Find L{f(t)} by first using a trigonometric identity. (Write your answer as a function of s.) f(t) = sin(5t + 6) L{f(t)} : %!

Q: 5s2-2s-19 F(s) = (s+3)(s-1)2 %3D

A: If the Laplace transform of a function f(t) is F(s) I, e L{f(t) }=F(s) , then f(t) is called an…

Q: Using the method of undetermined coefficients, find the particular solution of the following initial…

A: The given initial value problems  a)y''+4y'+4y=2te-2t, y(0)=1, y'(0)=-3 b)y'''-y'-y=0, y(0)=0,…

Q: Please answer number 1 use 4 decimal places. Find the positive real root of f(x) = x^4- 8x^3-35x^2 +…

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Q: uestion: The half-life of a certain substance is 5.9 days. How many days ill it take for 30 gm of…

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Q: Solve for the volume of the solid generated by rotating the plane bounded by the equation x2 below…

A: Sol

Q: Evaluate the upper and lower sums for f(x) = 1 + x2, -1sx< 1, withn = 3 and 4. Illustrate with…

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Q: Problem I. Find a lower bound for the radius of convergence of the series solutions about each given…

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Q: 2. Let X = R² – (0,0) and ~ be defined over X by setting x~y + y = tx for some non-zero t € R. Given…

A: Sol

Q: Consider the ceiling function [z] = min{z € Z]z >1}. This basically rounds up any real number. For…

A: To show that the limit doesnt exist the key idea is to show that the Left Hand side limit doesn't…

Q: A hiker set out from a straight east-west road on a bearing of N44° E and hiked for 22 miles before…

A: bearing N 300 E means the direction is 30º east of north. similarly  S150Emeans the direction is 15º…

Q: e) x·y= 0 iff x = 0 or y= 0. ) x<у iff — у < -х.

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Q: 9. Find the root of cos(x)-3x+1 using the Bisection Method. (use radian). (Use radians in solving)

A: Given: cos(x)-3x+1 To find the roots of the given equation using the bisection method.

Q: 1a. Give two solutions to the equation y = Vx³ + 2x² – x +5. Make a rough sketch of the %3D graph,…

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Q: Let R be a commutative ring with identity. Is it possible for R[x] to be a PID without being a…

A: Yes , it is possible for R[x] to be a PID ( assuming R[x] is PID ) without being a Euclidean domain.

Q: The HMS Sasquatch leaves port on a bearing of N23°E and travels for 6 miles. It then changes course…

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Q: x3 – 2x2 – 5 = 0, [1,4]

A: With the help of bisection method we find the root of the equation.  In this method we find a…

Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.

A: Given,          ∫-aa∫-a2-x2a2-x2dydx

Q: An international airline has a regulation that cach passenger can carry a suitcase having the sum of…

A: Here first we need to find the value of volume in terms of two dimensions using the given relation…

Q: Assuming a,b, y1,y2,y3 are all dimensional vectors, order matric A= (a,y1,y2,y3), B=(…

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Q: 1. sin 3at where a is any positive constant and s > a. 2. - (e-t - e-t) st – 3. (1 – cos 2wt) where…

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Q: Solve the initial value problem y"- 8y'+52y = 0, y(0) = 1, y'(0) = -3.

A: Note: We are allowed to solve one question at a time. Use the given differential equation.

Q: Question 4. Use Taylor's Theorem to estimate sin(3) to within 1/60.

A: This is a problem of series approximation.

Q: x3 – 2x2 – 5 = 0, [1,4]

A: Sol

Q: Use the cylindrical shell method to find the volume of the solid generated by revolving the shaded…

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Q: sin x – e-* = 0, [0,1]

A: Sol

Q: II. Solve the Inverse by Convolution theorem: -7 ( + 4)(s +2)

A: By the convolution theorem,  The above result can be written in the form ϕt=L-1 {F(s) G(s) }

Q: Example 3.32. Solve, by Relaxation method, the equations 9x - 2y + z = 50; x + 5y - 3z = 18 ; – 2x +…

A: Sol

Q: Final the complement afthe graphs in fig-1-34 figti3t

A: The complement of the following graphs can be found by adding the edges between every two vertices…

Q: x1 + x2 − x3 = −3 6x1 + 2x2 + 2x3 = 2 − 3x1 + 4x2 + x3 = 1 Please answer using Gauss Jordan…

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Q: es/ find the incdence madrix of K2,3

A: As per the company rule, we are supposed to solve the first problem mentioned from a set of multiple…

Q: Solve the following problems. Write your solutions and answers in your notebook. 1. A circular…

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Determine the exponential function given the graph. ... B = (-1,4) A = (1, 1) -4 -3 -2 -1 2 3 4 -1…

A: We want to find equation of given graph.

Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

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Q: Describe how to find the inverse of a one-to-one function. Choose the correct answer below. O A.…

A: We want to find the true option.

Q: 23. Find the coordinate vector [r]B of x relative to the given basis B = {b1, ...,bn}. 8 bị by 4 b3…

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Q: 2. Let E = a(a + b') +b be a regular expression over the alphabet E {a, b}. Use the template method…

A: Sol

Q: Solve the problems below: 1. Find the positive real root of f(x) = x* - 8x²-35x² + 450 x - 1001…

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Q: (BACKWARD INDUCTION) Two players have to share 50 coins (of equal value). Players' payoffs are the…

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Q: The residue of z cos (÷) at z = 0 is 1. 1/2 -1/2 1/3 4. -1/3 2. 3.

A: Residue of the function at z=0

Q: Given that A = (0,5), B = [- 3,1] and C = [0,0). Graph the number line and solve the following: (i)…

A: The given intervals are A=0, 5, B=-3, 1 and C=[0, ∞). We have to sketch the graph of the number line…

Q: 4. The equation f (t) = models the bacterial count, in thousands, for a sample collected from pond…

A: Given that,The equation f(t)=7tt2+5t+4 models the bacterial count, in thousands,for a sample…

Q: If the sum of eigenvalues of matrix 9. 7 16 A -9 k2 3 is 29, then the possible - 16 9 values of k…

A: We want to find the value of k

Q: sin x – e-* = 0, [0,1]

A: Let,f(x) = sin(x) - e-xso, f(0) =-1&lt;0 and f(1) = 0.47 &gt; 0 ⇒there is root between 0 and 1In…

Q: 3. Integration by parts a.J 18x ( x+ 4)»

A: Given integral is ∫18x(x+4)dx

Q: Is there any n n for which U2n = Dn?

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Q: Question A network of one-way streets is shown in the accompanying diagram. The rate of flow of cars…

A: Given that  the rate of flow of car into intersection A =500 cars per hour the rate of flow of car…

Q: Q3: Solve the following differential equation: coshx dy + (ysinhx + e*)dx = 0

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Q: sh(3t)-sinh

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Q: 1. Let f : Z6 → Z6 be such that f(7) = x² + 3. %3D (a) Is f a well defined function? (b) Is f…

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Q: (a) Give an example of a continuous function whose derivative does not exist at x = 0. (Hint: this…

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