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Q: Find the Ye neral solution of the eguation. 6y"_5y_4 y =o %3D

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Q: (b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

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Q: 1. Using the first prine =) , show that (1 – x*) + 4nxy = 0. %3D 2. If y = 1+x2, + qx2+rx +s passes…

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

Q: 16. If m/STU = (13x – 6)', mSƯ = (21x + 8)', and mUT = 143', find mST. %3D %3D U T

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Q: 2.Evaluate . xy+ds where C is the right half of x2 + y? = 16

A: Integrate with use parametric form

Q: Given: z = x3 + xy", æ = uv + w°, y = u + ve" az when u = 3, v = – 2, w = 0 Find

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Q: Give an e xam Ple of (T, m') ameasurable SPa ce F; x → T {E & CX : fCE) ET3 m is not

A: Given, Τ, m a mesurable space fi:X→Τ , m=E⊆X: f(E)∈Τm is not a σ-algebra on X.

Q: of the hghset of cheryt the t y temthe 2M percetaof the tres aea dy tn than ees hae ate your

A: Given that  The histogram data of heights of cherry trees. We write the given data in frequency…

Q: 3 - find the absolutt max. and min. o f the Punction rectangular Plate T = x + xy +y?-6 x O x < 5 on…

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Q: 4 - If w = x + 2y + z? , x =, y= r2 + In(s) , and z = 2r aw find at the point (r, s) = (-8,4). as…

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Q: for which the sys y +z = 6, 4x + Ay = -5 has infinitely m a root of which qu: %D :

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Q: In ARST, mZR = 47°, m 2S = 3y - 7, and mT = 2(y + 10). Find the value of y. %3D %3D %3!

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Q: Please answer in pen

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Q: Calculate fryr if Ar.y,z) = &r-9*y³-z³. OA foe =-322 OB fye =0 OC None of these OD fye = 3r2-3y2-322…

A: We have to find the partial differentiation of the function with respect to X y and z

Q: i =r+ 1+1 1le n de bifureation? on?

A: This is a problem of Dynatic Model, stability Analysis.

Q: AISO is isosceles with IS = IO. 22 = 2x+24, mZ3 = 6x– 52, %3D %3D nd mZ1. 1/ 3 bX 2 bx -52-180 S x-…

A: We have to solve the problem

Q: 0/ the Valke of & that makes the Velteof the fumetion 2.

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Q: 26. If RX = 6z+2, XS 18, and RS = 14z, find z. j %3D %3D

A: Recall: If XY is line given such that XZ=a ; ZY=b and XY=c then  XY=XZ+ZY   ⇒a+b=c   Note :…

Q: iP fca)ex+s and gixjex?-3- find the folllowiny D Rc fext

A: a)         f(f(x))=f(x+5)           =x+5+5           =x+10

Q: s) Given u(r, s) =r2 - 2s2, wheter= and s = y? - r, compute for du

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Q: Q4/is that, the Sulutton to the differentiel equation dy-tX+4. is it's

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Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

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Q: 4.2 ezt So 2(z – ni)3d%, with C : |z – 3i| = 1.

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Q: If y = x2 +1 and u= Vx? + 1, then at x = V3 equal to du 1 -4 -1

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Q: b) By using the given substitutions, show that i. Sx(x – 3)5dx =÷(x- 3)“(2x + 1) + C, z = x - 3 14…

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Q: W Given: OWXYZ with diagonals WY and XZ Prove: 21 = 22 2

A: Given: In figure  WXYZ is a rectangle with diagonals WY and XZ. To show: ∠1≅∠2

Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: X+ xy B. Evaluafe the tripe in tagral S5* xy dydzdx,

A: As we know that: The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 (B). From the given integration:…

Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: Which condition would prove AJKL AXYZ? K Y 7. 56 7. O A. JK XY %3D B. JL XZ 8. C. KL YZ 8. O D. JL…

A: The given sides are, KL=56  YZ=7

Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: 5Is there a value of r sotha X = 1 y = 2 and Z=r is asolution to the linear systen ? If there is ,…

A: Putting equations as;23-11-1241-2 xyz=11-712Augmented…

Q: 2s f( 8ts“, ), (x, 9) = 7xy, and af af ;(x, y) : Assume that w= Find and ds %3|

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Q: 11, If PQ = OR, JK = 3x + 23 and LM = 9x- 19, find PK. %3D %3D %3D K J R. %S'

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

A: given XZ=15, YZ=12, and ZQ=8What is ZP?

Q: find he querage vallwe of he fanction z-cor ox m De mternal ( )

A: fx=x-cos26x,   0, π6.

Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

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Q: If ø(x, y, z) = ry²z find grad ø at (2, – 1, 3).

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Q: Q- show that yo+(?) sy + (2) B²y_₁ = y + (1) DY...+ (1²¹) Ay -

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Q: Let w = 4x? + y? + z? x = psinpcose y= psinpstno z = pcoso Find dw dw dw de ee de

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Q: 3. If (x, y, z) = xy²z find grad 6 at (2,−1,3).

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Q: Determine C, and C, so that y(x) = C, e²* + C,e* + 2sinx will satisfy the conditions y(0) = and…

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Q: I For flay 2) = Vxy?z +4x*y, xy,?>0, compute and

A: Both differentiation are solved.

Q: Given that z = f (u,v), u=x + y and v = 2x - 2y. Show that 4. дхду ди?

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Q: 5) *=ClSln t ,y =4 csst t=-2 %3D a) determine dy b) and graeh

A: we have to find derivative

Q: BeR NOULLI 's EQUOTION (2yーX)d水+ラ×ydy:o ソ+PCx)yq(x) yh XrlwDepenとn 3 y= Depen Dest

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Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: 4 - If w = x+ 2y + z? , x= , y =r2 + In(s) , and y = r2 + In(s) , and z = 2r aw find at the point…

A: Using chain rule the given question has been solved in step 2.

Q: Which condition would prove AJKL - AXYZ? K Y 56 7. JL XZ 造=8 KL 8 JK %3D XY

A: We have to find which condition would prove ∆JKL~∆XYZ.

Q: 4. Show that 4= 3y'z' i+4x²:* j+6x°y°k is solenoidal.

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