Question 2 a) The following differential equation of y(t) is solved by Laplace transform. d²y dt² dy +4+3y= 3, dt y (0) = y(0) = 0; Determine: (i) the Y(s); (ii) the y(t); (iii) the steady state value of y(t) when the time t is tend to infinite i.e. t →∞0.

Q: 11. The base is the semicircle y = √√9-x2, where -3 ≤ x ≤ 3. The cross sections perpendicular to the…

A:

Q: Use the following graph of y = f(x) to graph each function g. A -1 3 4 (a) g(x) = f(x) - 1 (b) g(x)…

A: We know that, g(x)= f(-x) is reflection across y-axis. g(x)= -f(x) is reflection across x-axis.…

Q: 1. Determine the number of degree and the end behaviours of the polynomial y = (x + 5)(x − 1)(x +…

A:

Q: f(x) =4x^3 -24x^2 -60x a. find all values of x that correspond to horizontal tangent lines. b.…

A:

Q: √√(y - 3), 1 ≤ y ≤9

A:

Q: 4. The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is revolved…

A:

Q: Verify the identity. cos(+ x) + cos(-x) = = COS X X- cos(+ x) + cos(-x) = 2 cos ( 2 COS ( + + x + =…

A:

Q: 6 By power series method, Solve the following ODES? (2+x)=y ans: y = a. (1 + 1/2 X)

A: A detailed solution is given below

Q: Solve 7 cos(6x) = 5 for the smallest three positive solutions. Give your answers accurate to at…

A:

Q: Find the slope of the parametric curve x = -6t²-1, y = 2t³, for -∞<t<∞, at the point corresponding…

A: We can find the slope at the indicated point in the following steps.

Q: Use the second derivative test to find the location of all local extrema in the interval (0, 2π) for…

A: Here we have to find the local extrema.

Q: Find area bounded by the carves. (Round answer to 2 decimal places) y = 7x² −2x _y=x³ -7x+4 +

A:

Q: 1. A company's profit, P, in thousands of dollars, is modelled by the equation 3 2 P = 9x³ – 5x² –…

A: Given problem:- 1. A company's profit, P, in thousands of dollars, is modelled by the equation P =…

Q: Solve the following ODES by Undetermined Coeff 11 4X y - 16 y = 19.2 € + 60e, y(a) = Y(u) -4X HO 4X…

A:

Q: 9. Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If…

A:

Q: Use Heron's Area Formula to find the area of the triangle. (Round your answer to two decimal…

A:

Q: Find the missing values by solving the parallelogram shown in the figure. (The lengths of the…

A:

Q: Find the interest rate needed for an investment of $10,000 to grow to an amount of $13,000 in 6…

A: I have appended the formula used in the solution part of the question

Q: 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A:

Q: 6r (x²+3)²¹ 14. Given f(x). f'(x) = ²+3 (m). Write "none" where appropriate. (a) Domain of f: (b)…

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

Q: Find the vector component of v = (4, -1, 7) along b = (2, 4, -4) and the vector component of v…

A: As we know that; The expression for the vector component of v along to b is: Vector component v…

Q: Convert the point (x, y, z) = (4, 4, 3) to cylindrical coordinates. Give answers either as…

A:

Q: 42 1. Calculate the Laplace transform of f(t) = 1. 2. Calculate the Laplace transform of f(t) =…

A: Let's find laplace transform.

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1, 3, 3), b = (-1,…

A:

Q: Determine the intervals in which solutions are sure to exist. t(t2)y(4) + e'y" + 9t²y = 0 Enter the…

A:

Q: Analyze the function f(x) = x+17 4x +15 if x < 4 if x ≥ 4

A:

Q: 2. Find the area of the region enclosed by the parabola y = 2x² and the line y = -x-1

A:

Q: We assume that in a village there are farmers, carpenters, and tailors, who provide the three…

A:

Q: USE A DOUBLE INTEGRAL TO FIND THE VOLUME OF THE INDICATED SOLID Z 52 F2 z = 6-24 0≤x≤4 0≤4≤2

A: We will use concept of double integral to solve this.

Q: Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x…

A:

Q: 5. Find the volume of the solid of revolution formed by rotating the finite region bounded by curves…

A: Given :Curve :y=x-1 y=x-12

Q: Given P(x) 3x55x² - 4x³ – 8x² 64x + 48, and that 2i is a zero, write P in factored form (as a…

A: NOTE: Refresh your page if you can't see any equations. . the given root is  so another root must…

Q: You and a companion are driving a twisty stretch of road in a car with a speedometer but no…

A:

Q: Solve the following initial value problems: A. y(0) = − 5: B. y(0) = - 6: y = y = dy dt 2t

A: NOTE: Refresh your page if you can't see any equations. . take integration on both sides…

Q: . Find the solution of the differential equation. 25y’’-20y’+4y=0 theme: repeated roots; order…

A:

Q: C is counterclockwise around the rectangle with vertices (0, 0), (5, 0), (5, 3), (0, 3) (a) directly…

A: The given integral is: ∮xy dx+x2 dy C is the counterclockwise around the rectangle with vertices…

Q: Find the critical points c for the function f and apply the Second Derivative Test (if possible) to…

A: Given problem:- f(x) =-13/(x2 -11x+36)  To find:- Critical points where local maximum and minimum…

Q: Air traffic controllers continuously monitor the angles of elevation and to an airplane from the…

A: NOTE: Refresh your page if you can't see any equations. .   here we have

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A:

Q: Find a basis {p (x), q (x)} for the vector space {f(x) = P3[x] | ƒ' (−1) = ƒ (1)} where P3[x] is the…

A: We have to find p(x) and q(x).

Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (5, 3, 16)…

A:

Q: Find the general solution of the differential equation. y (5) — 11y(4) + 29y" — 11y" + 28y' = 0.…

A:

Q: Find dy/dx and d²y/dx2, and find the slope and concavity (if possible) at the given value of the…

A:

Q: The table below shows the velocity of an object (cm/sec) at each sec as it moves along a track for…

A:

Q: If a ball is thrown vertically upward with an initial velocity of 96 ft/s, then its height after t…

A:

Q: Find the curvature of the curve (t) Give your answer to 2 decimal places. = (4t, t², -5t4) at the…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z = y In(x), (1,…

A:

Q: Two ships leave a port at 9 a.m. One travels at a bearing of N 53° W at 12 miles per hour, and the…

A:

Q: Find the points of Intersection of the graphs of the equations. x² + y = 16 -4x + y = 11 (x, y) =…

A: Here we have to find the intersecting points.

Q: Your broker has suggested that you diversify your investments by splitting your portfolio among…

A: