Fnd the Laplace inverse Rün the Following (s°_4S+5)²,

Q: 4. The vector functions r(t) = (t, t2, t3) and s(t)3D (sin t, sin 2t, sin 3t) intersect at the…

A: 4 rt=t,t2,t3, St=sint, sin2t, sin3t     0't=1,2t,3t2     S't=cost, 2cos2t, 3cos3t…

Q: Write a function for the sinusoid shown. Ay 4 (0, 3) 3

A: The graph of kf(x) is the graph of f(x) vertically stretched (if k>1) /shrunk(if 0<k<1) by…

Q: Find torsion of the motion r(t) = . Leave your answer correct to two decimal places. Answer:

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Q: Find r'(t). r(t) = (tan¬(2t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k.…

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Q: Find Laplace 2 2 [sin(34) + 65inh czt) ]

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Q: L{(t+2)²et} L {e2t (3 sin 4t 4 cos 4t)}

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Q: Ex:57 Find the FisiE of the Juuctiou sin TIt ZL oくtくし - siu -Lくtく

A: Given, The formula for the Fourier series expansion is,

Q: Transform F(s) (giving you cos 5t + t³

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Q: Q.1 Evaluate –1)

A: Some of the properties of Laplace Lu(t-c)g(t)=e-csL[g(t+c)] L[tneat]=n!(s-a)n+1 Leat=1s-a

Q: Find T, N, B, K as functions of t if r(t) = (sint)i + (V2cost)j+ (sint)k.

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Q: The Laplace inverse of (3s -1) (s² +2s + 26) 3 -t te 2 sin Bt – 5C 1 - sin Et – t cos Ft ) is -t e A…

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Q: T = [ Cos(a)+Sin(a).Cos(b) ] A-) Find function's gradient vector B-) Find function's Laplace…

A: We have to solve given problem:

Q: let X ~ P()find the third central moment.

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Q: Plot r = 4 cos 0: 0° 30° 60° 90° 120° 150° 180° 210° 90° 120° 60° 150° 30° 180° 0° 210° 330° 240°…

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Q: dy if y=| cos Ode dx if y= [ cos Od0. Use the Fundamental Theorem to find 3

A: We will use newton leibniz theorem to answer the given question .

Q: The inverse Laplace of 28 (s+3)²+4? exp(-rt) Note: sin (wt + angle ()) to O 7exp(-3t)sin(4t) O…

A: Introduction: We know that from the Laplace table, inverse Laplace of function F(s)=b(s-a)2+b2 is…

Q: cos(2z) dz c = |Z| = 1 Evaluate where at oriented 5-4 cos(z) counterclockwise?

A: Let fz=cos2z5-4cosz Singularities of f are those points where the denominator is zero. So, put…

Q: The Laplace inverse of 4 L-1 is s2 + 4? O sin h(4t) O cos h(4t) O cos(4t) O sin(4t)

A: Inverse Laplace transform

Q: apply shifting property of laplace in the equation f(t)= t cos 2t and f(t)=t^2e^-3t

A: To apply the shifting property of Laplace in the given equations.

Q: i need the answer quickly

A: Given function is: f=s+1s2+s−6 Since the given function is already a Laplace transformation,…

Q: The Laplace inverse of (3s -1) s+2s + 26) 2 -t tet sin Et-t cos Ft) D is sin Bt %3D A 5C Then…

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Q: Find r'(t). r(t) = (tan-(4t))i+t cos(t)j – Vtk NOTE: Enter your answer in terms of i, j, and k.…

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Q: nd the Laplace

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Q: (s+2)? 5. Find the Inverse Laplace of

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Q: Define a vector-valued function as follows: 7(t) = (cos t, 4, sin t). Which one of the following…

A: Find your answer below

Q: Find r'(t). r(t) = (tan-(11t))i+t cos(t)j – Vtk | NOTE: Enter your answer in terms of i, j, and k.…

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Q: The Laplace inverse of L|- is s2 + 52 cos(5t) sin h(5t) sin(5t) O cos h(5t)

A: To find the Laplace transformation of L-1ss2+52. Solution: let φs be the function whose Laplace…

Q: s2 Q.3) Prove that L-1 () =(coshat sinat + sinhat cosat) 4+4a4, 2a

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Q: Cos t sin t Set A and x = [a b]T. Demontrate that ||Ax||2 = a² + b². %3D

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Q: Find Tand N for the circular motion r(t)=(cos 2t)i+(sin2t)j.

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Q: 2. Find Lt² et sin 2t] *

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Q: Find L{sin(t)u (t – T)} 82+1 s2+1 se 82+1 se 82+1 82+1

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Q: (sin(t*), t, cos(t)) Answer the following for the curve defined by the vector function r(t) domain…

A: our objective is to find a formula for curvature ,length of the curve,unit normal vector.

Q: 4. ".p>-1

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Q: Find inverse Laplace by re sidue theo'rem. (x,-2) S - 25 +5

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Q: ha)= Jo So Sin't dt

A: We have to find the given integral .

Q: trans, Fnd the laplace tansfam of fit) the oct<I

A: To find the Laplace transform of the below function. ft=t/τ          0&lt;t&lt;τ1             t&gt;τ

Q: et 7(t) = ( – t³ + 3, 3e-ª, 2 sin(2t)) ind the unit tangent vector T(t) at the point t F(0) - <[

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Q: Calculate us (t) * sin(t) using the definition of the convolution

A: Some of the Properties of Laplace transformation  Lsint=as2+a2Lu5(t)=e-5ssLf(t)*g(t)=Lf(t)·Lg(t)

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 3…

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Q: @lProve f A=3i+ rotating an ang

A: we have to prove that the length of the vector 3i+2j+k does not change when rotating the axes around…

Q: Let r(t) = (15, cos t, -3 sint) be the position vector of an object. Find the velocity and speed of…

A: Given that rt=15,cost,-3sint  find the velocity and speed of the object

Q: Use laplace trasfarng fo Solve dt² 2e cosi2t +e Sin at

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Q: -4 sin bt

A: Recall:         The First shifting Theorem:               L eat f(t) =F(s-a) ℒsin(bt)  =bs2+b2

Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 5 + 3…

A: Given x=5+3 cost -1   y=5+3sint -2  π2≤t≤3π2In compare 1 &amp; 2  with st.eqnx=h+r cost y=k+r sint…

Q: If sint = - - and t is in the 3rd quadrant, then tan t %3D V45 45 O V45 V45 2 V53 O O O

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Q: cot t Differentiate f(t) = et

A: We are given, f(t) = (cot t) / et We are asked to differentiate this function.  We will use the…

Q: Solve I V.P using laplace 5+225 -4ッ=)

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Q: Laplace inverse of L is |(8 – 4)2 + 6² e ot sin 4t O ebt sin 4t O et sin 6t O e 4t gin 6t

A: L-16s-42+36 Apply inverse transform rule: if L-1fs=ft then L-1Fs-a=eatft Noe for 6s-42+36⇒ a=4,…