1. (r - x) + (-2r + 3x) 2. (-y + 3) - (v - 2) 3. (-3a* + 4 + 2a') -(2 + Sa - a) 4. -(6 - b + 4b') -(-26' – 1+ 36) 5. (-Spg + 2p? + 3)- (p+ 2pq - 8) 6. -(2g* + 3pg - p*) - (-2p² + 4q² – 6pq)

Q: 7 --y2 Then 2 5 Q2: If z = –x² az + 5x ду az 7y ||

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Q: 3. tet-lu(t – 1) 4. t cosh 2t 5. (t – 2)²et-!u(t – 2) 6. te-'u(-t)

A: To find the Laplace transform of the given functions.

Q: (a) 3 Differentiate y= y 3= us ing first principle. 2x+2

A: we are allow to do one question at a time  if you rest of answere please specify that part and…

Q: fin (z° + 15z + 44)dz

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Q: ☺ cosh"z= Loy {2+/2

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Q: 7) Suppose y varies directly with x. If y=2 when x = – - what is y when 2 X--0.3?

A: Given the data :

Q: Solve using MUC. y" +4y=3sin2x 3+3+5+ y = C₁ cos2x+ C₂sin2x - -Xcos2x 4 y=C₁ cos2x + C₂sin2x +…

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Q: method; Inz VUna)²-y²

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Q: 31. If 9x² = y(y – 3)², show that (y + 1)² ds - dy². 4y

A: We know that Given Firstly, we find dx in terms of dy

Q: - 5x + 4y – 3z = - 1 - 10x – 4y – 4z = 46 20x – 4y – z = - 44 (x, y, z) =

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Q: 9) (3x-29 +2) ex+(39-2*-2) dyzo

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Q: (ost) X= 3サ-3 DiD X-2-2y ¥ーにh で3,0) D3 Dy メーと2 サ=スメート X-4 <-リ-3 toノー4)

A:

Q: Solve 2sinx- V3 = 0 on interval [0,2 t)

A: We have to solve  2sinx - √3 = 0 on interval [0 , 2π)  Since ,  2sinx - √3 = 0  2sinx = √3

Q: Find the number of solutions to 6z1+9z2+20z3=150 where the zi are nonnegative integers.

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Q: 15.f mOT-(27+ 3)', mRT- (9x – 5)" and MRST - (10x-2), find mi.

A: Given,         QT⏜=27x+3° , RT⏜=9x-5° and ∠RST=10x-2° .

Q: Find dy. y=5th root of x^2(8-2x)

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Q: X, t 2 X, < 22 X,t 3, 2x x, Z12 + 2xa=32 maxlimzed by 2=5x, t10x2

A: The solution of given linear programming is given by using graphical method :

Q: 2- S --y Vty zdzdxdy

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Q: 2ryy' –1-y - 0, y(1) = 2, one can fir

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Q: Max Z = 4X1+10X2 %3D s.t. 5X1+4X2 < 200 X1+2X2 s 50 X1+X2 s 20 X1, X2 0

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Q: 4y² – 25 -dy

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Q: 1, z2ー

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Q: -x+y+2z = -3 3x- y+z = -2 2х- Зу- 42 %3D 1 X = y =

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Q: 4. Find dyax and d2 x =V4- t , go t²-2t ye t'-2 get'.

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Q: dx 4. xV25-x2 5+vx2-25 In + C а. 5 b. In 5+Vx2-25 + C 5+v25-x2 In + C с. -- d. None of the above

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Q: If y = ((5z² + 8z)³ – 5-)°, then dy/dr is:

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Q: =--x+ 1 3. 2 1 -1 -6 3 4 5 6 -5 -4 -3 -2 -1 -2 -3 -4 -5 -6 C y=2* x + 3 3 2 1 -6 -5 -4 -3 -2 -1 1 23…

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Q: TRUE OR FALSE I: 2x+3y – 4z= 2 and x+ 2y+ 2z = 3 perpendicular to each other

A: We'll answer the first question since the exact one wasn't specified.  Please submit a new question…

Q: tion: y" – 3y' = e3 – 18x. - -

A:

Q: the of olution using simplex me Max z = 8x, + 10x, + 7x3 s.t: 4x + 6x3 + 3x3 S 60 7x, + 2xz + 5x, S…

A: In this question, the concept of Linear Programming is applied. Simplex Method An approach to…

Q: 7x-4y-3z = 21 -4x+7y-z = 0 -3x-y+5z = 0 x, y, z?

A: Given

Q: 13. -(р — q) -рл-а 14. (р — q) л(р — г) %3D р — (q л г) 15. (р — г) л (q - г) %3 (pvq) — r

A:

Q: 3)으 rcose de Jsine 1-x2 d ¿= xp 2

A: LEIBNIZ RULE

Q: suonenba 5x mons: (1) +- = 3x + 3 (ii) x + 7x + 12 = 0 In (x +4)- In (x*) = 4 = 15 (iii) %3D (iv)…

A: Simplification

Q: VAy 5-y-z 15z dz dz dy 2y2 2-y-

A: SOLUTION-

Q: y= cot(-2x) y4 3 12T 37 -1- -2+ -3+

A: We have to find

Q: 1. Find XY when X(-7, 10) and Y(3, 4).

A: GivenX≡-7, 10Y≡3, 4To find XY

Q: 11. Perpendicular to 5y = 2x – 6 and passes through the point (-1, 5)

A: topic - equation of a line perpendicular to given line

Q: (1 - V2) dt 44. 46. (2z – 3) dz - 3

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Q: 6) qyo -x² +2x + S%y +62=0 sty

A: 6)

Q: 3. Is (3,8) a point on y = 3x - 1?

A: if (3,8) is a point on the line y =3x-1 then it should satisfy the equation y =3x-18=33-18 =9-18 =8…

Q: Eliminate the arbitrary constants in y = ex + c1e2x + c2e-3x

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Q: ų (H)= - 2y, (t) + 24;(4)= Y,(4) - 2y, (t) +2t t 9,lFS +2

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Q: Which of these standard form equation is equivalent to the factored form y= (x+1)(x-2)(x+4)(3x-7) A.…

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Q: 2P 2+ y= since) see' (=?)

A: y=sin(z)sec-1(1+zz2)

Q: Differentiate x²y3 - y2-6x=0 with respect tox. A 3x²y2-2y −6+2ху 3 2х3у2-2y - 6 6-2xy3 3ху2+у В С D…

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Q: Use Cramer's rule to solve for y. 5x + 4y + 4z = 39 4x +3y-2z 15 4х - 5y - 4z%3D -15 |

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Q: find the first and second derivatives w = 3z7 - 7z3 + 21z2

A: Given the function, w = 3z7- 7z3 + 21z2 Differentiating with respect to "z" dwdz =…

Q: Find dy and simplify whenever possible. 1. y=(5-6x)¹2 4x-5 2. y=--- 2x + 1 3. y=(2x+5)(4x−1)

A: