Use Laplace transforms to solve the differential equation: d²y d1² =y=t where y(0) = 1, and y'(0) = 1

Q: Find the laplace transformation of the following function :- f(t) = Sint + i (il 000 1 f(t) = f(t) =…

A:

Q: . If you were to graph two quadratic functions on the same xy-plane, how many intersection points…

A: Given: Two quadratic equation. The given demand function is fx=0.02x-1002 and the given supply…

Q: Find the volume of the truncated cone generated by the rotation around ox of the area bounded by…

A:

Q: In the general equation f(x)=asin [k(x-d)] +c the equation of the axis of the curve is determined by…

A:

Q: (cos-isin) (cos 70+isin 70)-³ (cos 40+ i sin 40)² (cos+ i sin 0)³ Q2. Obtain the Power Series…

A:

Q: (1-x²¹) 22-x-x+ x + 2y = 0. d²y dy dx² dx Ay

A: Given : 1-x2d2ydx2-xdydx+λy=0 To Find : write given equation in form of Sturm-Liouville problem

Q: ln p= a + b/t + cln(t) + dt^2 Is this equation linear or non linear

A: To determine whether the below equation is linear or non linear. lnp=a+bt+clnt+dt2

Q: Differentiate the following function and name each property it uses to do so y = sen³ (3x)

A: Given  y=sin3(3x) Here we can differentiate the y with respect to x In order to differentiate…

Q: X, Y and Z be subsets of the set . Verify the following propert XU(YUZ) = (XUY)UZ, XN(YnZ) = (XnY)…

A: X, Y, Z be subset of a universal set Ω to verify…

Q: 6. Given the final tableau (after deleting the columns of the artificial variables) for phase 1 of…

A:

Q: Let a,b,and c be natural numbers and n be a natural number > 0. Prove that if a = b mod n, then a^c…

A: Use mathematical induction to prove the given statement.

Q: Question 7. (10 Marks) If K is a subgroup of G and N is a normal subgroup of G, prove that KnN is a…

A:

Q: Evaluate fx" In x dx for n ‡ −1. Which method should be used .-1 to evaluate fx-¹ In x dx?

A: We have ∫xnlnx dx   , n≠-1 Integration by parts is ∫fg dx=f∫g dx-∫ddxf∫gdx dx Using integration by…

Q: What if a1=16

A: Same procedure as before.

Q: Set up, but do NOT evaluate, the integral needed to determine the area A of the region between the…

A:

Q: D2 SOLVE STEP BY STEP IN DIGITAL FORMAT Consider a metal sphere that initially has a radius of 7…

A:

Q: (b) Find the optimal value of the objective function of the following LP problem by directly solving…

A: To find the optimal value of the objective function of the LPP by directly solving its dual problem…

Q: Solve the system graphically, and indicate whether the solution region is bounded or unbounded. Find…

A:

Q: Question 7. Solve the following initial-boundary value problem modelling the vibration of a string…

A:

Q: TM Ford Mustang Cobra The accompanying table shows time-to-speed data for a 1994 Ford Mustang Cobra…

A: Introduction: Trapezoidal rule is the tool to approximate an integration numerically. There are two…

Q: 3. A compression rod of length l is loaded by a sinusoidal force as shown in Figure. The bending…

A: Using the method of undetermined the coefficients for particular solution for nonhomogeneous part.

Q: Suppose an = n=1 Ž n=1 Consider the two series 1 5n n=1 and bn 2. n=1 ܬ ܀ n=1 an converges and an…

A:

Q: Use the Divergence Theorem to evaluate [/F. F. N ds and find the outward flux of F through the…

A: Given: Fx,y,z=xi+yj+zkS: x2+y2+z2=4 Using the divergence theorem we have to calculate the outward…

Q: y" + 2y' - 48y = 3e²t+4e-2t; y(0) = 0, y'(0) = 1.

A:

Q: Solve step by step in digital format a) Expand (1+x) In(1+x) in Maclaurin series. find the limits…

A: Given function is f(x)=(1+x)ln(1+x) As we know the Maclaurin series for a given function f(x) at a…

Q: - 4. y(x² + xy² − 1)dx + x(x² + y² + 1)dy = 0

A: Introduction: When a first order ordinary differential equation is not exact, we multiply…

Q: Give an example each of the following. Justify your choice of examples.  i) A non-trivial set in…

A: We have to give an example for each of the following statements ; (i) A non trivial set in Euclidean…

Q: Q5. Consider the vector field F(x, y, z)=xi + 2yj + (x² + 4y²) k and the closed surface S made up of…

A:

Q: 2. Diagonalize the matrix using normalized vectors. B= 3 1

A: Given,        B=1331

Q: Write out an expression for a set (in set notation) that includes all divisible by three and all…

A:

Q: Determine the Laplace transform of the differential equation. y² + 4y y (0) = 0 = Cost;

A: Sol:- y' +4y=costTake Laplace transform of both sides of the equationLy'…

Q: The function f is graphed below. State the values that fulfill the following requirements. If there…

A: According to the given curve, the curve is smooth continuous and nowhere we see any sharp edge.…

Q: B. Determine a lower bound for the radius of convergence of series solutions above the given point…

A: It is provided that x2+1y''+2xy'+4x2y=0. We need to determine a lower bound for the radius of…

Q: farmer can buy two types of plant food, mix A and mix B. Each cubic yard of nix A contains 42 pounds…

A: Given data for the plant food that farmer can buy is tabulated below Minerals per cubic yard Mix…

Q: Solve x (az + √2) dx y (az + √2) sin (ay²) dy + (az 4√2 ln az + √2 = C 4√2ln az + √√2 = C 4√2 ln az…

A:

Q: There are 100 people in a room, all born in the same year in the same 30 day month. What is the…

A: Given that: Number of people in the room = 100 Number of days in the month = 30

Q: Determine the solution of the following differential equation: d²y dx² dy 8-+16y=0 dx where y(0) =…

A:

Q: To approximate the integral of a function w(x) on [-1, 1] use the formula = [₁, w(t)}dt ≈ w(a) +…

A: Given: The formula Iw=∫-11wtdt≈wa+w-a and where 0<a≤1. The given formula is for approximation of…

Q: Prove ¬(3x € X : (Vy ¤ Y : E(x, y))) = \x € X : (‡y ¤ Y : ¬E(x,y)) (Vx X: (³y € Y : E(x, y))) = (3x…

A: We have to prove  a) ¬∃x∈X : ∀y∈Y : Ex, y=∀x∈X : ∃y∈Y : ¬Ex, y b) ¬∀x∈X : ∃y∈Y : Ex, y=∃x∈X : ∀y∈Y :…

Q: 1. A beekeeper estimates that the number of bees in a particular hive at the start of 2019 is 500,…

A: (a) Explanation: The general form of growth model when the initial size is given and the subsequent…

Q: Find the explicit solution to the following Using substitution method, find general solution to the…

A:

Q: Apply anthe problem y' = Richard san extra polation ity: Itt year=e. and approximate y and 1 ร 2 h =…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Consider the matrix A = Calculate a22 = 8 5 d n -( :-(29 766 b f 468 h с Calculate 932 = a e

A: It is provided that: A=852766468·dngbfahce. We need to calculate a22, a32.

Q: Let A and B be two finite sets such that |A| = 20, |B| = 28 and |A U BI

A: Given A=20B=28A∪B=36

Q: 1 If F(p) is the Fourier transform of f(x), then F(p/a) is the Fourier lal

A:

Q: Problem 2.8.4. Let k be a fixed positive integer. Let an be the integer an an (mod k) for an EZ. 1.…

A: Given :  Let k be a fixed positive integer  and  a¯n ≡ an mod k  for  an ∈ ℤ To prove : (1) ϕ : ℤx →…

Q: Find two natural numbers n and m with n, m>26 and gcd⁡(n,m)=26. Then, for the numbers n and m you…

A:

Q: 5. Find the volume of the solid that results when the region enclosed by the given curves is…

A:

Q: modulo them? For which of the following prime numbers are 2 a square 59, 61. 17, 19,

A:

Q: 8 people fit comfortably in a 2 yards by 5 feet area. Use the value to estimate the size of a crowd…

A: It is given that the area occupied by eight people is 2 yards by 5 feet. We will convert 2 yards in…