3. Obt nin the parh cular folu tion 9. xdx - ydx + 3x dy +ydy = 0 ; wun x - 5,4= -:

Q: Show the only soution to ax = 1, a + 0, is x = a^-1|

A:

Q: Tnd th gredient y te tengut y= 3x at te pont (3,-1)

A: See the detailed solution below.

Q: 5 If u =x² +y² and v = 4xy, determine дх дх ду ду du' dv' du' dv

A:

Q: If =x+3y-z,=4xyz, w=22 -xy evabuate d(u, v,w)/ (, 2). at (1-,0).

A: We have to first find all partial derivatives.

Q: 12 3. If u lx + my, v = mx-ly, show that ди 4 + m

A:

Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

A:

Q: 4/ur grans funthon y"-Uy't3y = et

A:

Q: 3 Find C at any time7 2l/min SIN SIO 6l /min 8 elmin C NI8 100 Pure waley

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Q: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: 2 If In(ax)dx = 3, then a = %3D %3D 1 4 4 e4 4 ез 4 O None

A:

Q: Solve the following first-order linear DE's. y' + (cotx)y = xcscx, yE) = 1

A: Two ways it can be solved. 1)By making exact form 2)Using integrating factor

Q: QUESton 12 H. Manufactuny Machine bas a 3% defect rate. tems an chalen at rendamr, What is Ahe trat…

A: Solution

Q: 4- Find Y/dz If x²(x- y)? = x² - y? dyla

A: Find the derivative

Q: if M Z- Sin (xy) fined 4 22 y= lint t-1

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2) Show that (1 – x²)P",(x)P'm(x) dx: 21(l + 1) Sim• 21 + 1

A: Given:-  ∫-11(1-x2) p'l(x)p'm(x)dx=2l(l+1)2l+1δlm

Q: Find the length of the curve y = In(e - 1) – In(e + 1), In 2 sxsIn 3.

A:

Q: In lam(플 + )1-men dy is dz et y

A:

Q: 10 q/ asing the TracZoidal Rue with n= dx Swbintevals, evalute the in tey ral I+2 and compare as…

A: Find the attachment

Q: given that y = 1 eries with h = 0.

A:

Q: Find dy ax 9=бл+бай

A: Given :y=x+1+xformula : ddxx=12x

Q: and 3 point Gauss Quadrature 2 By using e sfim afe : 2 dx メ-2 い)S, dx Nx

A: The given problem is to estimate the integral using 2 point gauss quadrature rule and 3 point gauss…

Q: EX. Apply 4th order Runge - Kutto to s olve the toll Valu e Problem 4'= 44 for hzoid , y(1) =1. and…

A: Given diffrential equation is, y'=x2+y having h=0.1, y1=1 and 1≤x≤2 Now,…

Q: 4) shao he eg Y+ oy-=3 3x-y422=1 are consitent folie thn 2l-2y+32= 2 Argoninl malrie of fa.B) ー1 3…

A: Given

Q: 3. Evaluate Se(x² – iy²)dz along the straight lines from (1, 1) to (1, 8) and then from (1,8) to (2,…

A:

Q: EXAMPLE 4: WY = In AWXY: WX = 9 m, XY = 15 m, and n ZW =31° m2X = mZY =

A:

Q: 3 Evaluate the gwen tri ple in legral. xsiny dy dz dx

A: Order of triple integral dydzdx

Q: You hare shown that e jul dw or , erchenying w and t Jlw) = Use a chume of veriables to genenle…

A: Consider the given information: δ(t)=12π∫-ωωejωtdω                  ..(1) δ(ω)=12π∫-ωωejωtdt…

Q: 1. Is the following always true? If yes, clearly explain why. If no, give a specific counterexample…

A: Note: AS per our guideline we are supposed to answer only one question. Kindly repost the other…

Q: If y= In Cschx + coth y Biod dy

A: Given: y=lncschx+cothx

Q: 5. It is desired to divert 5.1 m'/s water from a pool whose water surface elevation is 45 m, to an…

A: according to question ∆H=45-42m      =3m length of concrete culvert L=8 m now, find the slope S=∆HL…

Q: dT 4 dp 0; pdT T = To when p= Po dp Po e (T-To) O Option 5 L = e- (T-To) Po O Option 2 -0.5 (To-T)…

A:

Q: 23. If exy = 3, then what is Y at the point (1, In3)? dx -In3 3ln3 In3 -4In3

A: Given:- exy = 3 To find:- dy/dx at point (1,ln3)

Q: If In(ax)dx = 2, then a = %3D 1

A:

Q: - seyi + avīj + () dt = 3 3

A: We have to perform integration by parts and then insert given limit

Q: . If 4=(x+2y+az, bx-3y-z,4x+cy+22) is irrotational. Find constant a,b,

A: Follow the procedure given below.

Q: 15. If mOT = (27x + 3)', mRT = (9x - 5)° and MZRST = (10x – 2)°, find mRT. %3D %3D R S.

A:

Q: 7) [[3embch5y] dvl [jel*5) dy] „In[sec h 5y]

A: Using rule of logarithm & integration formula of sech(x)

Q: 43. In 00, OY=5 and XZ = 6. If XW WY, find WZ.

A: Topic = Circle

Q: 6. Consider the following model: Yi = Bo+B,D11 + B2D21 +u; O if person i is a non-immigrant) where…

A: Dummy Variable Trap: It is defined as the scenario when the attributes are highly correlted. One…

Q: In(v¤) dædy 6. 15. Calculate ry

A:

Q: If [ In(ax)dx = 3, then a %3D 1

A:

Q: P(x) 1 2 5 6 IRound to fonur darimal nlarae ae neerlad 4)

A: here use binomial distribution with parameter p = 0.7 and n =6 for binomial theorem ,…

Q: 10. If mZTSV= (6x + 17) and mSV = (15x + 13)', find mSUV. %3D T

A: A circle

Q: 7) If z(x,y) = x² + y², x=u+v, and y=u-v, find dz du

A:

Q: See image below.

A: Given that the tangent line touches the curve y = f(x) at (4, 3) passes through the point (0, 2).…

Q: 2 If [ In(ax)dx = 3, then a = %3D es 4 e4 4 O None e3 4 e6 4

A: Given that: ∫12lnaxdx=3

Q: = 11% and E = 715, calculate the Еxample 4: If К. stock value of XYZ Ltd. for: 2) r= 11%

A:

Q: 2. In AXYZ, PQ || XY . If XZ = 15, YZ = 12, and ZQ = 8, what is ZP? 2.

A: Use concept of similarity. In similar triangle, ratio of corresponding side are equal.