Determine the Laplace transform o sin (8t + 붕). +64 -a +(a) #() +64 +64 O 43 #() 2+64 O 4v3 7+64 +(a)

Q: 10 Consider A :3D and y:= Find all re R that minimize || Ar - y|l2.

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Q: 2. Express as a single power series form: Σ У(п - 2)аn+1(2х — 3)n+1+ > ап-1(2х — 3)п-1 n=0 n=2

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Q: Prove that the planes (i) 12x – 15y + 16z – 28 = 0, (ii) 6x + 6y – 7z - 8 = 0, and (üii) 2x +35y – 3...

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Q: e2z dz, I (z+ 1)* (b) Where C is a circle |z| = 3

A: The given integration is ∮ce2zz+14dz where c is the circle z=3 Here the pole z=-1,which is of order ...

Q: 5. Using De Moivre's Theorem, find the identity of sin e.

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Q: Find the maximum and minimum values of the function f(x, y) = 2x? + 3y? – 4x – 5 on the domain a? + ...

A: Given function is  fx,y=2x2+3y2-4x-5 on the domain g(x,y)=x2+y2≤121.

Q: Evaluate, in spherical coordinates, the triple integral of f(p,0, ¢) = sin ø, over the region 0 < 0 ...

A: Volume by using special coordinates.

Q: dy 6. +9y = 6e* +7e* - log 2 dx -2x -

A: Solution

Q: Find the argument of the complex number 3 + 17i 4 4. 47

A: Argument of the complex number

Q: d'y dy +9y = 6e* +7e* – log 2 6- 3x -2x dx? dx

A:

Q: 7 .Assune p is an odd prime such that p ≡ 1mod4 (that is p = 4k+1) Prove: if a is a primitive root f...

A: Given: p≡1mod4       ∵p=4k+1

Q: Evaluate. Express result in Rectangular Form correct to 3 decimal places. z = log(1-5i) (2 + 4i)(1-2...

A: To evaluate: z=log1-5i2+4i1-2i+ln2-3i1+3i2-i, in rectangular form correct to 3 decimal places.  

Q: from a solid right circular cylinder with height 10 cm and radius of the base 6 cm a right circular ...

A: We have to find volume of remaining solid.

Q: Consider the group (U(20), '20). 1. What is (7 ·20 13)-1? 2. Solve for x in the equation x '20 9 = 7...

A: Unitary group, multiplication madulo

Q: Out of a sample of 100 juice bottles, 95 bottles contain between 712 and 788 militers of juice. Use ...

A:

Q: Find the roots; express results in Rectangular Form, correct to 3 decimal places. 6(1 + 3i)4 + 5e-1....

A: The given problem is to evaluate and simplify the given complex expression and express the results i...

Q: Let B = {b1, b2, b3} be a basis of R where 3 bị -4 b2 b3 = Let v = -4 . Find the vector v]R of coord...

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Q: Now let G = S_10, acting on the set {1,2,3,4,5,6,7,8,9,10}. What is the index in G of the stabilizer...

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Q: If |<1, determine the maximum modulus f (2) :+1 (a) f(=)=='-2z+3, (b) f(=)==+=-1, (c) f(=)= (d) cos ...

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Q: A trough is shaped like a half cylinder with length 4 m and radius 1 m. The trough is full of water ...

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Q: Q. Solve differential equation by an appropriate method. (i) (x? + ху — у?)ӑx + хydy — 0 (ii) (x + v...

A: (i)  We have given a differential equation ,  x2 + xy - y2dx + xydy = 0 This is homogenous different...

Q: Determine which characteristics of an algorithm the following procedures have and which they lack. p...

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Q: 1. Verify whether the function f(2) = e=Y sin x – ie- cos x is entire or not. 2. Show that the funct...

A: Given: Let us consider the given, 1) fz=e-ysinx-ie-ycosx 2) fz=xy+iy

Q: calculate 1+3+5+...+(2n-1) for n = 1,2...,6.

A:

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y) = - 2x - 5xy- 4y ...

A: We have to find local maximum and local minimum value.

Q: ne-third th

A: Introduction   When the Earth is assumed to be spherical, the circumference varies as the cosine of ...

Q: 7. (a) cosh?1 (b) 2 sinh² 20

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Q: Show that (B- A)U (C-A) = (BU C)- A 1) Using Venn diagrams 2) Using the set-builder notation and log...

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Q: -6 2 Show that A = and B = 9 -3 are similar matrices by finding an invertible -3 -1 -15 matrix P sat...

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Q: (b) Prove that each of the following functions is continuous, stating any rules that you use. (i) s(...

A: The complete solution is in given below

Q: Solve this ODE using the Frobenius Method x²y"+x*y'-2y = 0

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Q: Fill in the membership table for the set in the expression AN(B- A) = Ø and determine if the equalit...

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Q: Let a * b = 2ab be defined on Z†. 1. Compute a * (b * c) 2. Compute (a * b) * c

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Q: [A] Identify whether the relation is linear, quadratic or exponential. [B] Write the equation for th...

A: Given table   

Q: Let V = R? and K = R. Which of the following are subspaces of V? Give reasons for your answers. *)(i...

A: We have to find the subspaces.

Q: The table shows the national expenditures for health care in the United States for selected years, w...

A: Solution:   x is the number of years past 1950 and y is the total expenditure for health care in (bi...

Q: Find the point of tangency and equation of the tangent line of the following functions given a singl...

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Q: Let V = R? and K = R. Which of the following are subspaces of V? Give reasons for your answers. *)(i...

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Q: Let u = and v = Select all of the vectors that are in the linear combinations of {u, v}. (Check ever...

A:

Q: – y² and consider the vector field F Consider two distinct points P1, P2 on the surface S. Find the ...

A: As per the question we have bto find the value of α such that the line integral of F about curve C1 ...

Q: Determine the z-transform of following sequences and state its region of convergence. i.) {(-3*; ii....

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Q: If |<1, determine the maximum modulus f(:) :+1 (a) f(=)==-2z+3, (b) f(2) == +z-1, (c) f(=)= (d) cos(...

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Q: Adam Lisa's a car with an upfront payment of $2,708 and monthly payments of $156 assuming there is n...

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Q: 1) 1+e" |dx+e" (1- xydy =0

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Q: DE MOIVRE'S THEOREM Copy the problems and show your full solutions on your answer sheet. Evaluate th...

A: use demoiver's  theorem 

Q: an electric generator is sold for rs 39000 cash or for25% cash down payment and eight equal monthly ...

A: cash price of the generator is rs 39000 in the instalments plan, cash down payment = 25% of rs 39000...

Q: (x) (x1) -2x +4

A: Evaluation of the integral by using Partial fraction decomposition

Q: 1.7-2 In the mean-value theorem for derivatives, Theorem 1.6, let f(x) = x?. Find the point & specif...

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Q: Find the Inverse of Matrix (M).

A: We can compute inverse of matrix as follows

Q: If six (6) people greet each other at a meeting by shaking hands with one another, how many handshak...

A: We know that a handshake is possible between two people at a time. It is given that six people were ...