Directions: Justify each statement by stating the property, theorem, postulate, or definition that supports the statement. Write your answer on the space provided before each number. 1. If a > 8 and 8>b, then a >b. 2. If R is between A and B, then AB > AR. 3. If a point X is in the interior of ZGAY, then ZGAY> LGAX. 4. If x < 10, then 4x < 40. 5. If mzC = 90 and mzE > m2C, then mLE > 90.

Q: 1. Describe the graphs of the equation (a) r = cos 20 in cylindrical coordinates. (b) p= sec otan 0 ...

A: First change cylindrical and spherical coordinates system to Cartesian coordinates system 

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Q: Hin Find Fourier trins form of fu) =/! Ixa ! sinp Then find: O :oS Ein Pa Cos px_dp , ☺ dp

A: We have to solve the given problem by Fourier transform.

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A: As per our company guidelines I am supposed to do only the first question kindly repost the remainin...

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Q: 7. Give an (i) a non-planar graph that is not homeomorphic to K5or K3,3 example of

A: We can solve this using definition of planar graph 

Q: S csch-x coth x dx

A: Given,             ∫csch2x cothx dx

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Q: Qz/ Evaluate the complex integral: dz (z+ 1)(z – 2) where C is: a) The circle Iz] = 3 b) The circle ...

A: Note:- If z =(x+i y)  then z =x2+y2 Cauchy's Residue Theorem:- ∮Cfz dz =2πi sum of residue   Given i...

Q: s evaluate e of 1. The

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Q: If X is a binomial random variable, compute the probabilities below: (a) X - Binom(8,0.4) P(X 3) %3...

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

Q: 1+ax log 1-ax dx x 1-x Evaluate

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Q: Given the graph of the cosine function f (x) = cos x, evaluate the following limits: 3 27 3 1. lim c...

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A: Introduction: A composite function is the composition of two different functions. For example, fx=es...

Q: Solve the following LPP problems using Simplex Method: 3. Max Z = 3x1 + 2 x2 + 5x3 Subject to X1+2x2...

A: The given linear programming problem is                         Max Z=3x1+2x2+5x3                   ...

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Q: Q4: Solve the following integrals:- dx 4dx (1) S: (2) S: sec xesin x (3) S x sec? x dx 2+cos x

A: Note:-  As per our guidelines, we can answer the first three sub-parts of this problem. For the rema...

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A: Solution :-

Q: Question 1 Eliminate the constants of the equation below: y = Cex + C2xex A y" - 2y' +y = 0 B y"-y'+...

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Q: None

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Q: Assignment Problem. Maximize Profit     Machines Worker 1 2 3 4 A 12 15 11 14 B 10 1...

A: Since, it is a maximization problem, we first subtract the element of the table from the maximum ele...

Q: - Part 1 Graph and shade the points (if any) that satisfy the following system of linear inequalitie...

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Q: dr kr(M- x)-h (5) models a fish population which is growing according to the logistic law, and harve...

A: The complete solutions are given below

Q: Find the round-off error of the following using 5 significant digits: 1 1. 3 2. tan 150 3. 1 — п 4. ...

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Q: :Q2. Solve the following IVP using Laplace transformation y" + y' + 9y = 0. y(0) = 0.16, y'(0) = 0.

A: Introduction: The Laplace transformation is very much useful to solve a higher-order linear or non-l...

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Q: 1. Prove that if m + n andn +p are even integers, where m, n, and p are integers, then m + p is even...

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Q: Give an example of C = diag(c1, C2, C3) and D = diag(dı, d2, d3) where Tr(C) det(D), but C is not si...

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Q: Another model for a limited population is the so-called Gompertz function, which is a solution of th...

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Q: Find the value of ( v1' and v2' ) for t D.E's if we use the variation of param

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Q: Use trapezoidal with 3 level Romberg ( k=3) to evaluate 1 Пх - Пх* cos dx 4

A: The complete solutions are given below  

Q: Consider a solid with uniform density bounded above by the sphere x^2 + y^2 = 1 and bounded below by...

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Q: 1. For each of the following vector fields F(1, y), decide if there is function f(z, y) such that F ...

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Q: 4 Find the dot product of 6 -2 3] and -1 2 O 28 Not possible. O 32 O 12

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Q: 4) If x and y vary inversely, and x = -3 when y = 1/3, what is y when x = 9?

A: If x varies inversely with y yα1x y=k1x put x=-3  y=k13-------(1) from our given y=-13------(2) comp...

Q: dr cos(t)r(4-r); r(0) = 1.

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Q: O Let (eto-) is aring of complex-numberrs and M be aringof2x2 matrices aud desined as sollows. g e M...

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Q: 15. Find the eigenvalues and bases for the eigenspaces of A A =

A: The given problem is to find the eigenvalues and eigenspaces of the given matrix A.

Q: dy of y = sin(3x² + 5x – 4) * In(e*) is dx

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Q: QI Find for dx dt dy 4e - 5x'e dx dy 3re + 5x'e" dx O 2, dy - 2e + 4xe dx dy 2xe dx dy dy 5x'er dx 6...

A: We have to compute dydx, where y=∫x6x5et2dt. Comparing the given integral with the equation y=∫HxGxF...