Find the area of the given reptunanalytically l.The inner loop of roZ +4 Cos &

Q: Find the product of the integral 1- LL,x? e*ydxdy

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Q: ( 6x-5/x +3x+4x -2 dp- 4

A: A function F is an antiderivative of f if F'x=fx for all x in the domain of the function f. Some of…

Q: Find f -6xydA over the triangular region D with vertices (0,0) (2,0), (0, 4) O68 -68 )-8 -16 16

A: Consider the integral

Q: 6. Find the integral Ssin T* jsin² 2 TTX 2.

A: We have to find integral

Q: 2. Given: PT || QS Prove: APRT O AQRS a. R. b. What similarity transformation maps APRT onto AQRS?

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Q: Find –3xyd A over the D triangular region D with vertices (0, 0) (2, 0), (0, 4)

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Q: Calculate the area of the inner loop of r = √3 − 2 cos θ.

A: To Find: Area of the inner loop of r.

Q: Find the dimensions of the minimum-cost open-top rectangular tainer. (Let v* = 10 m³.) con-

A: Given. We need to find the dimension of a topless cuboidal container. Whose volume is 10m³ And…

Q: Graph the limaçon. Limaçons with an inner loop r = 1/2 + cos u

A: To graph r=12+cosu

Q: Find -6xyd A over the D triangular region D with vertices (0,0) (2,0), (0, 4)

A:

Q: Compute the Wronskian of the following equation. y" – 4y' + 4y = xe2x %3D

A: Given: y''-4y'+4y = xe2x

Q: Find the area of the inner loop ofr= 3+4cose. 0.7612 0.4775 O 0.9551 O 0.3806

A:

Q: Suppose thet the filowing Aransforuution Conneclss the (x') and (ti) codmate ک ماول se4ス?) e え(スーx)…

A: Handwriting solution given.

Q: Evaluate the integral. w2 In(w) dw 1.

A:

Q: Let yk = k² and Zk = 2k|k|. Are the signals {yk } and {Zk } inearly independent? Evaluate the…

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Q: Verify Green's Theorem by evaluating both integrals ax dA ду for the given path. C: rectangle with…

A: From: (0, 0) to (5, 0)y=0, dy=0∫ y2 dx+ x2 dy =0From: (5,0) to (5, 9)x=5, dx=0∫09 x2 dy= ∫0925…

Q: 1 Use the Cauchy integral formulas to evaluate the e cos z *zp- 22(2: - 37) where C is the region…

A: Given: Let  I =∮C  eiz cos zz2 2z-3π dz  .....1 And,  C is the region covered by circle z-2=3.

Q: Let Ps have the inner product given by evaluation at-2,-1, 0,1, and 2. Let p(t) = t2- 2t and q(t) =…

A: Let P3 have the inner product given by evaluation at -2, -1, 0, 1 and 2 . Let p(t) = t2-2t  and q(t)…

Q: Find the area +6 C1 R -6 +6 C2: 4x2 + y² = 16 -6 using green's theorem.

A: We are given the above region of which we need to find the area and as per the instruction, we need…

Q: Solve the differenlial =* +y+Xy equa lion with initial condilion yco) = -I , andOSK<2 with step long…

A: Given y′=dydx=x2+y+xy, y(0)=-1,h=0.4Here, x0=0, y0=-1, h=0.4 , xn=2

Q: Find the product of the integral 1- S x²cos(xy)dxdy

A: We have to change order of integration first.

Q: Evaluate the integral S 3012 2/3 de using the two-point Gaussian quadrature rule. 1+16z4

A: Given integral is ∫−121221+16x4dx. We have to evaluate the given integral by using the two-point…

Q: Compute the Jacobian of the mapping. G(r, s) = (8rs, 4r + 6s)

A: G(r,s)=(8rs,4r+6s). We need to find the jacobian.

Q: In AABC andAXYZ, AB = AC = XY, BC =Y Z and mZZ = 90. Prove: mZX > mZA %3D

A: We have given two triangles , ∆ABC,∆XYZ and AB=AC=XY and ∠Z=90∘ . and BC=YZ We have to prove that…

Q: where A e C.

A: Complex Inner Product Space: For two vectors u and v in complex space ℂn, u,v is known as complex…

Q: Graph the limaçon. Limaçons with an inner loop r = 1/2 + sin u

A: Graph the limacon: r=12+sin u. Construct the table of values: u r=12+sin u u=0 r=12+sin 0=12…

Q: Find the decomposition of a(t) a = arT + așN into tangential and normal components for r(1) = (5t,…

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Q: 11. Obtain the Mx and My of the area generated y = 2x +1, x + y =7 and x= 8

A: Intersection points:x+y=7, y=2x+1y=7-x, y=2x+17-x=2x+13x=6x=2 → y=5Intersection point (2, 5)Line…

Q: 2. Solve the given SLE using LU-Factorization X, + x, +xz = 3 x, - x, +4x; = 4 2х, + 3x, — 5х, %3D0…

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Q: Find JJ-6rydA over the triangular region D with vertices (0,0) (2,0), (0, 4) O 68 O 16 O - 16 8 O -8…

A: Solution is given below:

Q: Is D3 a cyclic? Please prove and provide complete solutions. Thank you.

A: The elements of group D3 is given by { e, (1, 2, 3), (1, 3, 2), (1, 2), (1, 3), (2, 3)} Ord(D3) = 6

Q: (b) Evaluate the integral fxIn x dx using by parts formula.

A: Answer is:  (x2/2)lnx -x2/4 + C

Q: Given: PT || QS a. Prove: APRTO AQRS R T. b. What similarity transformation maps APRT onto AQRS?

A: Corresponding angles are the angles that are formed when two parallel lines are interested by a…

Q: N is the centroid of triangle HIJ. If KN=9, IM=15 and LN=5. Find KJ K. N/

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Q: Solve the given SLE using LU-Factorization X + x2 + x3 = 3 X, - x2 + 4x, = 4 2x +3x, — 5х, %3D 0 |

A: Given SLEx+y+z=3x-y+4z=42x+3y-5z=0convertit in to matrix form1111-1423-5xyz=340convert it in to…

Q: 3) Show that the following graphs Hamiltonian are hot a a) d d 137 c) d) ol

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Q: If A = 3.4xyâ + (1.7x² – 6.8y)âŷ, the circulation of A around the closed path shown below is

A: In this question, we have to find the circulation of vector A along the given closed field in fig.…

Q: Find the area inside the inner loop of r = +5 12cosθ .

A: Given equation as r=5+12cosθ

Q: Find the Runet'ion FCA] such that =t+ cost and such that

A: Let y"(t)=d2ydt2=t+cos t and y(0) = 1 and y'(0) = 2 Integrating on both sides, ∫y"(t)dt=∫t+cos t dt…

Q: Provide a homotopic squared parameterization of side one o_1= [-1,1] x [-1,1], other than this, and…

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Q: Find the of the GS that satisfies the given Cond hb Sum a n=4 b. h=6

A: Sum of Geometric series.

Q: Consider the following PDE Uxx + 2x uxy + Uy = 0 a) What is the class of the equation? b) Reduce the…

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Q: Find the solution of the following IVP using the characteristic method : u + uu= y у , и(1,у) %3D Зу

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Q: ***PLEASE HELP WITH THE FOLLOWING AND PLEASE PROVIDE HANDWRITTEN WORK ON PAPER*** (4) Find the…

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Q: In C[0, 27], with the inner product -2 (f, 8) = | f(x)g(x) dx, show that the set S = {1, sin x, cos…

A: Given: Inner product defined as: &lt;f,g&gt; = ∫02πf(x)g(x)dx To show that the set S = { 1, sinx,…

Q: Compute the given integral. Jac dx +C

A: Solve the integration

Q: r = √3 − 2cos θ.

A:

Q: determine the area inside of the inner loop of the limaçon r = 2 cos 0 – 1.

A: We have to find area of r= 2cos(theta)-1

Q: Evaluate the following iterated integral. -7cose 5 rdr de 49 2n+5sin 40 49 n+ 5sin 2n+ 5sin 40 () 49…

A: