The perimeter of a square is 50 cm. What is the circumference of the largest circle that can be drawn inside the square?

Q: .Solve for v(t) in the following integro-differential equation using the phasor method and write the…

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Q: Certain operating savings are expected to be zero (0) at the end of the first six (6) months, to be…

A: Solution :-

Q: dy Solve dx and find the particular solution when y(1) = 3 %3D %3D x(x+ 1)

A: given differential equation dydx=yxx+1 claim- solve the differential equation and find the…

Q: Solve the differential equation: y' = 2et; y(0) = -1 A. y = 2et – 1 C. y = 2et – 3 B. y = 2et – 2 D.…

A: Given y'=2et; y0=-1. Taking the Laplace tranform of both sides of y'=2et, we get,…

Q: 4. Is y' = sin (ty) separable a) not separable c) separable %3D b) for y =, yes d) with a proper…

A: We have to check whether the given differential equation is variable separable or not.

Q: Which of the following series diverge? I. cos (2n) n=1 II. 1 1+ - п n=1 1 n + n2 III. n= (A) II only…

A: Here we can use divergence test to check whether a series diverges or not. Divergence test states…

Q: By using vector scalar multiplication and vector triple product, prove the identity below: Ã x [Ã x…

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Q: a. ry dx -4y = x°e*

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Q: c) y" - 4y' + 49y = 0 y(0) = 0, y'(0) = 5 %3D d) y" -2ytv + y" = 0 %3D

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Q: Solve the following recurrence relations. 4an-2,n > 2; ao 0 and aj = = 4. a) an b) а, 3D 2ад-1+…

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Q: Solve the differential equation: y' - y = e-t ; y(0) = 1 A. y = -* C.y= * A. y = e - 3 C. y =et +e 2…

A: Given differential equation is y' - y = e-t ; y(0) = 1 As L{y'} = sY(s) - y(0)

Q: 2. A tank of water in the shape of a square pyramid is leaking water at a constant rate of 4…

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Q: Convergence of functional series 1. Prove that each of the following series converges absolutely:…

A: We have to prove that the given series is absolutely convergent.

Q: Use Webster's method of apportionment to solve the following problem. 2. Suppose a nation has 5…

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Q: 1.1 A mathematical model that describes a wide variety of physical nonlinear systems is the…

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. (-1)"…

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Q: Any soluhon äf thuis equation is called Legendre's clifterential equation Considir the (1-x²) Y" -…

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Q: Montserrat has $100,000 to invest in a saving account. She receives a steady interest rate of 3.75%…

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Q: : Find the exact area of the surface obtained by rotating the curve y? +x= 5, 3sxs5 a) about the…

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

Q: Find delta value for the limit of x-->0 of tan5x/sinx when epsilon = 0.1

A: Introduction: The limit of a real-valued function is the base of differential calculus. A single…

Q: Leave your answer in exact form; if

A: Given,

Q: Simpson's rule to calculate approximately the

A: simpson's rule,

Q: Proof by contradiction that if n is a positive integer, then n is odd if and only if 5n + 6 is odd

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Q: Estimate the length of the curve y=0.5x² over [1,4] using n=6 and trapezoidal method. Also determine…

A: In trapezoidal rule the value of a interval is computed by ∆x=b-an. In the above formula a is the…

Q: Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated…

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Q: 3. (2x + j3y)? - 6 - j12 = 0

A: (2x + j3y)2 = 6 + j12

Q: Apply the Jacobi method to solve. Iteration is to be stopped if either one of the required values…

A: Given the equations  5x1-2x2+3xn=-1-3x1+9x2+xn=22x1-x2-7xn=3

Q: Ken borrowed $2000 from Sam at 8% per annum. After 6 years he cleared the amount by giving $2600…

A: From the given information, we have to find the cost of the watch.

Q: Do not use a calculator in this question. (6+3 V5) cm area of this triangle is (36+15 V5 cm2 (ii)…

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Q: Com idr the Leyendre's difterentral equation n-constant -x²) y" - 2xy t nents) y=D0 Any soluhin…

A: Given the Legendre's differential equation 1-x2y''-2xy'+nn+1y=0....(1) where n is a constant  We…

Q: Consider the following differential equation. y" + 4y' + 4y = e2x + x. ) Find the general solution…

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Q: A certain chemical decomposes in which its equation satisfy the general exponential equation as…

A: Solution : Given that  General exponential equation    y = y0 ekt   ---(1)

Q: Estimate the length of the curve y=0.5x² over [1,4] using n=6 and trapezoidal method. Also determine…

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Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: 8. (The argument principle and Rouché's theorem) (a) Determine the number of zeros in the right…

A: (a) The given function is pz=z3+z2+9z+4 let's consider Pz=hz+qz such that hz=z2+9z+4 and qz=z3…

Q: Apply the Gram-Schmidt orthonormalization process to transform the given basis for R" into an…

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Q: Let K be a field. Consider the following set {(: :)e R:= a 0 a2 a1 (a) Show that (R, +) with the…

A: Let K be a field. R = a10a2a1 ∈ K2×2  : a1 , a2 ∈ K We need to show that , R , + with matrix…

Q: 3. Prove that if n is odd, then 8 divides n2- 1. Prove that 6 divides n п. 4. Let n and k be two…

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Q: Find the a and y intercepts of the equation: – 7x – 2y = 56 | The intercepts are: x intercept = (…

A: The solution is given as

Q: Find the solution to the system 2х —8y + 5z %3D-5 2х+ у—z%3D12 -5x+3y+9z=-17 .using (a)Jacobi…

A: Given equations  2x-8y+5z=-52x+y-z=12-5x+3y+9z=-17 We have to us¡ng (a) Jacobi lterative Method and…

Q: Express f(x)= 4+ 6 x² + 7 x + 2 in terms of Legendre Polynomials.

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Q: Find the Laplace Transform of the following functions 1) f(t)=t cos(@t) 2) f(t) =t sin(@t) 3) f(t)=t…

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. (-1)"…

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Q: when solving curvilinear problems, when do we use rectangular components and when do we use the…

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Q: find the fourier series for the half-Period sine of the function fx) = sinx inthe period 8. xx Then…

A: Given that, f(x)=sinx in the period 0<x<π. ∫n=1∞1(2n-1)2(2n-1)2. The objective is to evaluate…

Q: Find the equation of the tangent plane at the point a = xo = 4, y= yo = 1 of the surface z = f(x, y)…

A: Given z = f(x, y) = xyex+y

Q: Determine one real root of 2xcos2x – (x – 2)* = 0 on the interval (2, 3)using the Bisection Method.…

A: Given  -(x-2)2 + 2xcos(2x) = 0 Let f(x) = -(x-2)2 + 2xcos(2x)

Q: Find the steady periodic solution xsp = C cos (wt – a) of the given differential equation mx" + cx'…

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Q: Find the inverse laplace transform of 2s s2+9

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Q: Write the equation of the line show in the graph below. 12+ 10 4 2 12 -10 -8 -6 -2 4 10 12 -4 -6-…

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