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Q: Find r'(t).

A: We have to find r't: rt=4ti+t2tj+lnt2k We know that dxndx=nxn-1d lnxdx=1xd lnfxdx=1fxd fxdxdxdx=12x…

Q: find ---y (a) u•v, (b) u•u, (c) ||v ||2, (d) (u• v)v, and (e) u • (3v).

A: Disclaimer: Since you have asked a question with multiple sub-parts, we will solve the first three…

Q: Solve y′′ + 4y = u2(t), y(0)=1, y’(0)=2

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Q: If y(v) = V4+ a*dz then y'(v) =|

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Q: 3-Evaluate Fdr where 2X Cisgiven by rit) = t3+U-3t)rék

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Q: fin (z° + 15z + 44)dz

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Q: dy Find if y 3e2 3z 一山 %3D O -9e 2

A: Using chain rule of differentiation.

Q: sin Vr?+y? dzdy Vz²+y? Evaluate: 6' S O (V2 2) 8 (2–/2)= 4 (2-V2)T 8. O (V2 2)m 4

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Q: Evaluate the integrals

A: Disclaimer: Since you have asked multiple questions; we will solve the first question for you. If…

Q: If WZ = 68 and UV = 94, what is XY? %3D V W Y U Z

A: Given ,  WZ = 68 , UV = 94  We have to find XY

Q: Cind the Solution of dipperential equcetion イ+1-イ

A: See the attachment

Q: Find mZR. R 7 mZR %3D Submit

A: Solution: The objective is to find the required angle

Q: Evaluate ze -dz, where C is z+ 2 ((+2+2)?

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Q: If u * v = 2i - 3j + k, what is v * u?

A: As we know a×b = - b×a

Q: z dV Vx² + y? < z < V2 – x² – y? - -

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Q: Fiud He solution to Hil equetion iultrat ccudiitrou I loleo adduciing that R= 150 Sz, V (t) IJ…

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Q: Find Vz or Vw. 39. w = In /x² + y² + z²

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Q: Solve : dy- (- y) . Inn dy %3D ,13-1 Ordinery Dibberential equetion.

A: Solution:Givendydx=(1-y13)x2 ln xy13-1

Q: mTQ = %3D mQR = %3D U 44 mTS %3D T. R 25 MSQR %3D MRQT %3D

A: Problem 1   Problem 2

Q: Find mZB. C 10 10 D mZB %3D Submit

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Q: ize P= 3z + 4y E to 21 + vS 16 27+ 3y S 24 z20, v 20

A: Introduction: Linear programming is the most basic method for optimizing a problem. We can use this…

Q: y" + 4y' = 3sin2t + tcos2t %3D

A: The solution for the above question is as shown below.

Q: Show that d(y,u)/dv = (1– v²/c)3? for y, = 1//1- v²/c?. %3D

A: Given: γv = 1/1 - v2/c2

Q: (i) Find their means

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Q: JJJ Y G inder r2 + v2 = 4y bour inder

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Q: Solve Ut = Urx, x > 0, t> 0, u (x, 0) = f (x), u (0, t) = 0.

A: Given partial differential equation isut=uxx,     x&gt;0,     t&gt;0ux, 0=fxu0, t=0

Q: 2,t-3P dt, then %3D 12

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Q: 1 -dz O Vīo O vī2 VīI 6,

A: By see this solution below

Q: dz, C:z| = n. %3D 2++13z2+36

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Q: If VW = -2z + 29, UX = z + 9, and ST = z + 13, what is UX? %3D V U UX w/ ト

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Q: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

Q: XY = WZ m22%3D36°, m ZW = 57°, find m23

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Q: dr if r= Vs+1 dt and s=16r² – 20r 1. Find - %3D

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Q: -号。 - 4X u (x,o) =3 e 2 , ニ0 y2 Ansl ux,y) = 34(メ+) Ans.l ucx,y) 3 e %3D

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Q: واجبات اوجد الكل م ما ياني o y = 2t2 + 1, t 5x r2 + 1 y = r = 6x O y = V2u, u = 2Vx

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Q: Fx, y, z) = (10y – az – 5x)i + (3by – x + 8z)k + (z – 5y + 2cx)j %3D a

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Q: Find mZR. Q 28 28-/2 R mZR = | %3D Submit

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Q: Utt = v²u и (х, у, 0) — 0 k constant ,u (x, y, t) = k

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Q: O, x = 2, y = dy dz is

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Q: (a) P: 12x – 8y + 4z = 4 P2 : 30x – 20y + 15z = 7 Parallel Perpendicular O Neither

A: We have to state whether  the planes are parallel  , perpendicular  or neither the two.

Q: - a. ARWZ W WZ RW b. ? ZR %3D c. RW = 15, ZR = 10, and SZ = 8. WZ 2 and RS = ? R

A: Given, ∠WRZ=∠WZS

Q: yz 4. II »z dr dy dz Jo

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Q: Find the gereral Solution of the fille d dffferential equation. 3,n1 %3D | -

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Q: Evaluate R Vx2 + y + z2dV where B is the ball x2 + y + z < 10.

A: A detailed solution is given below.

Q: 9. Find y if (a) y = 2" In (cot² (v7))

A: We are authorized to solve only one independent question, please repost remaining questions…

Q: Use L and f' to solue ťtzyz fit), y0=5,where (2, 2)

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Q: xlet X,Y,7 be v.V.J with Joint fA くれく くらくtyerzc

A: The joint probability density function is given to us the conditions on x, y, z are also given to…

Q: dz and dz if rys + y2³ + zr³ = 7. Find

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Q: Solve the IVP y" + 4y/ + 5y = 38,(t), y(0) = 0, y'(0) = 1. %3D %3D

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Q: I = 4t? dt J2

A: