If s(0) dt: 20z 4, then f (t) dt is -3 E) divergent

Q: y"- y'- 2y = 0; y(0) = -2,

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Q: e Divergence Theorem to evalu (4x + 10y + z²) dS Js

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Q: use the laplace transform to solve the initial value problem y''- 4y'- 4y = t^3          y(0) = 1,…

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Q: Use the Laplace Transform to solve the initial value problem y" + 5y + 6y = 6

A: Given, y''+5y'+6y=6 with initial conditions, y0=0, y'0=0. Apply Laplace transform on both sides of…

Q: Suppose that a point is moving along the path xy= 1 so that dy/dt=4. Find dx/dt when x=3.  dx/dt=?

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Q: 3. Use Laplace Transform to solve the initial value problem. y" 6y + 5y=0; y(0) = 1 and y'(0) = -3 -

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Q: If  x2 +y2+z2  = 9,dx/dt  =5 , and dy/dt  =4, find dz/dtwhen (x,y,z) =(2, 2,1).

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Q: dy Compute dt t=to .2 x+6 y = X-6 X = 4 to = 3. dy dt t=to (Simplify your answer.)

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Q: Use the Laplace transform to solve the initial value problem y" + 2y' + y = 4e-t; y(0) = 9, y'(0) =…

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Q: Find the location and velocity at t = 4 of a particle whose path satisfies dt dr (3t-1/2, 5, 8t) and…

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Q: dz dS 2 If S = z3 and -2 when z = 3, find dt dt

A: Derivative

Q: If r + s2 + y3 = 12, dr/dt = 4, and ds/dt = -3, find dy/dt when r = 3 and s = 1

A: We are given the relation by

Q: Use the Laplace transform to solve the given initial-value problem. y" - 5y' = 8et - 4e-t, y(0) = 1,…

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Q: dz Suppose that z = x³ – 3y?, x = 4(t³ – 1), and y = Int. Find using the Chain Rule. dt %3D -

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Q: Compute dy/dt`t=t0  y = (x2 - 2x + 4)2, x = 1/(t + 1), t0 = 1

A: To compute dydt at t=t0 Given  y=(x2-2x+4)2y=2x2-4x+8 and  x=1t+1t0=1

Q: .3 Suppose that w = x³yz + xy + z + 3 and x = 3 cos t ,y = 3 sin t , dw z = 2t. Evaluate dt t= ドIN

A: Ans:  we will use product rule of differentiation to solve this question.

Q: Provide an appropriate response. If xy + x = 12 and dx/dt = -3, then what is dy/dt when x = 2 and y…

A: We will find the value of dy/dt with the help of the given data x=2 ,y=5 and dX/dt=-3 as following.

Q: Find the value of dr/dt at t = 0 if r = (u2 + 7)^(1/3) and u^2t + u = 1.

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Q: Sow that 2 x² + y² + z² - c²t² is Lorentz invariant.

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Q: 2. Use the Laplace Transform to solve the following system x'= x-5y, y'=-5x+y, x(0)=1, y(0)=1.

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Q: Q2) Solve the initiai value problem by Laplace transform. y" +4y=cos 2t y(0) = 1 , y'(0) = 1

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Q: find the linearization at x = a: y = ex ln x, a = 1

A: fx=ex lnx,  a=1 Differentiating with respect to x, we get f'x=dexdx·lnx+dlnxdx·ex=ex lnx+1xex Now,…

Q: ==4-x² - y² for which z ≥ 0 with upw= rcle x² + y² = 4 that forms the boundar

A: The Stoke's theorem states that ∫CF·dr=∬S∇×F·dS Where z=gx,y and dS=-gx,-gy,1dxdy.

Q: - 3y' + 2y = e3* when y(0) = y'(0) = 0

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Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y"" + 3y" - 3y - 2y =…

A: The given differential equation is; 2y'''+3y''-3y'-2y=e-t,y(0)=0,y'(0)=0,y''(0)=1.

Q: Use the Laplace transform to solve the initial value problem. y" – y' – 6y = 2, y(0) = 1, y'(0) = 0…

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Q: dy t² +3 21. Find 9 if y = In dt /1-t,

A: We need to find derivative of given function with respect to t

Q: Use the Laplace transform to solve the given initial-value problem. y(t) = 2y"" + 3y" - 3y - 2y =…

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Q: Suppose that z = xy² and x and y are differentiable func- tions of t with x =2,y = when t = -1. Then…

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Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: Use differentiation in time domain to solve the the Laplace transform: y"+7y'+12y=21e³t; y(0)=7/2,…

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Q: Use the method of Laplace transform to solve the initial value problem y" – 24y' + 169y = 0, y(0) =…

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Q: 2. Find the linearization of the function f(x, y) = In(x³y®) at the point (xo, yo) (4, 3). Leave all…

A: Consider the following function: fx,y=lnx3y6 fxx,y=ddxlnx3y6=1x3y6×3x2y6=3x…

Q: Suppose that x = x(t) and y = y(t) are both functions of t. If x2 + y2 = 25, and dx = 2 when x = 3…

A: Given that x=x(t) and y=y(t) are both functions of t . If  x2+y2=25           ..(1) Differentiate…

Q: Find the value of dr / dt at t = 0 if r = (θ2 + 7)1/3 and θ2t + θ = 1.

A: Consider the provided equation, r=θ2+713 and θ2t+θ=1 Find the value of drdt at t=0. Apply the chain…

Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 2, and dz/dt = 2. (Enter your answers as a…

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Q: Suppose that r = x(t) and y = y(t) are both functions of t. If %3D y = 2x/2 + 3, and dx/dt = 5 when…

A: The given function is: y=2x12+3

Q: If x'+y' +z-9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x,y,z) (2,2,1)

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Q: Use the Laplace transform to solve the given initial-value problem. y"+ 2y + y = 5(t-8), y(0) 0.…

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Q: Calculate dy/dt using the given information. xy+x=12; dx/dt=-3, x=2, y=5

A: To calculate (d y)/(d t). find the slope of tangent line of the given curve by using implicit…

Q: 2. Use the Laplace transform to solve the initial value problem y" + 4y' + 5y = 2, y(0) = -2, y'(0)…

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Q: Assume y′means dy/dt. Solve y′′+ 3y′−7y= 0

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Q: Solve the ODE dy/dt = -2y between t = 0..4, with the initial condition y(t=0) = 1.

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Q: dy – 2ty = –31²e? dt - and the condition v(

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Q: Use the Laplace transform to solve the initial value problem y" + 10y' + 25y = e-5t – te-st, y(0) =…

A: Given:y''+10y'+25y=e-5t-t2e-5ty0=0y'0=-7   Rules for Laplace transform: Leat=1s-a Lt2eat=n!s-an+1…

Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

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Q: If xy + z² = z, and dx/dt = -1, dz/dt = 3, find dy/dt when x = 2 and z = 4

A: Given: xy+z2=z and dxdt=-1, dzdt=3  Find dydt when x=2 and z=4 differentiate  xy+z2=z with respect…

Q: dy Compute dt t=to X+3 y=x-3x=7 to = 3. dy dt t=to (Simplify your answer.)

A: Solution: The objective is to find dy/dt at t=3

Q: Use the Laplace transform to solve the initial value problem ty''+(4t-2)y'+(13t-4)y=0,y(0)=0,y'(0)=0

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.