The area enclosed between the curves y2 = 4x and x² = 4y is 32 16 3 3 (b) 8 (c) (GATE-09 (d) 16

Q: Give examples of three relationships that show all possible combinations of minimum and maximum…

A: We need to give examples of three relationships that show all possible combinations of minimum and…

Q: (a) Please verify that = {1, cos x, cos 2x, ..., Cosmx, ..., an orthogonal set in a Hilbert space…

A:

Q: 1. Let B = (B₁)tzo be a standard Brownian motion started at zero, and let (FB)zo denote the natural…

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: 1. Evaluate the determinant of the matrix 2 -3 4 -2 3 -4 -2 3 -4 2 -3-4, P Show all your work. 1 -1…

A:

Q: If a is a group element, prove that every element in cl(a) has thesame order as a.

A: Given that, a is a group element. We have to prove that every element in cla has the same order as…

Q: (a) find the series’ radius and interval of convergence. Then identify the values of x for which the…

A: Given the series ∑n=0∞-1nx-12n+12n+1. To find the radius and interval of convergence. (a) Let us…

Q: Use the method of variation of parameter to solve ry" - 2xy' +2y=3√√.

A:

Q: the probability that scientists from Area 51 will begin selling pet aliens in the next month is 38%.…

A: The probability that scientists from Area 51 will begin selling pet aliens in the next month is…

Q: Describe all possible ways in which two planes (passing R3 could intersect. Suppose V is a vector…

A:

Q: The velocity of a falling rain is illustrated in Figure 1. Determine how far the raindrop travel,…

A: t 0 0.5 1 2.5 4.5 vt 0 4.51 7.34 9.33 9.43

Q: Find the Fourier series of the trapezoidal wave defined by the function…

A: Given: fx=x0≤x≤111<x≤23-x2<x≤3 We have to find the Fourier series of the given function.

Q: Determine a Green function for the equation x²y"(x) + 2xy'(x)-2y(x) = f(x), with boundary conditions…

A:

Q: Develop a model using the Analytic Solver Platform that will determine how many 130-inch rolls to…

A: The company makes standard 130- inch- wide rolls of thin sheet metal and slit them into smaller…

Q: An 8-lb weight stretches a spring 4 ft. The spring–mass system residesin a medium offering a…

A: Given: Weight stretches a spring is 8 lb. The spring–mass system resides in a medium offering…

Q: 1. Let V be an n-dimensional inner product space and let {u₁, 2,. for V. If v=au, and w= bu, where…

A:

Q: 1. modular arithmetic is the basis of many crypto-systems. Compute the result without a calculator.…

A:

Q: u(t) dt 0 For the special case of three-dimensional space (E1, E2, E3 defining a right-handed…

A:

Q: Straight lines passing through a fixed point (h, k). Parabolas with axis parallel to the x-axis.

A: We have to find the differential equation of the given families of curves.

Q: 1. We assume that the measured quantity y is a linear function of three independent variables, x1,…

A: x1 x2 x3 y 0 0 0 10.472 0 -1 0 7.253 0 1 -1 14.708 -1 0 -1 9.861 -1 -1 1 4.374 -1 1 1…

Q: s transformed it the Origin is si to the point (2-3) the axes reamining parallel to the original xxf

A:

Q: You are given the following system of equations:  x1 - 2x2 + 2x3 = 1, -3x1 - x2 + x3 = 4, x1 + 5x2…

A: The given problem is to find the solution for the given system of linear equations by using the…

Q: Given P(A) = 0.37, P(A and B) = 0.14, P(A or B) = 0.58, what is P(B)?

A: We have given that                P(A)=0.37 , P(A∩B)=0.14  and P(A∪B)=0.58Since we know that…

Q: If V is a vector space over F of dimension n, prove that V is isomor- phic as a vector space to F" =…

A: Proving that two vector spaces are isomorphic involves finding a bijective linear map between them.…

Q: Arzela–Ascoli Theorem). For each n ∈ N, let fn be a function defined on [0, 1]. If (fn) is bounded…

A: As per the question we are given a sequence of functions fn : [0, 1] → ℝ bounded by the number M…

Q: Given a compact set A and a closed set B. ShOw that AB is compact!

