Express the given complex number in exponential form into a + bi form. 157 2e 6 1 + i3 - \3 + i 1 - i3 3 + i

Q: nsider the differential equation: Vy' +y =

A: In this question, the concept of Integration is applied. Integration Integration is a method of brin...

Q: 1. Prove that for every real number x, if |x-3| > 3 then x² > 6x. (Hint: Consider two cases)

A: Solution

Q: 2. Describe geometrically how the linear transformation T acts on any vector x = in R?. (a) T(x) – 6...

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Q: Find the projection of v = -7 onto the -2 e of R' given by the parametric equation e = tu, [-11

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Q: Find the maximum valuue of the function f(z, y, =) =z² + 3? + subject to the constraint z+y z* = 16....

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Q: Let Au + u = x^2 + y for x and y be in (0, 1). u(x, O) = x^2, u(x, 1) = x, u(0, y) = 0, u(1, y) = 1....

A: We are given the following differential equation with the boundary conditions.              ∆u+u=x2+...

Q: Suppose n(ANB) = 3, n(AUB) = 38, and n(A) = 18. Use a Venn diagram to determine n(B). n(B) = %3D

A: Given n(A∩B) = 3,  n(A∪B) = 38andn(A) = 18

Q: Exercise: (2 7 4 i. Find the inverse of A =| 3 1 5 0 8

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Q: Find the Laplace transform of the following functions. a) f(t) = t sin tcos t. b) f(t) = te"8 (t – 2...

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Q: Consider the following transfer function: 2s° + 5s2 + 3s + 6 D F(s): = A + s3 + 6s? + 1 1s + 6 S + 1...

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Q: Problem 2: instructions for series on the coversheet of this exam. Explain whether the series below ...

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Q: 4x + 300 A garden shop determines the demand function q = D(x) = during early summer for tomato plan...

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Q: Compute the first 5 Legendre polynomi als , ..., L, (x), (These Solutions, P,x) , where n is a whole...

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Q: For each of the following matrices (with coefficients in R) compute the characteristic polynomial an...

A: Note: Our guidelines we are supposed to answer only three subpart . Kindly repost other subpart as t...

Q: Prove or disprove the following statement: There are real numbers a, b such that |a| + 2|b| = |2a − ...

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Q: The indicated function y,(x) is a solution of the given differential equation. Use reduction of orde...

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Q: Solve the initial value problems: y" + 4y = 2x; y(0) = 1, y'(0) = 2 y" + 3y' + 2y = e*; y(0) = 0, y'...

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Q: tan @ 240

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Q: Show that t (T (n)) = 2 if and only if n = p9-1 for some primes p, q. %3D

A: T(n) is the divisor function which counts the number of divisors of a number. 

Q: Find the coefficient a, of the Fourier series representation of the function with period T= 1/50 (1,...

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Q: 1. f'(x) is usually the same type of function f(x), unless f(x) is an exponential function a logarit...

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Q: Write a triple integral, including limits of integration, that gives the volume between 2æ + y 0, y...

A: Introduction: Triple integrals represent the iteration of three-variable functions, f(x,y,z). Instea...

Q: In y - e* + 2cos z = -3 In y +3cos z = 4- 2e* 2) e2x 1 +3 = +ln(z ex cos z +

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Q: (ху + 1)dx + x(х + 4у — 2)dy 3 0; у(1) — —1

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Q: Use separation of variables to find a solution to: du k >0 k

A: Solving a partial differential equation using separation of variables, we put dependent variable as ...

Q: (a) Find the parametric equation of the line that contains the two points A = (-4, 0, –1) and B = (3...

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Q: The table shows the total number of trade apprenticeships in Canada each year from 1991 to 1997 a) C...

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Q: (a). Use linear approximation to estimate In 1.03. (b). Compute the percent approximation, 100|Appro...

A: The linear approximation of of the function: f(x) at x=a is done using the formula: Lx≈f(a)+f'(a)x-a...

Q: 1. Use the Euler, improved Euler and Runge-kutta methods to solve the following ODES:

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not men...

Q: 5. Consider the equation f(x) = x - 2- = 0. (a) Show that the above equation has a solution on the i...

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Q: Find the coefficient a, of the Fourier series representation of the function with 1,0 <t < 0.01 f (t...

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Q: Evaluate the integral S dady by reversing the order of integration. Evaluate the iterated integral S...

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Q: The tangent plane to the graph of the function f(x,y)=x+xy+y2, which is parallel to the z=1+2x+3y pl...

A: Here given surface is fx,y=x+xy+y2 or x+xy+y2-z=0......1 Then, consider Fx,y,z=x+xy+y2-z

Q: (a) Which of the following statements are TRUE? (1) If T : R" –→ R" is a linear transformation, then...

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Q: n=] Зп + 2 (а) 5n + 3 n=1 102n+5n! (е) (2n)! n=1 n! (f) n" n=1

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Q: 3.1.3. (-) Let S be the set of vertices saturated by a matching M in a graph G. Prove that some maxi...

A: you Can Convert any non-maximal matching  into a maximal matching by adding edges.  And you Can tran...

Q: (a) The quadratic equation produced to model the trajectory of a test missile is y = -0.0822 + 2.15r...

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Q: . Use the Root Test to determine if the series (-1)" 2/n en? (2n² – 1)"¯ CONVERGES n=1 converges or ...

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Q: 1. Use the Euler, improved Euler and Runge-kutta methols to Solve the folllowing ODE s: 4 2 C. y co)...

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Q: 4*++3" Consider the sequence a, = (a) Is the sequence monotonic pr non-monotonic? If it is monotonic...

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Q: A diet is to contain at least 1003 units of carbohydrates, 2815 unids of protsins, and 2660 calories...

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Q: ce the triple integral

A: Given,          x=9y2+9z2, and x=9

Q: & 'Dashboard X (83) Quarter x 1 PM Schaffer Me org profle/e/ascignments/teacher/katd 443114613474327...

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Q: Use the Putzer algorithm to determine the exponential of the following matrix: 1 1 0 3 -2 0 3 -4 A =

A: The problem is related to linear algebra and matrix. We have to ask exponential of the matrix. First...

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Q: Use Bisection Method to find the root of r + 6x? – 12 = 0 that lies in the interval (1, 2) to four-d...

A: The steps to find the root of the equation fx=0 by the bisection method are as follows. Identify tw...

Q: 3By UBing the two iterative methrds Solve the following System of equation and compare the speed of ...

A: Given: A system of linear equations, 5x+2y+z=12x+2y+5z=20x+4y+2z=15 To find: Using two iterative met...

Q: 1. Consider the series (-1)"+1 n! (a) Determine if the series is absolutely convergent, conditionall...

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Q: What is the angle in radians between the vectors a = (-9, -7, -2) and b = (-6, 1, 4)? Angle: (radian...

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