5, or...

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Q: 1- Determine algebraically whether the function F(x)=(x²+ 3] (x'-2x)*is even, odd, or neither?

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Q: Find the slope of the line containing the given points.  P1(−1, −8), P2(−7, 4)

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Q: 3. Assume that f : R → R is such that |f(x) – f(y)| 0. (a) Prove that |æn+1 – Xn] 1. (b) Prove tha...

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Q: Exercise 3.1.18 State whether each of the following statements is true or false and give a brief rea...

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Q: Prove that the diagonals of an isosceles trapezoid are congruent D(,b) C(a-c, b) b A( 0,0) B(a, 0)

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Q: Exercise 1: f is a 27-periodic function, defined on [0, 2m) by Ssin(t), 0<t< a, S(1 = 0, ast< 2x Her...

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Q: Gauss-Jordan reduction: Го 1 16 -6 ГО 4 Г1 0 —67 0 4 4 [1 -6] 1 0 -6 → |0 1 → |a 1 0 0 1 0 0 1 1 A E...

A: Introduction: Any elementary matrix, denoted by E, is obtained by performing a one-row operation on ...

Q: 21. x+y-2x +4y-4=0 22. x² + y´ +6x – 4y-3=0 Written Mah A. Transform each equation into center-radiu...

A: according to our guidelines we can answer only three subparts, or first question and rest can be rep...

Q: The water level of a lake is increasing by h cm every week. Time (week) 1 3 water level (h cm) 10.5 ...

A: Richardson extrapolation formula for derivative  f'(x) =f(x+h) -f(x-h)2h

Q: 1. Compute the first two steps of the Jacobi and the Gauss-Seidel Methods with starting vec [0,..., ...

A: system to solve using Jacobi and Gauss-Seidel Methods : 2u-v=0  -u+2v-w=2  -v+2w=0  

Q: Functions are not differentiable at locations where they are not continuous, where they have vertica...

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Q: Cauchy-Riemann equations. Show that for a family u(x, y) = c = const the orthogonal trajectories v(x...

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Q: zation of ſ(x, y, z) = at the point (3, 2, 8). ers in exact form. Use symbolic notation and fraction...

A: Introduction: The formula of linearization of a function f(x,y,z) at (a,b,c) is given by, L(x,y,z)=f...

Q: 30260°. 50230°(6 – 8i + 2+i

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Q: What is the value of 322 + 7z +1 z +1 dz

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Q: State whether or not each of the following sets is closed under the operations of addition and multi...

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Q: -1 Write X = as a product X = E¡E2E3 of elementary matrices. E1 = E2 = E3 =

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Q: Q2) Verify v(x.y)-3x3y-y3+5x is harmonic in the entire complex plane then find the conjucte harmonic...

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Q: A tent has the shape of a regular pentagonal pyramid. The measure of one side of the pentagonal base...

A: Volume of a pentagonal pyramid = (5/6) abh Where, a is the apothem length of the pentagonal pyramid...

Q: Rationalize the denominator.

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Q: Let f(z)= for 0 <I<6, for 6 <z< 7. %3D Compute the Fourier cosine coefficients for f(z). Ao %3D %3D ...

A: Fourier cosine co efficient  A0=2L∫0Lf(x)dxAn=2L∫0Lf(x)cosnπxLdx  

Q: What is the degree of the function g(x)=-2x (2x-1)(x+1)*

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Q: Let {fn}n=1 and {gn}n=1 converges uniformly on E. Prove that {fr – In}=1 converge uniformly on E.

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Q: Express-3-2j in polar form and use the result to find (-3 – 2j) 4. A) Give your final answer in rect...

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Q: 22. f(x) = 1+x, g(x) = 1+x| %3D

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Q: Б) у —у +Зу — 5у%3D—-бе-t У () %3 1, у (0) %3D2, у' (0) %3D— 4

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Q: 8. Let A and B two 5 x 5 matrices of determinant 3 and 2. Compute: (a) |AB| (b) |2A| (c) |B-1| (d) |...

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Q: Determine whether the two given statements are equivalent. (YES or NO 7. -P v-Q and P^~Q Answer: 8. ...

A: We have to make truth table for both statement ,If for same input truth value of  both statement are...

Q: Determine whether the number is rational or irrational. V100 The number is because it be expressed a...

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Q: a) Given a proposition: 1+3+5+ ...+ (2n – 1) = n² + 1. Demonstrate whether the proposition is a fact...

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Q: Illustrate how you would use chip abacus or base ten pieces to find 532 – 346 AND explain how this r...

A: To use the chip abacus for subtraction proceed as follows hundreds tens ones ○○○○○ ○○○ ○○    ...

Q: 1. Solve for the PARTICULAR solution of the initial value problem y" – y = 0, y(0) = 2 y'(0) = -1 if...

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Q: Solve the problem below using the graphical method. maximize f(y1,y2) =2y1 + y2 subject to ...

A: Let y1=x and y2=y ( for easily plotting the graph on Cartesian coordinates) then equations becomes m...

Q: 7 (5+2i)(2e30i 1. (7480)3

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Q: Consider the following system of equations. Зх + 3у + 3z %3D —3 -2х + у — 2z % 5 —3х + у — 3z %3D7 -...

A: The given problem is to find the solution for the given system of linear equations using Gauss elimi...

Q: QUESTION 3. $4500 is deposited for 4.5 years in an account that pays 4.5% interest compounded monthl...

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Q: 2 31 3. Let A = 3 3 1 compute A-1 241 of the system, using A-1. 2. Ay 1

A: To compute A^(-1) from the given matrix and the  to find the solution of the given system. 

Q: By using L(x)%3D1and L(x)= 1-x in Lagure polynomials, calculate the value of

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Q: A population P obeys the logistic model. It satisfies the equation dP dt 5 P(9 P) for P> 0. 900 9 (...

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Q: For certain values of the parameters a and b, the fixed point iteration b. Pn = a p-1+ Pn-1 8 %3D - ...

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Q: Q1: If w-f(z)=z'-z²+2z+2 find u and y and calculate the value of f at z-1-21. V.

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Q: A forensic method for estimating the time of death of a body is based on the law of newton of coolin...

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Q: 3. State the maximum and minimum values of the following functions (a) y=4-5cos²x (b) 3 y= 2- sin x

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Q: Given an integer n 2 1, how many decimal strings of length n begin and end with the same digit? 2(10...

A: Given an integer n≥1 We have to find the number of decimal strings of length n begin and end with th...

Q: ) Tossing a coin three times b.) Ansring a two multiple questions with four choises each

A: Please find attachment for the details solution 

Q: For certain values of the parameters a and b, the fixed point iteration Pn = a p-1+ Pn-1 8. converge...

A: For the fixed point iteration, the equation f(x)=0 is expressed in the form of x=ϕ(x) and then the f...