7) V ?. 110⁰ T U

Q: 4) In AJKL, JK = KL. Ifl J= 4x-8 and L L= 3x + 15, find m2J and ml L. K.

A: Given :JK ≅ KL∠J = 4x-8∠L = 3x+15

Q: 1 In (a² + y? + 1) dædy -VI-y? |

A: I use polar conversion method to solve this double integral

Q: SI. 1dV, where B = {(x,Y, z): 1 < x² + y² + z² < 4, y 2 0}.

A:

Q: 15. Calculate (41 + 3, r?. –4r³)dt.

A: To calculate: ∫034t+3, t2,-4t3dt Solution: Power rule of integration states that: ∫xndx=xn+1n+1…

Q: for for w= rs ,Y=uV S=uーv, find and Jw

A: Given w=rsr2+s2, r=uv, s=u-2v To find  ∂w∂u and ∂w∂v By chain rule,…

Q: 1. Evaluate: e 3z I = dz (e² + e5z)2

A: given integral I=∫0∞e3zez+e5z2dz claim- evaluate the integral

Q: 4.) x : 12 required:a) find the value of x if y = 1/2

A: Given, x=-112y142y-y214We need to find value of x when y = 12

Q: 2.Rerolue 3r?+2 12 4+6n 12nt18 mto partial pachión

A:

Q: a²z If z = In(x² + y²)., find ax2 ay?

A: Here we have;  z=ln(x2+y2) ...................(1) partial derivative with respect to x

Q: 2. Show that 4=x i+y°j+:'k is irotational.

A:

Q: A Show that : tan" [ ica-a)' (2ta)) -i 2

A: Let ax=eiθ. So: tan-1ix-ax+a=tan-1i1-ax1+ax                         =tan-1i1-eiθ1+eiθ…

Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

A:

Q: ) Max z = 2x 75y Subject to: 2× + 9 y 4 10 3X ty E 12

A:

Q: 8. Let D be the rectangle given by -1<ys0, 1s x< 3. calculate ff,(x2 + y)dydx

A: 8. We will evaluate the given double integral. Given integral is ∬D(x2+y)dy dx with the limits…

Q: 2 and y = If x:y:z 4:6:9 and z = 45, then x =

A: Given:          x:y:z=4:6:9     and   z=45To…

Q: 2. Solve a-2 0 for a. No solution O a = 2 O a = 0 O a = 8

A:

Q: 10. Find x and y, given that (x² + y²,4) = (25, x).

A: When the Cartesian product is performed between two sets, as a result, an ordered pair is obtained.…

Q: Find Higher oxder dexivativese- %3D 2)Y. (ax+1)³ %3D 3)y: ex. 24:25x

A:

Q: @l1z.1-121151\2.-Zl By using:- Re(Z)sI ReCZ)l5|ZI V ZEC, Im (Z)<Imcz)

A:

Q: Find J2z Әх у of z = x3 + 5x² у + 6

A:

Q: Let A = {m CZ/m = 4k+8} where k CZ, and let B = {n CZ/n=2r + 2} where r CZ. Show |A| = |B

A:

Q: L [1\ucos Puf) Ju

A: 1st we will find value of integral using integration by parts and then use Laplace transformation…

Q: 2) 4= -4x required: a) Fih d the value of Y iF X=1

A:

Q: b) Consider the second-order DE. y" +25y = 0 rE (-00, 00) Show the zero’s of the solutions separate…

A: The given differential equation is y''+25y=0 If D=dydx then equation will be D2+25y=0 Now Auxilliary…

Q: 11. Prove that tanh y du = In cosh u + C

A: The integration of the integral is tanhu.

Q: Let U = x'e . Find dU .

A: The given function is: U=x2eyx Therefore: dU=∂U∂xdx+∂U∂ydy

Q: Set X = x 0 1 Y where x, y are unkonwns. Solve the equation X² = 10

A: given and

Q: Find the antideviVative 2+x € ) =

A:

Q: (Rightangle) a) DF = 13 and DE = 15 b) DF = 12 and ĐE = 812

A: Right triangle problem....

Q: 6. Find a line parallel to 3x - 2y = - 4 and passes through (4,-2)

A: We know if lines are parallel then slopes are equal  Given line equation is 3x-2y=-4

Q: y (5) + y(4) + 18y (3) + 18y(2) +9y(1) +9y=0

A:

Q: Let z = x³ 3xy² + x². Zzz = Zzy Zyz Zyy -

A:

Q: 17. Let a, = (-1)" vn 2 1. Calculate the value of an+1 - a, for odd values of n. A.-1 В. -2 С. 2 D.…

A: Given sequence is  an=(-1)^n

Q: xy W=Ze y=8+tZ-St (Hiw) at

A:

Q: If x + y = 2 and x2 - xy - 10 - 2y² = 0, what does x - 2y equal? 00 O 1 02 05 10 DITAUDE ONA…

A: