Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your answer as a function of t.) 4 S 1 - 36

Q: ³ [F Evaluate F. dr. F(x, y) = 9xi + 8yj C: r(t) = ti + √4-t²j, -2 ≤ t ≤ 2

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A: Given that : function   f(t)=t0≤t<11t≥1 To Find : Laplace transformation of f(t)

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Q: hot (1603).png hot (1597).png Determine (without solving the problem) an interval in which the…

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A: Solution :-

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Q: -10 -8 -6 -4 -2 Submit Question 10+ f(r) 14 12 10 8 6 4- 2 -2 -4 -6- -8- -10- -12- -14+ -16+ Find an…

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Q: Use the Laplace transform to solve the given initial-value problem. y" - 3y' = 8e²t - 2e-t, y(0) =…

A: Solution :-

Q: A DIGITAL CHIP MADE BY YOUR. MICROELECTRONICS DIVISION, COUNTS CONTINUOUSLY IN THE SEQUENCE: 1024…

A: The counts of the chip are 1024,2048,4096,8192,.... Now, we can see that 20481024=40962048=2 Each…

Q: Given: B and D are midpoints of the sides AC and CF, BD = DE Prove: BD || AF. (Use two-column…

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Q: 3. Let f(x, y, z) = 9 (√√x² − 4y² + 2²) √√x² + 16y² + 2², where g is some nonnegative function of…

A: Given: Let us consider the given data, fx,y,z=gx2-4y2+z2×x2+16y2+z2 The surface S is given as,…

Q: .y" +4y= cos x, y' (0) = 0, y' (n) = 0

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Q: e the following constrained optimization problem using the method of Lagrange multipliers: max (x³ +…

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Q: Express the following function in terms of unit step function and hence find their Laplace…

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Q: Show that the set of all polynomials with integer coefficients is denumerable

A: Given : set of polynomial with integer coefficient  To Show : set of polynomial with integer…

Q: A firm faces the following total revenue and cost functions. TR = 15Q - 0.20² and TC = 60+ 0.1Q +…

A: Breakeven levels of output is when total revenue is equal to the total cost. Given total revenue is…

Q: 2).  For an as follows, write the sum        an as a geometric series. a1 =  1 14 and  an an + 1

A: This is a question of infinite series.

Q: x² y² 9 4 2. Let C₁ be the ellipse + = 1 traced counterclockwise and C₂ be the paral- lelogram with…

A: Given: Let us consider the given vector field, F→x,y=1-y,x+ey2 And the define given curve, C=C1∪C2.…

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Q: x²y" - xy + xy = 0, y(1) = 0, y (L) = 0, L > 1

A: As per the question we are given a second order linear differential equation as : x2y'' - xy' + λy…

Q: Theorem: if I is a Positive implicative Bck-algebra Then (Lx),,Lo) is a BCK-algebra

A: Consider the given theorem, '' if X is positive implicative Bck-algebra then Lx,⊙,L0 is a…

Q: Which of the following is Eulerian graph? a. Graph F b. Graph E c. Graph B d. Graph C O a Ob

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Q: Prove that the messenger number M19 is a prime hence the integer n = 218 (219 -1) is perfect

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Q: Show that the differential equation x²y³ + x(1+y²)y' = 0_ is not exact, but becomes exact when…

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Q: ||r′(t) × r"(t)|| ||r'(t)||³ r(t) = 5 cos(7t)i + 5 sin(7t)j + 4tk Use the formula (t) = to find (t).

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Q: 5. Solve the following Laplace Equation With the conditions a²u a²u + дх2 дуг = 0 U (0, y) = F(y)…

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Q: Consider the following function. T: R² R³, T(x, y) = (√x, 3xy, √y) Find the following images for…

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Q: b B 490 9 a Note: Triangle may not be drawn to scale. Given the triangle above, find the following:…

A: Let us consider a triangle ABC right angle at B Sum of angle of triangle is 180° Properties of…

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = y""+ 2y" - y' - 2y =…

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Q: VIII. Evaluate the following definite integrals. (a) ₁²√³-5da

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Q: Let C₁ be the ellipse + = 1 traced counterclockwise and C₂ be the paral- 9 4 lelogram with vertices…

A: Given, The ellipse x29+y24=1F→(x.y) = 1-y, x+ey2

Q: (0-2) dy do With initial value problem // (0) = -1 - 2X - = 3 (8-2) seco tano

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Q: Eigenfunctions. In each of Problems 19 through 25, find the eigenvalues and eigenfunctions of the…

A: This is a problem of eigen value and eigen function of the differential equation.

Q: 5. Let S be the negatively oriented surface defined by R(u, v) = (u², v², uv), where (u, v) € [0, 1]…

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Q: y² 9 4 Let C₁ be the ellipse + = 1 traced counterclockwise and C₂ be the paral- lelogram with…

A: Given,  The ellipse x29+y24=1 F→(x,y) =1-y, x+ey2

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-¹AP is diagonal. (If not…

A: Solution :-

Q: Answer true or false. F(s) = s²/(s² + 4) is not the Laplace transform of a function that is…

A: Properties of Laplace transformation. L-11=δ(t)L-1as2+a2=sinatL-1aF(s)+bG(s)=aL-1F(s)+bL-1G(s)

Q: Find f'(3), where f(t) = u(t) · v(t), u(3) = (1, 2, -2), u'(3) = (4, 0, 7), and v(t) = (t, t², t³).

A: Introduction: The outside-inside rule, composite function rule, and function of a function rule are…

Q: Answer true or false. F(s) = s²/(s² + 4) is not the Laplace transform of a function that is…

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Q: Consider the matrix A = /a11 0 0 a21 a22 0 a31 a32 a334 What is tr(AA')? ] Show that |A| = [1 aii.…

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Q: 25. Consider the problem a²uzz ut, 00 u(0,t) =0, uz(L,t)+yu(L,t) =0, t>0 u(x,0) =f(x), 0≤x≤L. (a)…

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