Compute / 7(t)dt for 7(t) = (t – 2t, 7, cos (2t)) %3D А. 1 sin В. B. G*-t, 7, sin (2t) ) + č С. tA – ť°,7t, – sin (2t)) + č D. G* -t, 7t, 2 sin (24) ) + ē E. none of the above

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A: We need to  find Laplace transform.

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A: To determine the type of the differential equation, d4ydx4=4yπ21+dydx2.

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A: To find:- L{(2tn-3) (tn+2) }

Q: The Laplace transform of a constant, k, is valid for

A: The Laplace transform of a constant k, is valid for ______

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A: Given:    mg = 2    s = 1.5 inches = 1.5/12 = 1/8 feet     g = 32

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Q: 6. Determine the Laplace transform of y" given y (0) = 4 and y'(0) = 2. * O A.) (s^2)[ y (s)] – 4s +...

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Q: The independent variable(s) of the equation Urr B- uy + aug is/are ох, у a, ß о и, х, у

A: The given differential equation is:uxx=β2uy+αux

Q: 9. Tan -30 degrees 11. tan -960 degrees 13. cot -630 degrees 15. tan 90 degrees

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Q: traluate O T* 2T

A: To evaluate: L∫0tπ4e2πdπ Here, π is a variable. Formulas used: ddxxn=nxn-1∫exdx=exIntegration by par...

Q: Find L {(2t" – 3)° } . | O 4(2n)! 2n+1 12(n!) + sn+1 4(2n)! g2n+1 [ 2(n!) 8n+1 O 4(n²)! 12n! 9. sn2+...

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Q: Express the following differential equation in terms of a differential operator: d² 9. dx? •() + dy ...

A: The given differential equation is:9d2ydx2+12dydx+4y=0

Q: 2 - = 3t y+ x' = 3et * (0) = y (0) = 0 OL (x) = 3s2 (s+1)(s–2)(s²+1) 3(s-1) OL (z) = 76+1) (28²+1) s...

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Q: Consider the following functions: f(x)= 9 – 2x and g(x) = 21 – x – 2x². Evaluate (f – 9)(a² – 1).

A: Given functions are fx=9-2x and gx=21-x-2x2find f-ga2-1

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A: Exact differencal equation and second eliminate contact 

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A: Find the inverse laplace transform of Fs=6essn+1  

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Q: This evaluates as the following. '5 W = 176,400 (7х — х?) dx 15 = 176,400 = 176,400 The work W requi...

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Q: Given the curve y = x3 + 3x, at what point is y' = y'' ?

A: As we know that, The Power law: ddxxn=nxn-1 The sum/difference rule: f±g'=f'±g'   Given: y=x3+3x And...

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Q: ax + by + cz + d, = 0 13) Show that the distance between the parallel planes: and ax + by + cz + dz ...

A: here we have to prove the formula of distance between 2 parallel planes.

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A: The solution is given below

Q: with subsidiary cquatvon: * Solne the differential equatun with subsidiary cquatvon: 5. y (s) = (s+2...

A: 8)

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Q: 3) The magnitude of a velocity vector is speed. Suppose that a wind is blowing from the direction N4...

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A: Given that: ∫2dt(t-3)t2-6t+5

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Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y