Find all solutions for the following pair of simultaneous congruences. 262x = 3 mod 807 3x = 2 mod 5

Q: t2 2t – 8 t 6. Find the Laplace transform of f(t) 2 te-2t

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Q: An employee invests £1000 at the end of each month into her Pension Fund for 30 years. What is the…

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Q: Given the function f(x.y) = In (2 +7y), answer the following questions. a. Find the function's…

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Q: Consider a system of differential equations X Ax, where x = and the 2x2 matrix A has eigenpairs d1 =…

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Q: Evaluate the integral F· dr. F(x, y) : (7x² + y) i + (8x – cos y) j where C'is the boundary of the…

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Q: (b) Determine the following Laplace transforms: (i) L{cos² 3t}. (ii) L {cos ¿t sin t}. (iii) L {e'…

A: Laplace transform of following functions, (i)  L { cos23t } (ii)  Lcos12tsin12t (iii)  L { et cosht…

Q: Question 1: 259 11 12 (hours) L (t) 15 40 24 68 18 (cars per hour) The rate at which cars enter a…

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Q: 15. Consider a simple dice game in which you roll a single die. If you roll an even number, you lose…

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Q: 1. 'Let X = {a,b,c,d,e} . Define ze P(x) by r={ø,X,{a},{c,d},{a,c,d},{b,c,d,e}}. ond nterore d) Give…

A: Let (X,τ) be a topological space and A be a subset of X, then the closure of A is denoted by cl(A)…

Q: Show that the integral is independent of the path, and use the Fundamental Theorem of Line Integrals…

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Q: Let C1 be the circle r = 3 cos 0 and C2 the cardioid r=1+ cos 0. (a) Find all point(s) of…

A: We will find point of intersection by equating both r .  If f is continuous and non negative on the…

Q: Find the coordinates of the wedge product a AbAc for а%3 (6, —3, —2, 2), b = (-8,5,6, -7), с %3 (2,…

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Q: 1 3 2 6 . -1 -3

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Q: (1 145)(209#( 35")" * (32cjs40°) Let 0= Simplify o and write it in rectangular form.

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Q: 12. Given: F 12 . âp, determine F•â„. 2 r ||

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Q: H.W: Which of the sequences {a,} converge and which diverge: 2. an 1+- 1. a, = 2+(0.1)"

A: 1. Given sequence is  an = 2 + (0.1)n Here limn→∞an = limn→∞2+(0.1)n = 2 + 0 = 2 Which is unique and…

Q: the In verse Laplace Trans form s' +3s – s –3 Ans. - (s)- (s² +2s +5)? %3D

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Q: Determine maximum or minimum income, earnings and investments through the vertex of a quadratic…

A: When double derivative of a function is negative, then value of x found when single derivative of…

Q: Find the solution using LU Decomposition: 7x + 5y − 3z = 16 3x − 5y + 2z = −8 5x + 3y − 7z = 0

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Q: 20 (1). Consider the equation of the surface S given by -2xyz + xªz² + 3yB = 2, where a is a %3D odd…

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Q: J y'+2xyt.xy4 1 =D0; ylo) =

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Q: 21. е*, ті

A: This is a problem of complex analysis.

Q: Q\Find T4 and T6 and the solution by trial and error, in detail, and steps TH - To 28.75- T6 0.2=

A: We need to solve 0.2=T4-T628.75-T6 We need to solve this using trial and error. Let us assume T6=1…

Q: Let T: P2 P² be given by T(p(x)) = xp'(x) – x² S, p(x)dx a. Show that T is a linear transformation…

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Q: What are the singular points, if any, of each of the following ordinary differential equations?…

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Q: The probability distribution for the number of sales for a salesman each day is given below. What is…

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Q: ry? V1+ x²

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Q: x = 4+5 sine and y = 1+4 cos e Part 1 of 2 (a) Eliminate the parameter and write an equation in…

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Q: find Fourier coefficients

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Q: Determine the following Laplace transforms: (iii) mathcal L \ e^ t cosh t\

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Q: Using the table

A: Introduction: Chinese Numbering System The Chinese numeration system uses characters to represent…

Q: QUESTION TWO A company has three main departments, which are Sales & Marketing, Inventory and…

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Q: 9. Show that the function f:x V-1 is a ring homomorphism f: Z[x] C. 10. What is the kernel of f?…

A: Given: The function, f:x↦-1, which is a ring homomorphism f:ℤx→ℂ.   To determine: The kernel of f…

Q: Given the surface of revolution with equation 22 y? 3x. 3 3 Find a generating curve of the surface…

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Q: L {lostt sin ţ t}

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Q: 1. Solve the differential equation (x² + y)d.x + (x+ y²)dy = 0.

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Q: 1 2 3 4 6 7 8. 9 10 ATA 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

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Q: Write the Egyptian numeral using a Hindu-Arabic numeral. The symbols are shown below. 10 100 1,000…

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Q: Q3. (a) Use the definition of L{-} to determine L{te="}

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Q: Use the liner transformation T: (u, v) → (x, y) given by 1 1 T(u, v) = (-u + v)i + ÷(u+ 3v)j 4 4 to…

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Q: (a) Use the definition of L{·} to determine L{te=#}

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Q: (b) If f is a bounded linear functional on a Hilbert space H, show that there is a unique y e H such…

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Q: How many different initials can someone have if a per son has at least two, but no more than five,…

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Q: of of H.W: Find and for the functions: Ox 2. f(x, y) = x² – xy+ y² 4. f(x, y) =- (x² + y²) .2

A: We want to find partial derivatives of given functions.

Q: 0 27. [37] (a) Solve y"(t)+9y(t) = f(t), y(0) = 0, y'(0) = = -1, where f(t) · 9t Express the answer…

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Q: Evaluate the definite integral. Son f (x) dæ, ƒ (x) =6e" /(4+e*)

A: It is known that: ddxekx=kekx∫ekxdx=1kekx+C

Q: bound the module of the contour integral (image) where C= { z E C : |z - 1| = 2}}

A: Introduction: Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement…

Q: Given that z = a+(a+3) v3 and z2 = 79 + b v3, find the value of each of the integers a and b.

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Q: 1. Find the volume of the region between the graph of the function f(x, y) = 1 - (x² + y') and the…

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