Show that a positive integer a is & Perfect ube iff it has a prime facorzation of the form sai 392 30g Bam P2 Pz .- Pm where PioP2 Pg.Px are prime and gre non-negative integers

Q: Explain why the polynomial rings R[r] and C[x] are not isomorphic.

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Q: Using the sets you found on the slide 1, find the following set MUX

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Q: 3. Explain why the polynomial rings R[r] and C[r] are not isomorphic.

A: This is a problem of Abstract Algebra.

Q: Show that H ((12)) is not normal in S3. However, why is H' = ((123)) normal in S3? %3D

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Q: 1. What is the probability that a point chosen randomly inside the large triangle also lies inside t...

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Q: Solve ry + 5 y = 10a for y(1) = 2

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Q: 69 dx J-9 x2 + 4x + 8 6.

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Q: Let (X,} be a time homogeneous Markov Chain with sample space {1,2,3, 4}. Gi the transition matrix P...

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Q: If f(x) = x2 – 5x + 7, what are the co – ordinates of the minimum of y = f(x – 2)?

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Q: 2yı-y.cosx=-y3.cosx  solve differential equation

A: We need to solve a differential equation, 2y' - y cos x = -y3 cos x Divide both sides of differentia...

Q: 4. Consider the below data set: 65 87 x 75| 80 93 82 78 | 86 68 84 77 72 89 71 98 y 72 91 80 95 74 (...

A: Given: The data set: - x y 75 82 80 78 93 86 65 72 87 91 71 80 98 95 68 72 84 8...

Q: The given family of functions is the general solution of the differential equation on the indicated ...

A: Solution

Q: ( 3x²y + e' )dx + ( x³ + xe' - 2y)dy=0

A: We will first check whether given equation is exact or not ,then we find general solution accordingl...

Q: Find the shortest path in graph G from a to e using Dijkstra's Algorithm. The table below has 3 blan...

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Q: As an industrial designer you are designing a plastic bottle to contain a new soft drink product. As...

A: Given: Consider the varying radius of the bottle is given by xy=0.0018y3-0.067y2+0.5y+4.5 a) Volume ...

Q: 3. (a) Suppose N : V → V and N' : V → V are nilpotent of index r and s respectively and NN' = N'N. U...

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Q: 1. Show there exists an integer n such that n² + 3n/2 = 1. Is the integer unique? Explain your answe...

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Q: In Exercises 1 through 8 use the parallelogram law to form the sum and difference of the given compl...

A: Solution

Q: An integrating factor of

A: Given,             (x2y-2xy2)dx+(3x2y-x3)dy=0

Q: Answer T if the argument below is valid; F if it is invalid. No vegetarians eat meat. All vegans are...

A: Let 'p' denotes vegetarians, 'q' denotes those who eat meat and 'r' denotes vegans. Given statement ...

Q: find Òw and dw for the Solloing functions w= Ln (xッ2xy).cs答かうメ)

A: Given the function w=lnx2+2xy·cscx33+yx2 We have to find ∂w∂x=the partial derivative of w with respe...

Q: If A is 3x4 matrix and its rok is 2 then the nullity of matrix A will be be determined a) con つのt 61...

A: Let us consider the matrix A of order n x m  Then the Rank-Nullity theorem is  RankA+NullityA=m Rank...

Q: Assume (X,o) and (Y, on X x Y as are groups. Let X × Y = {(x, y) | æ € X, y E Y} and define the oper...

A: The given question is related with group theory. Given that X , ∘ and Y , ∙ are groups.  Let X × Y =...

Q: sider the differential equation x²y" – 5xy' + 8y = 0; x², xª, (0, 0). fy that the given functions fo...

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Q: Solve for the differential equations. (2х — у + 2)dy + (x— 2у + 4)dx %3D 0

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Q: Before arriving at his famous conjecture, Goldbach had conjectured that every odd positive integer g...

A: Goldbach conjecture says that every integer greater than 5 is the sum of three primes.  

Q: Let the function f (x) = x² . 5k (a) Find " f(x)dx by completing the following table using Romberg a...

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Q: Solve the system of linear equations using Gaussian Elimination method. x + y - z = -2 2x - y + z ...

A: we have given the linear system of equation x+y-z=-22x-y+z=5-x+2y+2z=1 we have to solve the linear e...

Q: Use the Laplace transform to solve the initial value problem y" + 4y' + 3y = 0 y(0) = 2, y'(0) =-1 (...

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Q: 3. Let V be a finite dimensional inner product space. If S = {u, v} is an orthonor- mal set, compute...

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Q: n yn let AEIR be a pasitive no tix defired with eigenolues 0eA Edas.<n and let E IR" be a vector of ...

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Q: 3. Ca For all sels A. Band C. A-CRIC) = CA-B)NCA-C)

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Q: 1 The sum of the series: 2 4 8. 16 equals to: -... 3 9. 27 81 3 5 10 Option 3 O Option 2 11 10 Optio...

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Q: Suppose that a family has 4 children. Also, suppose that the probability of having a girl (based on ...

A: The probability of having a girl is given as 12. Assume X as a random variable where n represents th...

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A: We will first try to write the given series in simplified form then we will check whether given seri...

Q: Try This Out! Simplex Maximization Problem Z = Subject to: -X1 + X2 0 X22 0 Maximize: 4x1 + 6х2

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Q: 0 -1 2 the 0 2|

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Q: Evaluate the integral. -7 et dx 1- e2x -8

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Q: Q 2: Halley's iterative method for solving a nonlinear equation f(x) = 0 can be written as 2f(xn)f'(...

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Q: Use undetermined coefficients to find the particular solution to y'' + 5y' + 6y = 3e t %3D Y(t) =|

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Q: 10. Without solving for the particular solution, what would be the correct form of the particular so...

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Q: Find a linear mapping that maps the set S onto the S’ where S is the square with vertices 1 + i, –1+...

A: Given  S is the square with vertices z1=1+i, z2=-1+i, z3=-1-i, z4=-i and S' is the square with verti...

Q: Suppose f and gbare functions with domain R . If both f and g are even but f+g is odd, the prove tha...

A: Even function :Let us consider  a function f then  f is said to be even if f(x)=f(-x) Odd function: ...

Q: = x2 – 5x + 7, what ar x- 2)?

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Q: Using Cauchy-Riemann equations, show that the function f (2) = (z+8)² is differentiable everywhere.

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Q: A school board announces an across the board salary cut of 3%. The superintendent makes $174,600 aft...

A: The calculation of percentage is very significant in arithmetic. When we want to find a percent of a...

Q: Solve for the missing information (Lines that appear to be tangent are tangent.) AC = 20 cm, AE = 37...

A: To find- Solve for the missing information (Lines that appear to be tangent are tangent.) AC = 20 cm...

Q: u 6 2 5 7. 8 4 a 1 4 G {c, m), {s, V), {s, u}, {a, m}, {a, s}, {u, x} {C, X}, {s, V}, {S, U}, {a, m}...

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Q: Which set of edges below is the minimum spanning tree of graph G? u 5 6. 6. 7 a 2 G {s, v}, {s, u}, ...

A: A minimum spanning tree or minimum weight spanning tree is a subset of the edges of a connected, edg...

Q: 1 1 1 If A =0 -1 2 then At- 2A³ – A? + 21 = %3D 0 0 2 A) 2A B) 2(I– A) C) 2(I+A) D) 2(A – I)

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