Find the length of the following curve at the given distance. Rie). cos'e ?a sin? t } Cos t i 2

Q: Find a general solution of the differential equation: у" — 4у" — Зу'+ 18у %3D Зе*

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Q: Show that every ring R is isomorphic to a subring of R[x]

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Q: Let x(1) = c,cos(5 t) +c,sin(5 t) be a two-parameter family of solutions of the Let y =c,e*cos(5 x)…

A: To find which of the given option is correct, about the given differential equation :-

Q: (x^2-x)y"-xy'+y=0

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Q: 9. Use the method of undetermined coefficients to solve the given system -4 X + 4t +9e X' %3D

A: To find- Use the method of undetermined coefficients to solve the given system X' = 1-441X + 4t +…

Q: Evaluate [[(x- )d4 ,R: the region bounded by y =x & y =x R

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Q: nts, in a line, or in a circle? sphere intersects the xz-plane ? sphere intersects the yz-plane ?

A: Introduction: If (a, b, c) is the sphere's center, r is the radius, and x, y, and z are the…

Q: 3) Con sider the Rolowina opo otor A: L'co,) l'Q0, Docs A heve eigenvalues? Find Hhe qpetrumof A

A: As per the question we have to check whether the operator A has any eigenvalues. Then we have to…

Q: Q) find Fourier series on [0,21] (3) ƒ(x)=cos x = COS X

A: find the fourier series on0,2π fx=cosx fourier series is given by…

Q: Which sets are proper subsets of set A? A = {1, 3, 5, 7, 9} Select all that apply. O {1, 2, 3, 4}…

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Q: Based on the density graph below, what is the probability of a value in the sample space being…

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Q: Solve the following system 2x1 – 6x2 – x3 = -38 -3x1 – x2 + 7x3 = 34 -8x1 + x2 – 2x3 = 20 | using…

A: Coefficient matrix not diagonal

Q: Question Identify any misrepresentation issues in the given graph, Select all that apply. 100 80 60…

A: Given, Graph showing temperature variation in Fahrenheit Vs hour of the day. To check the…

Q: Suppose the function g is on the interval [a, b], and |g(x)|< B for all x E R. I) Prove that |g(x)?…

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

Q: Iuse series representation to approvimate the integral Hint i Sum the first four terms of the series…

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Q: Let R be the relation on the set of ordered pairs of positive if a +d = b+ c. Show that R is an…

A: Introduction: An equivalence relation is a type of binary relation in mathematics that should be…

Q: Find a particular solution to -18.5e-21 y" +4y +4y = t2 + 1 Yp =…

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Q: A tank initially contains 100L of brine in which there dissolved 20kg of salt. Pure water flows into…

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Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 8t – t³, In(t))

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Q: 1. Find the unique solution first-order boundary value problem 2ru, +4r u, +6u=-2zte u(0, y) =…

A: As per our guidelines we are supposed to solve only one question that is the first one.For the…

Q: et A = {a}

A: Given,        A = a

Q: 5. (a) Consider the I.V.P dA kA A(0) = Ao dt as the model for the decay of a radioactive substance.…

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Q: Solve the differential equation (D+ + 5D² + 4) y = sin x + cos 2x.

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Q: B) Find the unique polynomial P(x) of degree 2 or less such that P(1) = 1, P(3) = 27, P(4) = 64…

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Q: In (x,y,z) space we consider the filled-in triangle T that has the corners A(0,0,3), B(0,2,0) and…

A: see the attachments

Q: 3. Find the component form of v given its magnitude and angle e with the positive x-axis: V = 8, e =…

A: Given, |V|= 8, θ= 150° We have to find component form of v Where V = V1 i + V2 j = &lt; V1 , V2 &gt;

Q: Q3) Use the Newton-Raphson method to find the root of f(x) = -0.5x *(4 – x) – 2 with initial guess…

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Q: Evaluate the integral by making an appropriate change of variables. 5 cos 9 dA where R is the…

A: where are is the trapezoidal region with vertices(8,0),(10,0),(0,10), and (0,8).

Q: (6) If u, = x-Pa(x)Pn-1(x) dx, show that nu, + (n – 1)u,-1 = 2, | and hence evaluate u.

A: To get the desired result first we will the recurrence formula for pn(x). Then after simplification…

Q: 9. Use the method of undetermined coefficients to solve the given system 4t +9e X' = 4 %3D

A: Given that X'=1-441X+4t+9e6t-t+e6t            (1) let                                 A=1-441 The…

Q: (r' x r") · r" Ir' x p"|2 Find the curvature and torsion of the curve x = 3 sinh(t), y = 3 cosh(t),…

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Q: Apply the following transform to the point (1,-1, 2). Find the coordinates of the transformed point.…

A: Given: Let us consider the given matrix is, A=120-10-121-21-13-1011

Q: 1. Use Green's Theorem to find the counterclockwise circulation and outward flux for the given filed…

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Q: For the following system of linear equations, one equation has been omitted from the system. 2h + 4n…

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Q: Find the quotient of z1 & z2, leave answer in trigonometric form: z1 = 2 – 3i & z2 = 1 – V3i

A: Introduction: Division is also performed between two complex numbers. But in order to convert the…

Q: Use False Position Method. • Compute Es according to 4 significant figures according to the formula…

A: we have given function  defined on the interval [2, 3] Clearly  Hence we confirm that g(x) has a…

Q: 3)L. y" + y – 6y = (12 – 16x)e*. i Consider the nonhomogeneous DE: A) Verify that y, = 4xe* is a…

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Q: write the Princi fal Partof the function at itsisamtal Singular Point and detelmine whether the…

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Q: (6) If u, = x-Pr(x)Pn -1(x) dx, show that nu, + (n – 1)un-1 | and hence evaluate u.

A: To get the desired result first we will use the recurrence formula of pn(x) and rearrange it after…

Q: 00 and bi liz =1 ニ 1 1 4 3 3 こ 16 16 Findd acu) and ce) with syodem of recucrens sceladianships)

A: the generating functions a(x) and b(x) with system of recurrent relationships

Q: Sketch a continuous function satisfies all the following conditions and label your sketch with the…

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Q: OI tr surface obtained by rotating the curve 1 y = 4 1< x < 2, 3x about the x-axis. b). Consider the…

A: a. Consider the surface y=x34+13x, 1≤x≤2. To find the exact area of the surface when rotated about…

Q: Find a particular solution to -18.5e-21 y" +4y +4y = t2 + 1 Yp =…

A:

Q: ) If we substitute the polar coordinate x = r.cos0 & y = r.sin0 continuous function w-f(x,y) that…

A: Here we use basic chain rule to Show this

Q: use Euter me thed to solve y's 2-24

A: Let us consider the given function y'=f(x,y), y(x0)=y0 Solving using the Euler method  Then the…

Q: e.Solve the diffusion problem uų

A: Given,           ut=uxx in 0&lt;x&lt;1                    ...(1)            u(0, t)=u(1, t)=0…

Q: Q1. For the periodic function: f(2) = {* r+1 -1<r<0 1 05ISI Determine: 1. Is it Odd, Even, or…

A: Given, f(x)=x+1 , -1≤x≤0           1       ,    0≤x≤1 To find: a) Whether a given function is even,…

Q: 1. Solve the following linear systems using Cramer's Rule and Gauss Elimination Method. 0.5x + 3.5y…

A: Since you have posted a multiple question according to guildlines I will solve first question{Q(i)}…

Q: Show that (p-q)–(r¬s)and(p-r)-(4-s) are not logically equivalent.

A: To show that p→q→r→s and p→r→q→s are not logically equivalent.

Q: 3. Find the mean, median, mode, and Standard deviation of the following data: 15, 11, 18, 9, 15, 18,…

A: The mean can be calculated as follows: