Let x and y be positive integers. When is x + y3 a prime number? When is x+y a composite number? Prove your answer. ,3.

Q: SET B: Solve by using Gauss Scidel iteration method the given equations a. Write down the given equa...

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Q: Let T = {o E S4|0(3) = 3}. (a) Show that T is a subgroup of S4. (b) Prove that T= S3.

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Q: Fill in the blanks: (a) C.P. = 400, Profit per cent = 15% %3D %3D (b) C.P. = 300, Loss per cent = 25...

A: a Given CP=400 and Profit per cent=15% We have to find the profit. The formula for the profit is giv...

Q: It suspect that the five data points: (-2, y1), (–1, y2), (0, y3), (1, ya), (2, y5) lie on the curve...

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Q: Find the angle between the vectors. (First find an exact expression and then approximate to the near...

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Q: Prove the following inequality п(п — 1) (1+ x)" 21+ nx + x², r20 2 for any n > 1.

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Q: 01. Determine the splitting field of x4 + x2 + 1 over Q. Also find its degree over Q.

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Q: Compute the LU factorization of the following matrix. No row interchanges will be necessary. You can...

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Q: 2s e Determine L-1 3 -

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Q: Check that F(r, y, z) = (yz + y)i+ (xz+z + sen(z))j+ (ry+ 2z+ ycos(z) + 1)k is a conservative field ...

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Q: Prove the following inequality, (1+x)^n>/= 1+nx+(n(n+1)/2)x^2, x>/=0 for any n>/=1

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Q: y In a = (1)²

A: Given differential equation is yln(x)dxdy = y + 1x2

Q: For the function f(x) = x² +3x + 1 (a) Construct the divided difference table for the points xo=1, x...

A: Introduction: For the given set of data points x0,y0,x1,y1,...,xn,yn, the divide difference table is...

Q: Write the following base 2 numeral as a base 3 numeral: 10010,

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Q: Find -the solution of the following 0.0. E ニーメ) ) y'- 2. %3D aこo

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Q: 3. Convert the polar equation to a rectangular equation. r = 64

A: Given,             r = 64 We have to convert the polar equation to a rectangular equation. 

Q: Example of a mathematical statement in this type of categorical preposition All S are P All P are R ...

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Q: Which of the following relations is a partial order relation defined on A={1,2,3} O a. R = {(1.1),(1...

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Q: The dot product of two vectors in R³ is defined by b2 = b3 = a,b + azb2+ azb3. a2 a3 Let i 2 |. Find...

A: Given that the dot product of two vectors in ℝ3 is defined by                                       ...

Q: QUESTION 3 Consider the following sets A = {1, 2, 3, 4, 5 } and B= {x, y, z} Find the Cartesian Prod...

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If yo...

Q: a. Determine if f is continuous or discontinuous at r 0 and at e = 3. If dis- continuous, classify t...

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Q: (x + 1)2 and the line (x+1)², 1, where a is the same constant. 4. Let Si be the area of the region b...

A: The complete solutions are given below

Q: -4 3 If 8 2a is a singular matrix, then a

A: Introduction: If a matrix is a singular matrix, then its determinant is zero. Let A is a singular ma...

Q: 1. -5?/20

A: This is a problem of complex analysis.

Q: Find the area of the region enclosed by the curves: y = e2", y = et", æ = 1

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Q: If matrix A is 12 xc and matrix K is 4 x t, their product AK is r x 7, what are the values of c, t, ...

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Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

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Q: f(x) = -5x6 + 8X5 + 9X4 -10X3 +2X2 -22X +45

A: To do the calculations in Excel, first enter the numbers in separate cells. Each number is identifie...

Q: Find an expression for x, the x- coordinate of the centroid of the region bound by the curve x = 9 -...

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Q: 5. Use the method of proof by contradiction to show that the following state- ment is true. Suppose ...

A: Introduction: The method of contradiction is a tool to prove the validity of a mathematical statemen...

Q: 2. Convert from a rectangular equation to a polar equation. x = 2y2

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Q: 3. You roll a pair of fair dice, one blue and the other gray. (a) (5 pts) What is the probability th...

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Q: eiz 0o cos x dx? cos z Can you use - 1+ z2 instead of - 1+ z2 to obtain the integral for Jo 1+x²

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Q: 3) What were the steps used in measuring the measurable objects? Write in bullet form.

A: Measurement, The process of associating numbers with physical quantities and phenomena. It is nothin...

Q: Show that x2 + 3 and x2 + x + 1 over Q have same splitting field.

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Q: The preference ballots for three candidates (A, B, C) are shown. Fill in the number of votes in the ...

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Q: 3.

A: This is a problem of Z transform.

Q: s-4 s+1 2. L(sin 2x + e2x+3) = . s²+4 s-2 Hint: e²x+3 = (e2x)(e³) -7s*+2s²+24 3. L(x* + x² – 7)

A: L{ eat}  = 1s-a    ,  L{sinat} = as2 + a2,     L{xn} = n!sn+11. L( e4x + e-x + x2  ) =L {e4x} + L{ e...

Q: ) Solve the following (1) [10–3x|13.

A: (i) Given 10 - 3x≤17⇒ -17≤(10 - 3x)≤17⇒ -7 ≤ -3x ≤ 27⇒ -27 ≤ 3x ≤ 7⇒ -9 ≤ x ≤ 73 Thus x ∈ [-9, 73]

Q: Solve the system of equations below using Gauss elimination without pivoting. 2?1 + 5?2 + ?3 = −5 5?...

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Q: Employees at the Me, My Mop and I cleaning service are choosing a new company logo. The choices are ...

A: Solution:-

Q: 7. Consider the following diagonalizable matrix A. 1 2 -2 A = -2 -2 -6 6 -3 (a) Show that v = 1 an e...

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Q: Find the matrices of the following linear transformations from R³ to R³. The orthogonal projection o...

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Q: Solve the following system of equations y + x² –x = 0 x²+ 2xy+y = 0 Initial guesses Xo = 1, yo = 1 P...

A: Use the following formulae, to find the approximate solution of the non-linear system by the modifie...

Q: this response. Quèstion 16 a +b -1 If 0 a then 0 5 a = -4, b= 5 0=5 b = -2

A: Introduction: Matrix elements are nothing more than matrix components. They can be numbers, variable...

Q: 6. Using the quotient, remainder theorem n = qd + r, 0sr < d a) Given n = 39 and d = 7 find the g an...

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Q: al equatio of the dif

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Q: How many times must l'hôpital's rule be applied to evaluate ex - e-X – 2x lim X + 0 X- sinx

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Q: 2. The equation 2x + x? - 1 = 0 has exactly one real root. Find its solution between points 0 and 1....

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Q: (i) What is the system of equations that would need to be satisfied if the points did lie on the lin...

A: This is a problem of linear transformation.