1. Solve the following ODE by the method of variation parameters 4y" – y = 1. (Other methods are not accepted).

Q: 7. Find the inverse of the following linear transformation: [3x + 2y] 5x +3yl

A: 7 Given linear transformation is Txy=3x+2y5x+3y

Q: 3. Find the dot product of à = and B =. 4. Find the scalar product of P = 10î – 4f + 7k and Q = -2î…

A:

Q: f(t) = t5et 120 А. (s-4)6 24 C. (s-5)6 120 В. (s-4)5 24 D. (s-5)5

A:

Q: f(x, 3) = In(x? + Y²òf function P(3,4) at the point of i = (9, 12) Directional derivative in the…

A:

Q: FALSE and give a counterexample and justify or explain briefly why this is such. (a) Let A and B be…

A: Here we use examples and theorems for sequences.

Q: Let a = 64 · 9 . 121 · 125 · 17 and b = 4 · 243 · 11 · 5· 169. Determine the value of gcd(a, b). O…

A: GCD of the two numbers

Q: Problem 1 I'm tired of being a professor. My latest scheme to get rich quickly is to produce a…

A: Hi! As per norms, we will be answering the first three sub-parts. If you need an answer to others…

Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…

A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…

Q: For integers æ, y, notation æ|y means that x is a divisor of y. (For example 5|30, but it is not…

A: After the assumption that 3| (22k - 1), we need to mathematically formulate this.  i.e., from the…

Q: Let G = { a+bi ∈ ℂ : a and b are rational numbers, not both zero } . Prove that G with the operation…

A:

Q: 3) Show that (a + bi)º = (a – bi). Hint: for any x, y in a field containing Fp, (x+y)º = xº + yP.…

A: As per our guidelines, we are supposed to answer only one question if there are multiple questions…

Q: Question B1 a. Calculate the line integral [F•dr. where F = 3x²y²i + 2x°yj for the curve C. Here C…

A: We need to find line integral of vector field  line integral of vector field F→ along a curve C…

Q: DIRECTIONS: The entire test has been answered for you. Your job is to check the answers for errors.…

A:

Q: 3. Determine which of the following sets of functions are subspaces of F[a, b]. a) All functions f…

A: NOTE: According to guideline answer of first three subpart can be given, for other please ask in a…

Q: Write out the subsets A, B,C defined below by listing their elements between braces. A = {x € S : x²…

A:

Q: Use a compass and stralghtedge to decide whether each set of lengths can form a triangle. 7 cm, 6…

A: Concept: To form a triangle, the sum of any two sides of the triangle should be greater than the…

Q: Graphs of f(x) (solid) and g(x) (dashed) are given below. Use them to find the following yes. Show…

A:

Q: Value of cos15° sin15°| is: sin 15° cos15 (a) 1 (d) none of these Select the correct response: a

A:

Q: The value X2 .2 ... -2 x1 + 6 x2 + x3 = 9 - X1 + x2 + 7 x3 4x1 – x2 – x3 = 3 = -6

A:

Q: Problem 10.1.2. Let (xn), (yn) be sequences as in the NIP. Show that for all п, т € N, zn < Ут-

A: see attached image

Q: 5. Show that the functions x,x? -,x³ -x x are mutually orthogonal in the interval [-1,1].

A:

Q: Determine which number, 0 through 7, is the given number equivalent to in modulo 8. Write your…

A:

Q: f(t) = t cos 4t 8s 8s А. (s2-16)2 C. (s2+16)2 s2 +16 В. (s² –16)² s2-16 D. (s2+16)2

A: We have to find the Laplace transformation of ft=tcos4t

Q: . Use Taylor's series, to prove that Bin z tan (x+ h)3Dtan%4 (h sin z). sin 2z +(h sin zj?. sin 3z -…

A:

Q: Prove that if S is a bounded set then S is bounded.

A:

Q: The coefficient of sin(x) in the antiderivative of COS is Blank 1 (use fraction form not decimal no…

A: Solution

Q: w the depth first traversal of the following graph. Start at vertex 1. Ties are resolved in…

A: Here I run a python script and see the result.

Q: Card 1 Card 2 16 17 18 19 20 21 22 23 4 5 6 7 12 13 14 15 24 25 26 27 28 29 30 31 20 21 22 23 28 29…

A: A person has chosen a number between 1 and 63. he tells you that their chosen number lies on cards…

Q: Example: Solve the following system of linear equations using Crout method. 1 1 -4 -1) x2 = (2 0 -1…

A: Given a system of linear equations                                                 4101-4-10-14…

Q: Зх — 0.1у — 0.2z%3D 7.85 0.1х + 7y - 0.3z %3D —19.3 0.3х — 0.2y +10z %3D 71.4

A:

Q: a 1.F.5 To any vector v = in R³ we can associate a polynomial p.(x) = ax² + bx + c in P<2. There is…

A:

Q: 4. Determine the Fourier sine series of f(x) = x + 1 0<x <n

A: The given problem is to find the Fourier sine series of given half range periodic function. Given…

Q: Tank # 1 initially holds 50 gals of brine with a concentration of 1 lb/gal, while Tank # 2 initially…

A: Given: Tank1: The volume of tank 1=50 gals x1(t)= amount of salt at time tx1(0)=50 gals× 1…

Q: G1 = Z÷ and G2 = Z, *

A:

Q: fj+1 - fj-1 2Ax Assuming a uniform grid spacing of Ax, derive a finite difference approximation to…

A:

Q: What is the radius of convergence of the series below? 2-n (x – 1)" |n + 1 n=0

A:

Q: Calculate Vf when f 3x z-y7+ 4x'y+ 2x - 3y-5 at the point (1, 1, 0).

A:

Q: f(t) = cos² 3t %3D s2 +9 A. s(s2+36) s2 +18 C. s(s2+36) s2 +6 B. s(s2 +9) s2+18 D. s(s2 +9)

A:

Q: 21 then find the value of (- A2 + 6 A)? 4 If A 3 -2 1. -2 [2 07 0 2 [2 4. elect the correct…

A:

Q: (3) A firms production function is Q(L) = 15L -0.1Ľ , where output (Q) is a function of a single…

A:

Q: Consider the sequence {a„} where a, is given by (n³ – 1)/nº, (n² + 1)/n², if n is even. if n is odd,…

A: The given question is related with  sequence. Consider the sequence an , where an is given by…

Q: If F (2x + y)i + (3y 4x)j evaluate o. F.dr around a triangle ABC in the xy-plane with A(0. 0). B(2.…

A: Line integration of the function

Q: 4. Determine which of the following sets of n x n ma- trices are subspaces of Mnxn (R). a) The n x n…

A:

Q: f(t) = sin* 3t A.G 12 24 + s2 +36 8 (s2 +144 B. 8 \s2+144 . (t 4s + s2 +36 c. * ) D.(14 12 24 С. 8…

A:

Q: Question A1 Consider a vector field F= 2x° yị +x'j., and a curve C defined by the equation y = 2x².…

A:

Q: x+ 2 2x – 3 x+1 4 If A = is symmetric, then what is x equal to? | 1. 2 2. 3 3. -1 4. 5 Select the…

A:

Q: f(t) = t² cos 6t 2s(108-s2) 2s(s²-108) А. (s2-36)3 C. (s2-36)3 2s(108-s?) В. (s2+36)3 2s(s?-108) D.…

A:

Q: x' 3 27 x+39 2 (2) For the function f(x): 3 4 (i) Determine the coordinates of the turning points.…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Use Fermat's Little Theorem to find each value. Remember, x-1) =1 (mod p). Write your answer in…

A:

Q: f(x) 2 4 8. 10 12 14 CO

A: