Q.1 Find Laplace Transform of the given functions: 1. f(t) = (0, 0≤t

Q: 5. m 1, k-8, b=0 Underdamped Overdamped Critically damped Undamped; Natural period a

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Q: problem Solve the following equation the laplace transform. using 2 2 aw a t² w (x₂0)=0 c²a² w дяг…

A: The given P.D.E is                        ∂2w∂t2=c2∂2w∂x2 , wx,0=0, ∂wx,0∂t=0 Also w0,t=sint    ;…

Q: A nature reserve has one bird of an uncommon species which frequents the large expanse of reed beds…

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Q: 2. Consider the matrix A = (-₁-¹) Y, -9-P guarantees: (a) that A has two real eigenvalues? (b) that…

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Q: Find the Fourier Series of the given periodic function. 4, f(t) = (-1; if-T5 t < 0; f(t + 2m) = f(t)…

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Q: s 19 a prime in the Eisenstein integers? is 79? If they are, explain why, if not, display a…

A: Given: Primes in Eisenstein integer. To find: a) To check wheater 19 and 79 are primes in Eisenstein…

Q: 2. 2y dx - x dy = 0

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Q: 2. The following is the historical data of inflation rates in the Philippines from 2011 to 2019.…

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Q: 4. How to solve optimization problem and under what circumstances would the answer be…

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Q: The asymptotes of the curve r = are 2a (a) rsin (3-0) = √3 √3 (17-0 3 2a √3 o)= (F — 3 a (b) r sin…

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Q: Solve the following system of equations by Gauss-Jordan in terms of k, then find the values of k for…

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Q: A city is described parametrically by the equation r = (ai + bj+ck) + svi + tv₂ where v₁ = 3i+j+ k…

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Q: Find the least squares quadratic & bj xj which best fits curve Y = sin(x)

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Q: Evaluate D = ܚ ܘ ܝ ܗ 2 4 7 9 -2 -8 -3 695 ܗ ܗ 4735

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Q: 2. Ifƒ (x, y) = log (x² + y²), then f +f, is equal to yy 1 (a) x² + y² (b) 0 y²-x² (c) (d) • (x² +…

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Q: Let A be an n x n matrix. Let n-1 c(z) := det(zIn − A) = 2² - Σckzk - k=0 be the characteristic…

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Q: Solve each of the following by Laplace Transform: dy 1.) +2- + y = sinh 3t – 5 cosh 3t ; y (0) = −2…

A: We have to find the solution to the given equation using the Laplace transformation.

Q: Find all solutions of the Diophantine equation 1245x-365y = 4567

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Q: Is the graph below planar? Is it maximal planar? if it is not a maximal planar either remove or add…

A: Given: Graph G To find: To check whether given graph G is a planar or not.

Q: Q3\Find trigonometric function =3/2

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Q: Use the induction argument to prove that 1+2+ + n = n(n+1) 2 for all natural numbers n ≥ 1.

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Q: Prove that the only idempotent elements in an integral domain R with unity are 0 and 1.

A: Idempotent element : An element a in a ring R is said to be an idempotent element if a.a = a .…

Q: 2. Consider the groups (R, +) and (Rx R, +). Define the map: RX (RXR) → Rx R defined by r(x, y) =…

A: Note:  Since we can solve at most one problem at a time we have solved the first problem that you…

Q: (f(t)} = (s > 0) f(t) (2, 2) 1 5. L Use the definition of the Laplace transform to find (f(t)).…

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Q: Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² = 4…

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Q: The slope field for the equation dP/dt = 0.0333333P(30 – P), for P≥ 0, is shown below. Pl 11 1 1 1 1…

A: The given differential equation is dPdt=0.033P30-P , for P≥0. To find:(a) In which interval P is…

Q: dx Show that a solution of the differential equation is y = (1 + 2x) sin3x Sketch the graph of y(x).

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

Q: Four asymptotes of the +y+1=0 forming a square are (a) y = 0, y = 2, x=0, x=2 (b) y = 0, y = 4, x=0,…

A: In this question, the concept of asymptotes is applied. Asymptotes Asymptotes are imaginary lines…

Q: Obtain a family of solutions using the indicated process. For those items with initial values,…

A: solve using substitution  2x-y+1dx-y-2xdy=0 with initial condition y1=2

Q: . Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² =…

A: We will find intersecting curve and then parametrize it .

Q: Find the value of (D) solve in detail 1219 1.85 (0.015/60). = 20.88 * 4.87 D

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Q: $ Σ(-1) () is n=1 Verify using the Alternating series test that the series convergent

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

Q: 1. If f(x) = x³ + x is a periodic function with period 2π, then the Fourier series will have the…

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Q: . A varies directly as b and c and a-90 when b-6 and c-3.Find a when b-4 and c= ½

A: Since you have posted multiple question and we can answer one question. So, answered the first…

Q: a Let r Q (0, 1). Write r = where a 21 and b 21 are coprime natural numbers. Show that there exists…

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Q: Solve d'y dx² cot x dy - sin² sin²x.y - dx = cos x - cos³ 3 OHS X.

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Q: Find the first-order and the second-order Taylor formula for f(x, y) = (Use symbolic notation and…

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Q: problem: Solve the following equation using the toplace transform. 2² w 2 z²w дяг a t² I sint с ₂ W…

A: Introduction: An initial boundary value problem (IBVP) is said to be properly stated mathematically…

Q: Water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. Suppose that the…

A: Given that water is leaking from a 2 foot tall rectangular tank at 0.1 cubic foot per hour. And the…

Q: 5. Consider the problem of taking the zeros of the the polynomial P(x) = ³x² - 6x over (2, 4). Below…

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Q: 2. It takes 5 hours for 3 men to paint a house. a. How many men would it take to paint the same…

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Q: Use the definition of the Laplace transform to find {f(t)}. (Write your answer as a function of s.)…

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Q: Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of…

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Q: В

A: Washer method : When the palaner region is rotated about a line parrallet to…

Q: Use Laplace transform to solve the partial differential equation: d'y dy ox² at -+xt where y(x,0) =…

A: The given P.D.E is ∂2y∂x2=∂y∂t+xt where yx,0=0, y0,t=0 and yx,t is bounded for t&gt;0 and x&gt;0. To…

Q: (1) Determine what comes next in the given pattern and provide solution/explanation: -7, 2, 11, 20,…

A: Given pattern, -7,2,11,20,__,__ Firstly compare the first digit is -7 and 2nd digit is 2 This…

Q: Sketch the graph of the function

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Q: If S., t, = \n(n+1)(n + 2)

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Q: dY 2 (-²1) Y. Y, dt (a) find the general solution; and (b) find the particular solution for the IC…

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Q: Please identify some species having 13, 21, 34, and 55

A: Here we give some examples of flowers that have a Fibonacci number of petals.