A: Given Data: Let us consider the given data, A is a compact set B is closed. To show that : A∩B is…

Q: The curve y = sqrt ( 4 - x sq. )  ,-1 < = x < = 1  , is an arc of the circle x sq. +  y sq. =…

A:

Q: Theorem 2.1. For n ≥ 1 we have Σμ(α) d|n 1 -W-{ = 0 = if n = 1 if n > 1.

A:

Q: on metho partial pivoting, the following system of equations : x+y+z = 7,

A:

Q: Find a real root of the equation     e^xtanx=1 by using iteration method  and also apply Aitken's…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Show that x is not a generator of the cyclic group (Z3[x]/<x3 + 2x + 2>). Find one such…

A: The given cyclic group is: Z3x/x3+2x+2*. We have to show that x is not the generator of the given…

Q: With conductances c1 = 1 and c2 = c3 = 2, multiply matrices to find ATC A. For f = ( 1, 0, -1) find…

A:

Q: Let G be a noncyclic group of order 21. How many Sylow 3-subgroupsdoes G have?

A: As per the question we are given a group G of order 21 and we have to find how many Sylow…

Q: Use a purely group theoretic argument to show that if F is a fieldof order pn, then every element of…

A: As per the question we have to use pure group theoretic arguments to show that if F is a field of…

Q: (Which one is a solution corresponding to the eigenvalue X = 4 of the following system of…

A: x'=2xy'=-x+4yz'=-3x+6y+2z

Q: For any prime p, find a field of characteristic p that is not perfect.

A: To find for any prime p a field pf characteristics p that is not perfect. We know that a field K is…

Q: (2) Let U = ((1, 1, 0, 1), (0, 1, 2, 3), (2, 3, 2,−1)) and W = ((1, 3, 4, 4), (1, 1, 0, 2)) be sub-…

A: The given U=1, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, -1 and  W=1, 3, 4, 4, 1, 1, 0, 2 be a subspaces of ℝ4.…

Q: (a) State which of the following matrices are in row-reduced form: /0 0 /1 0 4 -1 A = 0 1 012-2 10…

A:

Q: Problem 2. Let C([0, 1]) be the set of real continuous functions on [0, 1], induced with the norm…

A:

Q: How many polynomials of each degree 0≤d≤5pass through the points (-1,–5), (0,−1), (2,1) and (3,11)?

A: We first state polynomial interpolation theorem. Polynomial Interpolation Theorem: Given a set of n…

Q: If A is nonsingular then det (adj(A)) = [det(A)]n-¹.

A:

Q: For a commutative ring with unity we may define associates, irreducibles,and primes exactly as we…

A: Given: Z12=0, 1, 2, . . . , 10, 11. To show: Both 2 and 3 are prime in Z12 but 2 is irreducible and…

Q: xample 1.22. Let p, q be two positiv ppose (a1, a2,..., an) is an n-tuple of n Σακοκ k=1

A:

Q: The properties that could be used to find laplace of (t+sin2r + cos2r) 2U (1+6) for all 120, are…

A:

Q: $12,000 is borrowed for 140 days at an 8% interest rate. Calculate the maturity value by the exact…

A: Given thatThe principal amount P=$ 12000Interest rate  R=8%=8100=225Time T = 140 days

Q: In Tasks 1-3 we will study a combination of the transport and heat equation called the…

A: To solve : The given problem.

Q: Prove that for every field F, there are infinitely many irreducibleelements in F[x] .

A: To Prove: There are infinitely many irreducible elements in F[x].

Q: Let f(x) be an irreducible polynomial over a field F. Prove that thenumber of distinct zeros of f(x)…

A: The relationship between the number of roots of a polynomial and its degree is a fundamental…

Q: 1. If A is nonsingular then [adj(A)]-¹ = adj(A-¹). 2. The linear system AX = B has a solution if and…

A:

Q: Exhibit a Sylow 2-subgroup of S4. Describe an isomorphism fromthis group to D4

A: Given: A Sylow 2-subgroup of S4To find: Describe an isomorphism from this group to D4.

Q: The sides of a triangle lie on the 3x+y-5-0, x-3y-1=0, and x+3y+7=0. Find the equation of the circle…

A: