Use Laplace transforms and the convolution theorem to solve the integral equation t y(t) + / (t – x)y(æ) dx = g(t), where 1-t if 0 < t < 1, |0 g(t) = if t > 1.

Q: The population of a country has been increasing for several decades. In 1990, the population was abo...

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Q: 1. Why we need Laplace Transform. Introduce at least 4 relevant applications of Laplace transfrom. F...

A: We have to find the laplace transform .

Q: [A] Identify whether the relation is linear, quadratic or exponential. [B] Write the equation for th...

A: Given table   

Q: Ais an n x n matrix Check the true statements below. DA. To find the eigenvalues of A, reduce Ato ec...

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Q: Find the magnitude of (5 + 10i)(5 + 107) O 5/10SV10 O 5/55V3 O 10/5105 O 2/52V3

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Q: A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D...

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Q: Prove this theorem Let a,b,c be an element of real numbers where a is not equal to zero. The equatio...

A: Use the provided information.

Q: to hundrea

A: Introduction: A number system could be a means of expressing numbers through writing. it's a notatio...

Q: The population of a country has been decreasing for several decades. In 1990, the population was abo...

A: The population has decreased to 151 million from 154 million.  So, that is a decrease of (154 - 151)...

Q: Given the set C=(2,4,6,8}.Consider the relations R 1 and R 2 defined on C as follow: (x, y)e Rz if a...

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Q: The approximation of 1 = , tanx dx using composite Simpson's rule with n=5 is: O None of the choices...

A: Given that I=∫01tanxdx. We have to approximate of I=∫01tanxdx by using composite Simpson's rule with...

Q: 2) The Math Club consists of 15 members. Four of them will represent the school in a math competitio...

A: Given Total number of members of Math Club is = 15

Q: Let B, D be the following two bases of R°: 2 -1 B = 2 4 D = -3 -3 a) Find the change of coordinates ...

A: Given: B=222, -122, -320 and D=4-3-1, 0-3-4, 1-2-2  To find: Change of coordinate matrix PD←B from b...

Q: Given the set C=(2,4,6,8).Consider the relations R 1 and R 2 defined on C as follow: (x, y)e Rị if a...

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Q: Solve the system of linear equations. (If there is no solution, enter NO SOLUTION. If the system has...

A: we can solve as

Q: Given the Euler equation 2a?y" + ry' – y = 0. i. Find the initial value problem with y(1) = 1, y (1)...

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Q: Construct a truth table for each of the following compo [(p→g)^ (g → r)]→(p →r) 1.

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

Q: (a) What is the cardinality of the set containing only the number 0? (b) Write the question and answ...

A: (a) If a set contains 0 element, then there is 1 element in the set. So cardinality of the set conta...

Q: 1 1 -3 1. Let A = 1 1 -1 -4 (a) Find row(A), col(A), and null(A). Find a basis for row(A), col(A), a...

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Q: D. lhustrate using Venn diagram. 1. Not Prime Number Prime Number Odd Number Card Not Odd Number Car...

A: Given are three parts where in each part there are given sets and we have to write them in Venn- dia...

Q: Obtain the general solution of the following differential equations. 4. x(x² + y*)*(ydx -xdy)+y°dy =...

A: We have given differential equation ,  xx2 + y22ydx - xdy + y6dy = 0 Clearly , this is homogenous di...

Q: Com Pare with C.R.I (n) fc2) AZ 27 %3D

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Q: Plot the following cosine functions, y1 = 2 cos(x), y2 = cos(x), and y3 = 0.5 + cos(x), in the inter...

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Q: Let D be the region of the plane bounded by the curve C parameterized by f(t) = [3 cos(t) – cos(3t)]...

A: (a) D is the region of plane by the curve F(t)⇀=[3cost-cos3t]i⇀+sin3t-3sintj⇀,              (1) wher...

Q: Use the circle graph to answer the question. A library classifies its DVDS into one of the categorie...

A: Introduction: The percentage plays an important role in the calculation. It helps to understand the ...

Q: 1 1 -3 1. Let A = 2 1 1 -1 -4 (a) Find row(A), col(A), and null(A). Find a basis for row(A), col(A),...

A: Given: A=11-30211-1-4 To find: 1 a) row(A), col(A) and null(A). Also find a basis for row(A), col(A)...

Q: 4 4 Let v, = - 3 V2 = 1 V3 = - 6 p = 1 and A = V1 V2 V3 4 24 44 a. How many vectors are in {v1, V2, ...

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Q: Determine whether or not the sequence (2 + i)" + (1+ i)" (1 – 2i)" + 2" n = 1,2,.., converges, and i...

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Q: Define a sequence by recursion An + an+1 an+2 = with initial conditions aj = ì, a2 = µ where 1, u E ...

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Q: find two addi n<0<2n. 4,- |

A: In this question, the concept of the Polar Coordinate System is applied. Polar Coordinate System A p...

Q: Jason purchased items for his backyard. The total length of wood Jason bought to make a raised garde...

A: We know, 100 centimeters = 1 meter. So, 1280 centimeters = 1100×1280 meters. i.e. 12.8 meters.  

Q: +2+n-3 Simpli fy, O -1+ i" O -1+i O1+i O in+1

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Q: f(g(x))=x f(x)=x\x+2 find g(x)

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Q: Question 4. The following are logical laws shown in our lecture. Find their dual versions if exist. ...

A: We have to find dual versions of given logical laws, if they exist. Pre-requisite :  P1) Two formula...

Q: . Solve the following initial value problems: (a) Given the differential equation y"+ 2y'-3y = e- wi...

A: As per our guidelines, we are supposed to solve only first subpart. Kindly repost other subpart as n...

Q: A radio commercial for a loan company states: "You only pay 25¢ a day for each $500 borrowed." If yo...

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Q: (-1)"(x+2)" The interval of convergence of the power series n=0 (n+1)422n A. -65x<2. B. -6<x<2. C. N...

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Q: Given the set C=(2,4,6,8}.Consider the relations R 1 and R 2 defined on C as follow: (x, y)e R; if a...

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Q: Use the Root Test to determine the convergence or divergence of the given series or state that the R...

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Th...

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Q: Find the inverse of the matrix. 5 4 -3 -2

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Q: The power series representation of f (x)=- will be given by 3+x DAŠ Σ (-1)" x" – 3<x<5. n=0 2" +1 O ...

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Q: On what quadrant you can see the quotient of -5+2i 2-2i O 3rd O 1st O 2nd O 4th

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Q: Jo borrowed $1,900 for 8 months from a bank. The bank discounted the loan at 5.5%. a. How much inter...

A: Given that Jo borrowed $1900 from the bank for 8 months. Discount rate is 5.5% Since 8 months=812=23...

Q: Prove using the generating function of the Legendre Polynomials: t2 [xP(x) – nP,(x)]t": (1- 2xt + t²...

A: We have to prove ∑n=0∞xPn'(x)-nPn(x)tn=t21-2xt+t232 We know the generating function of the Legendre ...

Q: 4- A right trianglewi th dimensious of X = 3 Cm. and y = 4 cm increasing at arate of 2 Gml sec and C...

A: For the solution of the problem follow the next step.

Q: A direction field for the differential equation y' = cos(y) – sin(x) is given %3D below. a) Sketch t...

A: Introduction: Every first-order ordinary differential equation has a slope field. The slope field is...

Q: To support the wiffle ball program at your school the wiffle ball boosters are having a raffle. Each...

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Q: Find the Laplace transform of t + 2t -4

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Q: ONo:03: Calculate the value correct of NToz -Jiol to fecr significant' figutes.

A: Linear approximation, value of the root(x)