b) Golve: 4x°y*+4x°4- sx y' + 24= 60x?+8x +1 on Co,00) (2) vsing the Method of Uaniation of parameters.

Q: .3. Let K be an extension of a field F. Let

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Q: V. Determine all the relative minimum and maximum values, and saddle points of the function h…

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Q: 6. (a) Carefully sketch (and shade) the (finite) region R in the first quadrant which is bounded…

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Q: EL be three fields. If L is an algebric exte Es an algebric extension of F.

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Q: PROBLEM NUMBER 1 A farmer can plant up to 8 acres of land with wheat and barley. He can earn $5,000…

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Q: B. Switch the order of integration: cos (x2) dædy. Just SET UP with the order switched. DO NOT…

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Q: SOLVE FOR INVERSE LAPLACE TRANSFORM 3s + 2 4s2 + 12s + 9

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A: As per our guideline,we are supposed to solve only first three subparts. Kindly repost other subpart…

Q: Express the following complex number in its polar form. 2+5i 6.- -4-7i

A: Solution :-

Q: I. Show that the function f defined by 1, (x, y) = (1, –1) %3D f(r, y) = { 1² + y (x, y) # (1, –1) x…

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Q: •x² if 5 solve the 1UP: y% 4y(2)+ 3y'= Y0)=e+ % ,uG) = et %

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Q: 6. Show that when a hole of radius a is bored through the center of the sphere of radius b, the…

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Q: (b) Unitarily diagonalize the following matrix 3 -6i 6i 6 -

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Q: Determine the area of the region below. A. 1.5 sq. units B. 1/2 sq. units C. 1 sq. unit D. A sq.…

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Q: ») Shade the region in the complex plane defined by {rec: s |z+ 2+ 2i <1 4i E C

A: Complex plane

Q: Find the mass of a plate bounded by one arch of the curve y = sin x, and the x-axis, if the density…

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: 6. Setting æ = cos 0 show that T.(e) = [(- + ivI- =')" + (* - ivī- =')"] n where i = V=1.

A: This immediately follows as a consequence of De Moivres formula which states that e^(it)=cos t + i…

Q: 4) golve the luP : ty"-24'+ty = t Chne 'a ) yro) = |

A: Solution: given, ty''-2y'+ty=t  y(0)=1, y'(0)=0 it is a non homogeneous equation so solution will be…

Q: 10. Particular solution of y" – 64y = 16, when x = 0, y = 1, y' = 0 %3D

A:

Q: Question 3 While investigating the effect of temperature on CPU performance, analysts determined…

A: Solution : A) x%=pf(p)=-1.515p-5 8-0.04p+0.48p17f is rate of change of frequency to find freequency…

Q: Find the Laplace Transform of the following function as a function of “s” and simplify the result.

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Q: Q3: Find f(t) ( Inverse Laplace Transform )of the following functions s+1 1. F(s) = 2.F(s) = s4+s2 2…

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Q: Example 2: Find the Fourier series -1, f (x) = 1, f«) = - 1< x < 0 0 <x < 1

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Q: to (x) preof: H.w.

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Q: For the normal distribution shown below, what area is contained between -2 and 1? -3 -2 -1 3 T2

A: Normal distribution is the most common continuous probability distribution. In a normal distribution…

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Q: If D = 4x'a - 3za, + 2ya_C/m², find the following: V•D a Answer. the total charge lying within the…

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Q: (a) The P -value of a test of a null hypothesis is O A. the probability the null hypothesis is…

A: Solution:-

Q: 7. I-J 8. S-I 9. IAS

A: This is a question from the set theory.

Q: 4.) Verify the Divergence Theorem where F(x, y, z)=(x',xz,3z) given by x' + y +z² <4. and E is the…

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Q: Evaluate the definite integral using all three composite rectangular rule strategies with the…

A: We will find value of integral by using left Riemann sum , right Riemann sum and Mid point rule

Q: II. Consider the function g defined by 1 g(x, y) = cos (Tx Vy) + log3(x – y)" Do as indicated. 1.…

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Q: 4. (a) (i) Calculate (4 + 10i)². Answer: (ii) Hence, and without using a calculator, determine all…

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Q: Let X be a normed space. (a) Find all subspaces of X which are contained in some ball B(a; r) of X.…

A: Given: X is a normed space. To find: All subspaces of X which are contained in some ball Ba;r of X…

Q: 1. Solve the linear system using Jacobi and Gauss-Seidel Method 2л — у 3 2 x – 3y + z = -2 -x + y –…

A: We need to solve the system of linear equations:  2x-y=2x-3y+z=-2-x+y-3z=-6 using Jacobi and…

Q: Theorem 12. Let V be a finite dimensional inner product space and te Hom (V, V). Then linear…

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Q: Allora has 264 feet of fence, a spacious yard, and a little dog. He wants to set up a rectangular…

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Q: Prove that the sum of the angles of an elliptical triangle is more than two right angles.

A: Solution:-

Q: Set up the double integral f 2x + y2dA where R is the region above the x-coordinate bounded by the…

A: Double integration: Let f(x,y) be the two variable function. Then the integral defined on Region R…

Q: prove it .The set of all optimum solution of the general convex programming problem is a convex

A: Proof

Q: 4. Let f:R→Rbe a function defined by f(x)=x for every xe X . Show that f is a continuous.

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Q: What is the dual of the phrase “three collinear points and a fourth point not on the line of the…

A: Answer :  Dual of any phrase can be find by replacing the conjunction connective with disjunction…

Q: 3. In an interval, in which of the following conditions a continuous function is decreasing? A) the…

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Q: Solve the complex equation sin(z) =−4

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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

A: Given function: hx,y=x3-3x+3xy2 To find: all the relative minimum and maximum values, and saddle…

Q: 4x2-y = -28, Consider solving the system of nonlinear equations 3+ 4v? = 145. %3D %3D Use Newton's…

A: (Multivariate Newton Raphson method uses the formula: xn+1yn+1=xnyn-∂f1∂x∂f1∂y∂f2∂x∂f2∂y-1×fxnyn to…

Q: 2. Calculate the divergence of D = (÷)[10xyzảy + 5x²zãy + (2z3 – 5x²y)ã,] at P(-2,3,5).

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Q: 3. Find the angle of the largest right circular cone which can be inscribed in a sphere of radius 9…

A: Let the radius of the cone = r  height of the con   x = √(R^2 – r^2) and h=x+R , h is height of the…

Q: (b) Calculate sin(arccos()) exactly, i.e. without using a calculator.

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Q: Find the Laplace of the following Periodic functions: 1. f(t) = t 0 <t < 2 2. f(t) = ksin(wt) 0 < t…

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