Use the parametric equations of an ellipse, x = 3 cos (0), y = 4 sin(0), 0≤ 0 ≤ 2T, to find the area that it encloses.

Q: Use the separation of variables to find, given partial differential equation

A: Given the partial differential equation is                              k∂2u∂x2-u=∂u∂t,    k>0…

Q: Problem 10. vectors of the matrix Find the characteristic polynomial, the eigenvalues, and…

A: Solution :-

Q: Hello, How can I integrate Z2  sqrt (9+Z2). This is not a graded assignment please.

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Q: In your answers below, for the variable > type the word lambda; for the derivativeX(x) type X'; for…

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Q: solve: fx"- 4x-3y=et-6 5x+y + 4y = 8+ cost

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Q: In the quadratic equation Ax²+BX+C =0' describe the roots when B2-4AC is positive. O The roots are…

A: Roots of quadratic equation

Q: e²-s L-1 s(s-3) O [(-1/3)+e^(3(t-1))/3] e^2 U(t-1) O [(-1/3)+e^(5(1-1))/3] e^2 U(t-1) O…

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Q: Let A, B, C be three non-empty sets. Suppose that A× C = B× C. Prove that A = B

A: Here given that A, B, C be three non-empty sets. And suppose that A×C=B×C. We have to prove that…

Q: To integrate x3 ex2 x " 0x we apply integration by parts and in the form u dv, dv is set as:

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Q: Plot the following curves in polar coordinates. 4. r r = sin() 5. r= 1 + cos 50 6. r² - sin 0

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Q: Definition: If A, B E Matnxn (C), we say A and B are conjugate if there is an invertible matrix CE…

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Q: Consider the following subsets of real plane R termine with graph: Arcwise connected A = ((x,y): 0 ≤…

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Q: Problem 6. ing holds. Let W₁ and W₂ be subspaces of a vector space V. Show that the follow- W₁UW₂ is…

A: Given: W1 and W2 are subspaces of a vector space V. To show: W1∪W2 is subspace of V if and only if…

Q: Use the linear programming diagram below to answer the question that follow. y B (c,d) Feasible set…

A: To find the given points A, B, C, D :-

Q: Graph the equation 9x² - 24xy + 16y² - 80x60y + 100 = 0 relative to the 'y system (with rotated…

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Q: g mall, restaurant c

A: Given, in certain shopping mall, restaurant charges are  125 150 200 165 175 190 230 180

Q: Qt Define fct) = {ext tie + cost if t solve: y(3) - 2y (²) + ý' - 2y = f(t) y(0) = 1, y'(o) = 2, 4"…

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Q: Q2: The table below represents the vertical coordinates of the hydrograph of a rainstorm over a…

A: The solution is given below

Q: (e) Two different matrices may have the same eigenvalues.

A: We consider the two different upper triangular matrix A and B

Q: FLM SWAYY Praw are function in cacn case. Q2. Find the exponential Fourier series for f(t) = { 0<t<1…

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Q: Given the function y(t) with y(0) = 1, then False True L (y² + ²) = SY(s) - 1 + y(s)

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Q: Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing…

A: Let at any instant t, The weight of salt in tank A is 2 And tank B is y By using given conditions…

Q: Solve Usiy: Gaux Sied! Meble 500 500 500 1500 ич L43 1000 HU₁ Uz 1000 1000 1000 1000 1000

A: As per the question we are given a grid with temperature distribution u And we have to find the…

Q: As you are walking in the forest you look up just as a boulder becomes dislodged from the side of a…

A: Let us solve the given problem in the next step.

Q: + 4x² - 4x1 - 8x2 + 2x² + 4x1 + 4x2 R-4x² 3 2.2

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Q: 8+89 78 ¹}₁-T 7

A: The given expression is s+2s2-6s+8 make the partial fractions of the given expression…

Q: Solve each of the follwong differitial equations using Laplace transform. All initial conditions are…

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Q: Decide, with proof, which of the following form a basis for a topology on R, stating clearly any…

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Q: Let A & M and μ*(A) < oo. st B₁, B2,..., BEC, k <co with Bin B „²(AAŬB₂) <« j=1 any two sets E₁ and…

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Q: 29. Performance Task The Oval Office in the White House in Washington, DC, is actually elliptical.…

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Q: 1. Given a two variables function z = f(x, y) = √√√36 - 4x² — y². (i) Determine the domain and range…

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Q: uy uz ux fff dx dz dy ly lz 1x represents the volume of the region in the first octant that is…

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Q: The inverse image of the disk | z |< under T(z)=is z+1

A: You will find solutions in next step

Q: Use the power series 1 -Σ (-1)^x, x < 1 1 + x n = 0 to find a power series for the function,…

A: The Maclaurin series is a special case of Taylor series. When the Taylor series is centered at any…

Q: Find the set A on which the sequence {fn} converges pointwise. Find the limit function. Choose two…

A: According to the given problem we have to do only two parts of our choice So we select Ist and third

Q: Let (S,F,u) be a mee e B₁, B2 E F satisfying (E 1) = μ(B₂) for any pair of B₁) = 0. Then ao-algebra…

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Q: The auxiliary equation of the differential equation -5y""+y' + 2y = 0 is -5m² + m² + 2m = 0. O False…

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Q: 1. Prove or disprove that (pg)→r and p(q-r) are equivalent.

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Q: Problem 8. In R4, let W be the subset of all vectors a1 a2 V = az a4 that satisfy a4a3 = a2-a1. (a)…

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Q: 18.5 Given these data 1.6 X 2 2.5 3.2 4 4.5 f(x) 2 8 14 15 8 2 (a) Calculate f(2.8) using Newton's…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: Plot the point that has the given polar coordinates. (-3,1) x/2 0 x/2 x/2 x/2 0 Give two other polar…

A: Any point on the polar coordinate system can be represented using the ordered pair: r, θ. The…

Q: C Let a and C be positive constants. Let be с the upper semicircle (x − a)² + y² = a² y ≥ 0, from…

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Q: Let X be a normalized space. holds in general for x E X and y EX: ||x*y|[ <||x|*|ly|l Prove or…

A: As per the question we have to prove/disprove the following inequality : ||x*y|| ≤ ||x||*|y||  ,…

Q: 2) For the Fourier series of the function f, ao + Σo acos (kx) + bxsin (kx) we have |bk| ≤ 211/11.…

A: Solution:2)b)FalseWe can solve it by taking a simple exampleFourier series of any function f is a0+…

Q: Prove that any subgroup H (of a group G) that has index 2 (i.e. only 2 cosets) must be normal in G

A: To show that H is a normal subgroup we have to show that every left coset is also a right coset. We…

Q: 4. Let D be the region in the first octant bounded by the coordinate planes, the plane x + z = 1 and…

A: D be the region in the first octant bounded by the coordinate planes, the plane x+z=1 and the…

Q: Problem 2. Let f be a homomorphism from a group G into a group H. Prove that f is one to one if and…

A: Let f be a homomorphism from group G into group H. Suppose f is one to one . We need to show that ,…

Q: Make a linear systems only for this problem. The sum of the digits of a 3-digit number is 11. If the…

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Q: (Show your solution using Excel) Find the positive root of the equation ex = 3x using Regula Falsi…

A: F(0) = 1F(1) = -0.28171817Therefore , root lies between 0 to 1a=0 ; F(a) =1b=1 ; F(b)…

Q: The auxiliary equation of the differential equation -5y""+y' + 2y = 0 is -5m³ + m² +2m = 0. O False…

A: