H3. Show that the convolution of class functions is a class function.

Q: (2x)dx + (y - 3x2y-1)dy=0 1 y x² An implicit solution in the form F(x,y) = C is v3 (Type an…

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Q: 2. Use polar coordinates to carefully calculate an exact answer for SS √x² + y² dA on D = = {(x, y)…

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Q: Show that the vector field F = (yz² ye, rz² - e, 2xyz) is conservative, and find a potential…

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Q: 1. Complete the following to find a density function 8. A) Suppose that the density at each point in…

A: Solution :-

Q: At any time t, the rate of growth of the population N of deer in a state park is proportional to the…

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Q: Let B₁ and B₂ be orthonormal bases for an n-dimensional vector space V. Let A = JB₂B₁ be the…

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Q: Find a function of the form y A sin(kx) + Cor y = A cos(kx) + C whose graph matches the function…

A: We need to determine the equation of the given graph in the form of y=Asinkx+C or y=Acoskx+C.

Q: Use a power series centered at x = -4 to represent the function f(x) 11 5-2x Provide your answer in…

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Q: Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) =…

A: We have to solve given problem:

Q: Determine if u = (4,3) and v = (1/2 , - 2/3) are orthogonal, parallel or neither.

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Q: Using the following data: ReceiptID juices 1684164 2294086 587482 2610745 1630056 true true true…

A: From the given table of data it is clear that for Receipt Id (2294086); Only juices, paper goods and…

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: We want to find Laplace inverse of given function.

Q: Use a power series to solve 2y" — y = 0, - Find the radius of convergence. y(0) = 4, y'(0) = -9.

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Q: Determine

A: We use definition of basis.

Q: What is the null space of this matrix:   A = 3 0 0 2 0 0 1 1 1

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Q: please

A: We solve by two different method.

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Use the frequency polygon to identify the class with the greatest, and the class with the least,…

A: Solution:-

Q: Let A be the set of all constant sequences in R^N. Prove that A is a closed set relative to the box…

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Q: 1. Given the function f(x) = ln x a) Find the Taylor polynomial p5 for f(x) = ln x at a = 3. b)…

A: Sol:- Taylor series of function fx at a is defined as:fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+…Apply…

Q: Determine the number of solutions of the equation x₁ + x2 + x3 + x4 + X5 = 15 in positive integers…

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Q: DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then the integral L {f(t)}…

A: ℒf(t)=∫0∞e-stf(t)dt We have  f(t)=00≤t<π/2cos(t)t≥π/2

Q: Solve the diffusion problem u(x,0) = {_-^2 otherwise {4 Ut - 3uxx = 0, -∞0 0 4 |x|>2 Write the…

A: The diffusion equation may be a parabolic partial equation. In physics, it describes the macroscopic…

Q: Q4. Let A = {6m + 1: m € Z} and B = {12n-5:n € Z} be subsets of a universal set U. a. Show that A &…

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Q: In words, communicate parent function the function : all transformations f(x)=2x g(x) = 3.2 2.…

A: Given f(x)=2x.

Q: The region S is the base of a solid with parameters y=x^3 x=4 y=0  For this solid, each cross…

A: Given: The region S is the base of a solid with parameters: y=x3, x=4 and y=0. For this solid, each…

Q: please

A: We use definition of Heaviside function.

Q: Find a power series expansion about x = 0 for a general solution to the given differential equation.…

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Q: Match the equation with the graph. Include the directrix that corresponds to the focus at the…

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Q: Consider the initial value problem (sin y)y' (t) = +¹⁄2, y(3): = −1. The largest open rectangle in…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: If cot(x) 3 8 Give exact answers. sin (-2) = cos (²) = | a(²/2) = tan || (in Quadrant 3), find

A: Explanation of the answer is as follows

Q: 1. The outside temperature of one day (from midnight to midnight) can be modeled as a sinusoidal…

A: The minimum and maximum temperature are 420F, 580F.  The minimum temperature occurs at midnight. We…

Q: Question 4. Apply the reduction of order method to find the general solution of tx" − (2+t)x' + 2x =…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: √1-y²6-x²-y² Let I = ²₁¹ 4+x+y dzdxdy. By converting I into an equivalem triple integral in…

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Q: describe a solid generated by rotating R about an axis. Find the volume of that solid (you do…

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Q: Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) =…

A: To solve given question first of all we use the trigonometric identity and then use the Laplace…

Q: (a) Set up (but do not evaluate) an integral that calculates the volume of that part of the solid E…

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Q: 24 If cot(z) = Give exact answers. sin ( 2 ) = cos (1/7) = | tan(²/2) = (in Quadrant 2), find

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Q: Given that cos(8√t) √nt find the Laplace transform of√√cos (8√t). {√² cos(8√7)} = 0 = e-16/s √s

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Q: 6 F(s) = ((28 $3)2 + 3) +²+ e + 3)²

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Q: Use Gaussian Quadrature of order 5 to approximate 08 6 2 x-1 To how many decimal places is this…

A: Given that,    f(x)=∫286x-1dx                                  1 using the Numerical Integral by…

Q: Find the absolute extrema for the given function on the interval [1.2, 3.7]. Write your answer in…

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Q: Use the method of Lagrange multipliers to find the maximum and minimum values (if they exist) of the…

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Q: + The function h(t) = 6sin(3πt 3 where h(t) is in metres and t is in seco models the movement of a…

A: The given equation is ht=6sin3πt-π3+4  where h(t) is in meters

Q: Use a power series to solve 3y" - y = 0, Find the radius of convergence. y(0) = 7, y'(0) = -8.

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Q: Suppose the function  f(x) = 9x2 − 2x + 6  describes a physical situation that makes sense only for…

A: As per the question we are given an integer optimization problem with objective function : f(x) =…

Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = (t + 1)³ L{f(t)} =

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Q: 3. Solve the following problems: 1. Find the area of the figure shown using: 12.22 11.32 8.82…

A: The integrals in the form ∫abfxdx represent the area between the curve y=fx and x-axis from x=a to…

OOPs

In today's technology-driven world, computer programming skills are in high demand. The object-oriented programming (OOP) approach is very much useful while designing and maintaining software programs. Object-oriented programming (OOP) is a basic programming paradigm that almost every developer has used at some stage in their career. 

Constructor

The easiest way to think of a constructor in object-oriented programming (OOP) languages is: