Factorise x6+1

Q: Suppose X is a continuous random variable having probability density function (PDF) f(x). Which of…

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Q: Solve the following initial value problem (IVP) of y" – 3y - 10y = 2 where y(0) = 2 and y (0) = -1.…

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Q: 1- 2r (1 + y')dx - y (1 + 2x)dy =

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Q: a. UW) = In(W) b. U/W) = w^3 C. U(W) = w13 d. U(W) = 3W. The utilily function, U(Wy= In(W), Implies…

A: (a) The utility function is defined as UW=lnW.

Q: 17 s+ 270 675 s - 4s + 85

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Q: Solve for y" (1) : y" – 4y' + 3y = 6t – 8, y(0) = 0, y'(0) = 0 %3D

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Q: Solve the following initial value problem (IVP) of y" – 3y – 10y = 2 %3D where y(0) = 2 %3D and y'…

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Q: Use substitution to find the Taylor series at x = 0 of the function 18 sin (- x). What is the…

A: Given function is f(x) = 18sin(-x)

Q: 5. Let V = R³ and let (-, ) be the standard dot prod- uct. (a) Calculate (3e, + 2e, – €3, 2e2 +…

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Q: 2 Jo x2+4 n = 6

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Q: Vhat is the gradient of g(x.y) = ye* and its maximum value of its directional derivative at P(0, 5)?…

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Q: f(t) = te2t sin t

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Q: 45+8 d. F(s) (s2+4)(s²-6s+13)-

A: We can solve this using Laplace transform

Q: f(t) = te¯3t cos² 2t -3t cos 2t

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Q: Let G(r, s) be the graph with vertex set V= {(a,b) e Zx Z|1<a<r,1<b<s} and edge set = {(a,b), (c,…

A: Given G(r, s) is a graph with vertex set V={(a, b) ∈ℤ×ℤ| 1≤a≤r, 1≤b≤s} and edge set E={{(a, b), (c,…

Q: 11. solve the following differential equation. 1 dy y = 4(x - 3)y X-3 dx

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Q: the IVP ly a Sum of povers up to and including x5. cx-2) y'= xy, yroje 4 Q.6. Salve pover ceries and…

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Q: Observe that 213 = 8192 = 8191 + 1, and 8191 is prime. Use this data to compute an eight-digit…

A: We have given relation 213=8192=8191+1, where 8191 is prime. We need to calculate an eight digit…

Q: where m and n are constants. Which of the following is the answer for the inverse Laplace transform…

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Q: 7. Suppose X is a continuous random variable with 0 sX s 4 with valid probability density function…

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Q: . Let x and y be two orthogonal vectors. Then prove that

A: If x is any vector then Euclidean norm or 2-norm is denoted by ||x||2 and is given by  ||x||2 =…

Q: 24. Use what you know about an icosahedron to derive a formula for its surface area. What is the…

A: We have given three-dimensional shape icosahedron.  We need to derive the formula of surface area…

Q: Determine the supremum of the following set with full justification, if it exists. = (-1)" (","). n…

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Q: 1] Solve the following complex number problems. Solutions for complex number ormation is required in…

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Q: Find the arc length of the graph of r(t) = ev2li+e¯v2lj+2tk, 0<t < v2 In 9 NOTE: Enter the exact…

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Q: Which of these statements about the poset ({ 3, 6, 8, 9, 10, 12, 16, 20}, I ) are true? (Select all…

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Q: Determine the simplified form of (4 – 37) (–9 + j) – (8 – j5).

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Q: 2ea

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Q: Solve the following PDE: а. у иху +и %3D 0 a²u a2u + at2 = 0 b.

A: Solution :-

Q: Mathematical Communication Chapter 3.7 Rational Incqualities Planting Crops A farmer has 500 acres…

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Q: Find the Laplace transform of f(t) = cos(2t) + 7 sin(2t). s+1 s2+4 _s+14 g2+14 s-14 s2+4 s+14 s2+4

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Q: Determine the particular solution of the given differential equation: y" - 4y +3y = e' + t? O y, =…

A: The solution is given as

Q: 7. Find the real part of the dot product of the vectors u" = (i, 1+ i, 1) v* = (5 + i, –2 + 2i, –1+…

A: Dot product of complex numbers

Q: 5. Convert each vector equation to matrix equation. Afterwards, solve and show the solution in…

A: An equation of the form Ax=b is called the matrix equation, where A is an m×n matrix, x is an n×1…

Q: What is the volume of the solid formed by revolving the region bounded by the graphs of a2 = 9y and…

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Q: Ex. (12) Solve [D2+3D -4]y=2sin (5x) Sals-

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Q: sin 3t f(t) t

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Q: Using Modified Euler's Method, approximate the initial value problem for various values of x given…

A: Given y′=9x2-4x+5, y(-1)=0 , h=0.2, y(1)=?Here, x0=-1,y0=0, h=0.2,…

Q: We consider the vector space R3 which has the standard basis S = {e1,€2, €3}, where e; is the i-th…

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Q: A tank is being filled with a liquid. Z (1), given below, is the amount of liquid in liters in the…

A: For the inverse of linear function we replace input variable as output variable and vice versa.

Q: Let A be a 7x7 matrix with the characteristic equation ita - 6)(A - 15)2 What are the possible…

A: Given that A is a 7×7 matrix with characteristic equation  λ4λ-6λ-152 To find: Possible dimensions…

Q: .Use the De Moivre's Formula to show that if z = (cose + isine), then z" + ; ÷= 2cos (n8) and (금) 3…

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Q: Find the real part of the length of the vector v° = (5 + i, –3 – i)

A: Use the given vector.

Q: B. Find the indicated powers of the given complex number. Express the result in polar form, then…

A: We have to find   -3 + 3i31  and express this result in polar and rectangular form.

Q: Solve the equation. dy dx

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the point S so that ray (PQ) and ray (RS) are each of the same vector where P = (2, 5), Q = (1,…

A: For two vectors to be equal, their magnitudes and directions must be the same. The formula to…

Q: a.JFind the equation of the sphere that has a center at (2,1,4) and a point on the sphere at…

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Q: You save 500 each month by depositing into an account earning 7% monthly. After 15 years you stop…

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Q: π L1 2. z(4 +s),

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Q: Obtain the X-value of vertex for the parabola defined by y = x2 +8x - 5

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