Ans: Find the remainder (smallest nonnegative integer) when 1015!-1010! is divided by 1013-

Q: (c) Find the inverse z-transform of Y(z) = (z-1)(z+3) * [Hint: Express Y/z in partial fractions]

A: Inverse Z transform

Q: 4e-2s 1. Calculate the inverse Laplace transform C-1 J (-2s – 4)e¬³ s2 + 6s + 25 (s + 1)3 2. Solve…

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Q: Let F(n) = Ea2n P(d). Show that if F(1) = 1 and that if n > 1 factors as %3D am then la:/2] a1 F(n)…

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Q: Points B = (5,9,7) and c = (9,3,7) are on a sphere centered at A = (1,2,3). To two decimal places,…

A: This is a problem of Differential Geometry.

Q: о3 - 1) у 3 alculate

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Q: Solving a differential equation using the Laplace transform, you obtain Y(s) = L{y} to be 24 10 4…

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Q: a) Find Y(s)/X(s) for the following differential equation d³y dydy. d?x dx +6+5y=- +2+9x, where the…

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Q: 4. Consider the following boundary value problem for y(x) on 1(-2, 2]: (*) y" + 6y + dy = 0, y(-2) =…

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Q: sin 8 cos (cos a cosec 0) do 1/2-a (1-cos a).

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Q: Determine whether there is sufficient information for solving a triangle, with the given combination…

A: The Law of Sines states that asin A=bsin B=csin C. Solving a triangle is to determine the unknowns…

Q: |미350, | w|= 12, 0=35° A) B) W W

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Q: Define a relation R on the x-y plane as follows: Given two points (x1 ,y1) and (x2 ,y2) in the x-y…

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Q: Prove the following theorems using direct proof, indirect proof(contradiction, contrapositive),…

A: We have to prove or disprove the following statements : (i) For every pair of positive real numbers…

Q: and ug at the points Pi, P2, P3, and Pa respectively, given uz + us + 100+ 100 4 200 + uz + uz + 100…

A: From the given statements, we have to solve the system by finding the coefficient matrix.

Q: Find the solution. (x+e") dy – dx =0 A x=ce' + ye* B x=ce + ye y=ce' +xe D y=ce*+ ye

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Q: 3. (Analytic branches of multiple-valued functions) (a) Let w+ w denote the principal branch.…

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Q: Which of the following is/are true? Select one or more: a. Given e = 0.03, a suitable value of & is…

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Q: Solve dy/dx =( y+x-2) /(y-x-4) Equation s reducible to homogenous form

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Q: 2. Determine the Fourier cosine series for the following functions: 3 – 2r? +1 for 0<I<a 7 for…

A: If f(x) is an even function with a period {\displaystyle 2L}, then the Fourier cosine series is…

Q: Solve the following heat flow problem:

A: Given,            ut=3uxx, 0&lt;x&lt;π, 0&lt;t&lt;∞                ...(1)u(0, t)=u(π, t)=0,…

Q: Describe the type of intersection that exists, then, determine the intersection.

A: First find row reduced eclone form then calculate intersection.

Q: Proble Consider the following graphs and determine the degree of each vertex : d. C (ii) b. (iii)…

A: find degree of each vertex  every edges count 1 and self loop count 2

Q: cosz 3 3 Let f(z) and C is |z| = positively directed and C is ]z| = positively %3D %3D (z²–1)2 2' 2'…

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Q: 5. Show a separate graph of the constraint lines and the solutions that satisfy each of the…

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Q: -X f(x) =x + e Solve this question by the Bisection method on the topic of solution of Algebraic and…

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Q: 6 ý x In x=y 2/y-1 (も 2y=y cotx

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Q: Find the solution. dy 3+9y =2ty53 (A) y- 3er - 3 (B © y - 34-3e2

A: To solve the given differential equation first we will arrange the differential equation in the form…

Q: ie LAPIACE nstorm OT 1. f(t) = e-5t cosh(6t) – (9t)"/2 2. f(t) = t³ cos(5t) + cos(2at) cos (3at)

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Q: Evaluate This Integral if curve C consists of curve C₁ which is a parabola y=x² from point (0,0) to…

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Q: Relate the concept of Laplace Transform to solve the following problems. A. Compute the Laplace…

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Q: For each scenario below, choose the graph that gives the best representation. (a) A sight-seeing…

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Q: Solve dy/dx =( y+x-2) /(y-x-4) Equation s reducible to homogenous form

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Q: For the given differential equation, apply the Laplace transform and solve for Y(s) = L{y}. y" + y'…

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Q: Find the solution. (40-4D- 3D2 - 20 + 1ly = 0. В

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Q: Solve the differential equation by using the separable equation method 2 dx -sin 2t = 3 7 dt

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Q: Find the solution. (D3 +7D2 + 190 - 13ly =0; when x =0, y=0. y =2, y"=-12 A B) y -esinde D y =e…

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Q: f(x) =x – x + sin(x) – 1 - 1 Solve this question by the Newton-Raphson method on the topic of…

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Q: A solar oven is to be made from an open box with reflective sides. Each box is made from a 30-in by…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: ind the volume

A: Given,

Q: Solve the following heat flow problem: 3uxx, 0< x < T, 0<t <∞ u(0, t) = u(n, t) = 0,0 < t < ∞ u(x,…

A: Using separation of variables and superposition principle and Fourier sine series.

Q: 3 The population of the city of Miami is approximately 463,300 and is increasing at a rate of 3%…

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Q: Find the solution. y'- y =y"e* A B D y

A: Solution of the differential equation

Q: If M and N are metric spaces, the Cartesian product M x N is again a netric space with the distance…

A: We have given that , M and N are metric spaces. We have to show that , M × N is again a metric space…

Q: y" + 6y"+ 11y' + 6y = cos(x) +e^{-x} %3D

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Q: Find the solution. (D2 - 60 + 9ly = 0

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Q: Lemma 36 Let F CK be an algebraic extension. LetL be an

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Q: n the vector space P2, of polynomials of degree less than or equal to 2, with real coefficients,…

A: On the {\displaystyle n}-dimensional Euclidean space {\displaystyle \mathbb {R} ^{n},} the intuitive…

Q: Solve the following heat flow problem:

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Q: Evaluate y*dV, where E is the solid hemisphere x? + y? + z² 0. E (Hint: spherical coordinates)

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Q: Consider the functions y = sin x and y = cos x . Round your answers to the nearest degree. a.) Find…

A: (a) Let the  a,b,c,d be the first positive solution of sinx=0.60182≈35 So, a is in the first…