(a) The sum of infinite number of terms in G.P. is 20 and the sum of their squares is 100. Then find the common ratio of G. P. (b) If each term of an infinite G. P. is twice the sum of the terms following it, then find the common ratio of the G.P.

Q: Find a vector that spans the kernel of the following matrix: [ 1 0 2 4 ] [ 0 1 -3 -1 ] [ 3 4 -6 8 ]…

A: LET MATRIX IS A=1  0   2  40  1-3-13  4-6   80-1   3  4 NOW, THE KERNEL OF A DEFINED AS-:…

Q: Find the outward flux of the field F = 8xyi + 4yzj + 2xzk across the surface of the cube cut from…

A:

Q: Which of the following series is convergent? Select one: Ο Σα 1 8" n=1 7" +4 3 n=1 7" +4 Ο Ο Σ 1 ∞…

A: The given problem is to check whether which of the following series are convergent.

Q: A raffle is going to be held in which the winner will get $200. If 1000 tickets are to be sold, what…

A: Given, In a raffle, winner will get $200.    We have to find the fair price for a ticket if 1000…

Q: B. For each of the following series, determine whether the series converges or diverges. (Sum from 1…

A: A Series is the collection of a sequence. Let a1,a2,...., an be a sequence then the series is…

Q: Find the complex form of the Fourier series f(x)=e*, -1<x<1 Ans. E

A: As per the question we are given a piecewise defined function as : f(x) = e-x  for  -1 ≤ x ≤ 1 Now…

Q: Find a parameterization your parameterization for a circle of radius 6 with center (1,-3,4) in a…

A:

Q: Determine the general/particular solution (whichever applies): y"' + 4y' + 4y = ( 3 + x) e −2, when…

A:

Q: Jse Lagrange multipliers to determine all points on the graph of 3x2 + 2y² -z = 0 nearest the point…

A: To Find: All points on the graph of 3x2+2y2-z=0 that are nearest to (0,0,2) using Lagrange…

Q: -15 8 -7 2 8 -5 -1 1 Determine the four eigenvalues of A. ● Determine all of the ordinary…

A: Given system x'=Ax = -158-164-72-1058-57-1-11-2-2 x, Part (1):- Determine the four eigenvalues of A.…

Q: You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped…

A: To find the highest floor from which a ball can be dropped without being damaged, we can use a…

Q: Question 2 Let z = 2y - ln(2x + y). Find the second order Taylor polynomial at x = 0 and y = 1 and…

A:

Q: Get the function in algebraic form, state its representation in terms of the function unit step and…

A:

Q: Find the value(s) of A such that h(x) ODE y(³) + 4y' = 3e". Ans.: A = = Ae solves the third-order

A:

Q: 6.Find half-range Fourier cosine series for f(x)=x in (0<x<2π)

A:

Q: If D is the triangle with vertices (0,0), (99,0), (99,21), then 11 D dA=

A:

Q: 2. Determine y when x = 2 using the fourth order Runge-Kutta algorithm, in five decimal places, for…

A:

Q: n=1 11" (x − 4)"(n+1) n+ 11

A:

Q: The set of polynomials {3t²-3t+5, mt+6t²+10} is a linearly dependent set in P, if 2 m=6 Select one:…

A:

Q: Find the surface area of the portion of the graph of x² + y² + z = 9 that lies above the xy- plane.

A: The given problem is to find the surface area formed by the portion of surface x2+y2+z=9 that lies…

Q: Cos sin 0 = Let A-s (a) (b) sin 0 со B = (1 − A)(I + A)−¹ and C = (I − B³)(I + B³)−1 Assume (I +…

A:

Q: If a Gaussian quadrature formula n [ f(x)w(x) dx = [A₁f(xi) a i=0 holds for all f(x) = P2n+1, show…

A:

Q: What can we say about the below alternating series? Σ(-1)n-1 n=1 2n 2+1 Select one: O More than once…

A:

Q: Do as indicated. 1. A certain province widely cultivates maize crops during the dry season. The…

A:

Q: Given f(x, y) = 4x cos (y), find 4x³ fay(x, y) = fyy (x, y) =

A:

Q: A window has the shape of á parabola above and a circular arc below. Find the area of the window.…

A:

Q: 7. Let X be a connected space. Let C be a connected subset of (X, T). If X\C=BUD where B and D are…

A:

Q: ommon e 2 and the last (2m + 1) erm /2. If the middle term of both A. P. and G. P.

A:

Q: Define a binary relation =3 on Z by x =3 y if x - y is divisible by 3. 1. Prove that = 3 is an…

A:

Q: 9. Find the equation y = ax² + bx + c of the least-square parabola that best fits the given data…

A: The given problem is to find the best fit parabola can be formed with the given data points by using…

Q: Find the term a45 for the arithmetic sequence with first term, a₁ = 13, and common difference, d =…

A:

Q: Given the matrix A = system X'= AX. 04 1 00 4 " find the general solution o the linear

A: Eigenvalue: A number λ is said to be an eigenvalue of the matrix A if there exists a non-zero vector…

Q: ILLUSTRATION 5.40 If (p+q)th term of a G.P. is 'a' and its (p - q)th term is 'b' where a, b>0, then…

A:

Q: Answer the following questions about the equation 1 4x³ − y² + ²⁄yz² − x(y − x)e² +1=0. (1) Does the…

A:

Q: 16.4 Euler's Method 16-23 In Exercises 5-10, find the orthogonal trajectories of the family of…

A:

Q: (1) Let T: P→ Py be a linear transformation such that T(ar²+bx+c) = (a-3b)z²+z+2c. Then a basis for…

A: (i)  The linear transformation T: P3→P3 defined as Tax2+bx+c=a-3bx2+cx+2c        Let  α=a,b,c ∈…

Q: Not the right answer

A:

Q: Iff, g, and h are f A(x) = (xf)' (x²f)" differentiable functions of x and 8 h (xg)' (xh)' (x²g)"…

A:

Q: Evaluate the integral ff ds, where f(x, y) = y cos(2x) and C is the triangle with vertices at the…

A:

Q: Given: A = [1 3 3 202 € M3 33 (a) Find the eigenvalues of A and determine their algebraic…

A:

Q: To find a particular solution for the differential equation 3y"-24 y' +36 y=e10x with the variation…

A:

Q: An engineer wishes to make 50 concrete posts (0.8 meters high), each in the form of a frustum of a…

A: Total number of concrete post 50 Height of each post 0.8 m Base of the frustum have side 0.10 m  and…

Q: For each of the following series, determine whether the series converges or diverges. (Sum from 1 to…

A:

Q: Question 1 Let W be the set of all vectors of the form a) [α] b where -2a +6b-6c = 0 Lc -3 Determine…

A:

Q: Write a definition for the nth term of Sequence B

A: A sequence is a function from set of natural number including zero to real numbers.  Example: let…

Q: You need to provide a clear and detailed solution for the following Questions: Question . Let W be…

A: Basis: A set of vectors S is said to be a basis of the vector space V if it is linearly independent…

Q: Q2. Evaluate Sdx using Simpson's rule with N = 4 and hence find the 1+x³ approximate value of In 2

A: The given problem is to evaluate the given integral by using Simpsons rule and find the approximate…

Q: Determine which theorem applies to simplify the following. It is possible that more than one will…

A: Given  Find the work done by the vector field Fx,y,z=yzcosxyi^+xzcosxyj^+sinxyk^ along the…

Q: Discrete mathematics Proof by contradiction. Assume for the sake of argument that the set P of all…

A: Here we want to prove that the set of prime numbers is infinite. Proof by contradiction is given. We…

Q: An architect designs two houses that are shaped and positioned like a part of the branches of the…

A: