Determine the inverse Laplace transform of G (s) = 28 (8²-4)² Og(t) = t cosh 2t O g(t) = }t sinh 2t Og(t) = tet Og(t) = 2 cosh 2t

Q: A forest has a population of lynx and a population of rabbits. Let a represent the number of lynx…

A: Solution: x'=dxdt=-0.25x+y  .....1y'=dydt=-x+4y  .....2B.C.S: x0=0 and  y0=1From equation 1  and 2…

Q: Find vectors A and B such that A is parallel to (2, 1,-1), B is perpendicular to (2, 1, -1) and A +…

A:

Q: Given the formula, S n =a 1-r^ n 1-r what is the sum of the first nine terms of the geometric series…

A: Note: The geometric series has to be 324, -108, 36, -12,....., Otherwise there will be no common…

Q: Identify and sketch the graph of the following SURFACES. 2 = √9-y²

A: We have z=9-y2 Since z is square root of 9-y2 so z is positive always. We can write z=9-y2 as:…

Q: Q1: Solve the following differential equations (A) 2xydx + (x² +8x+17)dy = 0 (B) y'-- 4 2x+1 - y = =…

A: According to our company policy we can only do three subparts at most of a question posted, if you…

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Let S be the quadric with equation    4x2 - (y-3)2 + 4z2 = 4 ⇒x2 - (y-3)2/4 + z2 =1

Q: a. Find -R(t), . give the parametric equations of the tangent line to the graph of -R(t) at t=0: 1…

A: Given that R't=4e2t,11+t2,2cosht R0=1,−2,3 To find: R(t) Parametric equation of the tangent line…

Q: 2. Given the figure below, find a single vector that is equivalent to C B tw b) 10 14 וד --(A-F+C) G…

A:

Q: ach of these algebra

A: Given that the London bus tour company function                            T(x)=-x2+50x-225 where…

Q: 5. || x+y cosx 1+sin x

A: Solution

Q: || = 8, || = 3 and the angle between them is 125°. Determine |u-v|

A:

Q: E be a Euclidean space of dimension (E(1, f)) = dim(Ker (f- id)), then s minimal.

A:

Q: Solve the system of differential equations. -17 x' = [3¹] 15 x₁ (0) = 8, x₂(0) = -8 x₁(t) = x₂(t) =

A:

Q: 8. Time to explain: a) why does the vector equation of a plane have two parameters, while the vector…

A: Part (a) A line is a defined in one dimension, whereas, a plane is defined in 2 dimensions. So, for…

Q: Given any undirected graph G, for any orientation o of G, if Bº is the incidence matrix of the…

A:

Q: Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar,…

A: The solids represent cones. These are similar if the ratio of their dimensions are equal.  So, we…

Q: Solve the system of differential equations. Jx₁' = 6x12x2 x2 = 2x1 + 10x2 x₁(0) = 16, x₂(0) = − 16…

A:

Q: III. Let S be the quadric with equation 4x² - (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: 4x2 - (y-3)2 + 4z2 = 4 (C) The quadric S can also be identified as a surface of revolution.

Q: What is the answer to Euler's question? If the "journey" is possible, describe it. If the "journey"…

A: Solution: Graphical Representation:• The nodes vertices; numbered as A, B, etc represent land'• The…

Q: 8x Show that the three functions: f₁(x) = ex-8, f₂(x) = e³x, f(x) = 4(2x-2) are linearly dependent.

A:

Q: Let n ≥ 1, x be a real number, and x ≥ −1. Prove the following statement using mathematical…

A: The principle of mathematical induction is a technique or method that is used to prove the statement…

Q: Separation of variables The lateral radiation of heat from a bar of length L insulted at both ends…

A: There are so many subparts, as per our guideline we can solve only first three subparts. Please…

Q: 9.W.1 The Gram matrix of an inner product on R2 with respect to the standard basis is G = 1 2 -1…

A:

Q: 7. xdy = (5y + x + 1)dx

A: xdy=(5y+x+1)dx ⇒ dydx=5xy+1+1x⇒ dydx-5xy=1+1x

Q: 1. If x=27-3k and y = 7+57-4k, express each of the following in terms of i, j, k a) 5x-2y

A:

Q: Л Define R as the region that is bounded by the graph of the function f(x) = -3√3 sin (x), the…

A: To find the volume of the solid that is obtained by revolving the region bounded by below curves…

Q: Solve the following differential equations: 1 √1-3x (a) - dx + sin y dy = 0 cos 2y +1 (b) x²y + x³…

A: Using separation of variables for first problem and using integrating factor for second problem.

Q: Find the power series representation for f(x) = = 2x (1-x²)² and then find its radius of…

A:

Q: d). Integrate f(x, y, z) = -√√x² + z² over the circle r(t) = (a cost)j + (asint)k, 0≤t≤2.…

A: Solution:-

Q: Consider the vector-valued function Ŕ(t) = a. Find the domain of R. b. Determine if R is continuous…

A:

Q: If M‡ Ø is any subset of a Hilbert space H, show that M is the smallest closed subspace of H which…

A: Solution:Hilbert space H, M⊥⊥ smallest closed subspaceWe first show that for any M⊂H, M⊥is closed.…

Q: In Exercises 23-26, use the shell method to find the volumes of the solids generated by revolving…

A: Note. 1: Since you have asked multiple questions, we will solve the first question for you. If you…

Q: Let A be a nxn square matrix having rank 2 then rank of (A^t A) is (A^t- Transpose of A) Option A))…

A:

Q: Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

A: The quadric equation given is as follows: 4x2-y-32+4z2=4 (a) Rearrange the above equation.…

Q: Consider the following IVP: y'=1+ 1st≤2, y(1)-2. The actual solution of this IVP is y(t)= t ln(t) +…

A: Here we have the following differential equation : y'(t) = 1 + y/t With initial condition : y(1) = 2…

Q: Evaluate the volume under the surface given by z = f(x, y) = x² + y, over the region bounded by the…

A: Imagine a parallelepiped with small base area dA with height z, then volume of this parallelepiped…

Q: Find the power series representation for f(x): = 2x (1-x²)² and then find its radius of convergence.

A:

Q: 2. What is the largest possible c in (1) if X=R² and x₁=(1,0), x₂ = (0, 1)? If X = R³ and x₁ = (1,…

A: Given: c To find: a) X=R2b) X=R3

Q: Evaluate the following definite Integrals by using Gamma or Beta Functions: 5 (a) [√4x In (V√x)] idx…

A:

Q: Given the polar curves: C₁:r = 2 cos 0 π 2 C2 B(0,0) C₁ A(2,0) C₂:r = 2 cos 30 Find the (sum of)…

A:

Q: 17. Find a combinatorial proof that n("z ¹) = (k+1)(²1). k 19

A:

Q: g. L-12_3 s2-8s+251 -1 h. L-¹ [25²-35+4]

A:

Q: Find the area bounded by the inner loop of the curve(limacon) r=2(1+2cos(theta)). Please make a…

A:

Q: Find a solution to the given IVP using Laplace and Inverse Laplace Transforms y" + 3y' + 2y = 4t²,…

A:

Q: Use secant method to find the root of x^3 –x^2 – 3x – 3 with two initial points xa=3 and xb=2 and ∈=…

A: FIND THE ROOTS USING SECANT METHOD

Q: x"" (t)- 3x"(t) − 4x' (t) + 12x(t) = 12e-t; x(0) = 4, x'(0) = 2, x'(0) = 18

A: The solution is given as

Q: 1. (a) Find the rank and nullity of th4e following system of linear equations: x₁ + 2x₂-x₂ + 4x₂ = 0…

A:

Q: x Given the quadric surface T: + 3y² = z + 3. 3 Find an equation of the traces of T on the planes x…

A: Let us find the equation of the traces of T on the given planes one by one.

Q: Determine the two values of z such that the middle 58% of the data lie between the two z-values.

A:

Q: 2. Show that if the orthogonal dimension of a Hilbert space H is finite, it equals the dimension of…

A: Given: Finite dimension To find: Former finite