Q3. By applying. a suitable operational theorem, determine -1 ड 2 [ 5 in (5-10 ) ], 3 where In (x) = loge (x).

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A: See solution in image Explanation:Using d(sinx)/dx=cos(x) d(cosx)/dx=-sin(x) d(e^(ax))/dx=ae^(ax)

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A: Here both p(x)=32xand q(x)=−1+x2x2 aree non analytic at x=0 so 0 is a singular point. But both…

Q: || = y = Find a solution to the initial value problem, y" + 18x = 0, y(0) = 1, y'(0) = −5.

A: Consider the given differential equation  with initial conditions .We know that .

Q: 3. Prove that 3kN, Vn N, [n>k][1000m² + 10 ≤ n²]. Hints: you can divide both sides by n² and…

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

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A:

Q: prove the formula of Mersenne primes

A: A number of the form is a Mersenne prime if and only if p is prime.To prove this we need to show…

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A:

Q: Can you check if I have done this right please, thank you.

A: Your answer and method is absolutely correct as you mentioned.Explanation:Step 1:The equation…

Q: ) Calculate (8(x² - y)i + 8(y² + x)j³) · dř if: (a) C is the circle (x − 4)² + (y − 8)² = 25…

A: (a) We have to calculate  where .in parametric form Now  and Now

Q: give examples how to find mersenne primes

A: a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime…

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A:

Q: 19. Maximize subject to P = 10x + 12y x + 2y ≤ 12 3x + 2y ≤ 24 x = 0, y ≥ 0 : =

A:

Q: b 5. Does the graph bellow have a Hamiltonian path? Hamiltonian circuit? a 4 جوه a h g b с e

A: A Hamiltonian path in a graph is a path that visits every vertex exactly once. It's named after Sir…

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A:

Q: 3. Use the short truth table method to determine the validity or invalidity of all the argu- ment…

A: Let us construct a short truth table.(b)We will assume the premises to be true, and the conclusion…

Q: Use Laplace transforms to solve the following initial value problem. x''+x=sin 2t, x(0) = 0, x'(0) =…

A:

Q: Here are two new definitions about graphs. The distance between two vertices in a graph is the…

A: The diameter of a graph is the greatest distance between any pair of vertices in the graph.We have…

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A: If f(x) is continuous on  then the improper integral of f(x) over the interval  is…

Q: Problem 4. The homogeneous differential equation 5x²y" + 11xy' + y = 0 has general solution: У a = x…

A:

Q: Consider the initial value problem mx" + cx' + kx = F(t), x(0) = 0, x'(0) = 0 80 modeling the motion…

A: From the given values of m,c,k,F(t), the equation of this model is2x″+8x′+80x=80cos⁡(8t)

Q: Three water purification facilities can handle at most 10 million gallons in a certain time period.…

A: Three water purification facilities can handle at most 10 million gallons in a certain time period.1…

Q: Σ° (4)" n = 1 Σω, 3 (1) 8 Σor1 2 ( 33 ) " What n=1 is the convergence of each Previous example?

A: Question explained below:Explanation:ANSWER : 1 ​​   ANSWER : 2 ​​   ANSWER : 3 ​​

Q: What is the coefficient of 10 in the expansion of (x + 2) 15 + x4(x+3)16? Submit Randomize Reset

A: The required value of coefficient of x10 for the given expression is 472960488Explanation:

Q: If a bank pays interest at a rate of i compounded m times a year, then the amount of money Pk at the…

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Q: I don't understand how you got 4,-7,1

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Q: You are considering 3 different job offers in education publishing: 1. You can work at McCray-Hall…

A: To calculate the gross annual income, total annual hours worked, and effective hourly rate for each…

Q: Assume that N is a normal subgroup of a group G. Assume E is asubgroup of G/N. As in Problem 10.3.11…

A: Here I have provided the detailed solution but If you know that ϕ:G→G/N is a homomorphism, all this…

Q: a) Does the poset (P(Z), C) have minimal element(s)?

A:

Q: Solve by trigonometric substitution 2x² S- dx 1-x2 Draw the triangle with values on each side

A: We have to solve the integration  by trigonometric substitution.

Q: Instructions for forms of answers in differential equation problems: constant times a decaying…

A: The heaviside unit step function u(t)={0t<01t≥0The equation for t<0, y″+8y′+15y=0The equation…

Q: Use Laplace transforms to solve the initial value problem y"+4y' + 13y = f(t), y(0) = 0, y'(0) = 0.…

A: Given, a second-order linear differential equation .Initial conditions:  and The piecewise function…

Q: (Review of Complex Numbers) The three most important facts to know about complex numbers are that •…

A: (c) 1 + 0i(d) -1 + 0iExplanation:

Q: 16. Find an interval representation for the poset in Figure 6.38 or give a reason why one does not…

A: Not a poset is not an interval order.

Q: Given the sequence defined by the following recurrence relation: a₁ = 2 a=a- for i≥2 Prove that a,…

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Q: Let T': R³ → R4 be a linear transformation so that T(x) = Ax, where 1 -2 -3 0 1 -1 A = 0 0 1 0 0 0…

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Q: Let f be the function defined by the rule f(x)=√√ on the interval (81, 84). Since f is known to be…

A: The Mean Value Theorem (MVT) is a fundamental theorem in calculus, which states that if a function…

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A: The objective of the question is to calculate the future value of a series of equal deposits…

Q: a contract requires payments of $1700 in 50 and 100 day with simple intrest at 6%. what is the value…

A: We'll use the present value formula: Present Value (PV) = Future Value (FV) / (1 + Interest Rate *…

Q: A tank contains 460 gallons of water and 45 oz of salt. Water containing a salt concentration of…

A: Let  be the amount of salt in the tank at any time t.Salt enters the tank at a rate of , oz/min and…

Q: 1. Let a, b and c be positive numbers. The set of points (x, y, z) in R³ such that (x/a)²+(y/b)2-…

A:

Q: (a) Write the following curves in parametric way z(+) = x(#+ight). is) Im ( 2 ) = ZZ + i(z-Z)-2=0…

A:

Q: y" + 4y = 2 sin 3x + 3 cos 2x Find the solution y(x)

A: Given differential equation We have to find the solution of the differential equation.

Q: 1. Find the Fourier series of f(x) = x² F(-2)? - x defined for -2 ≤ x ≤ 2 if ƒ (x + 4). What is…

A: Fourier Series RepresentationThe Fourier series of f(x) = x²-x defined for -2 ≤ x ≤ 2 (and periodic…

Q: 1.20. Show that (a) r sin(ak) k=1 = r sin a r2-2r cos a+1'

A:

Q: Use the Laplace transform table and the linearity of the Laplace transform to determine the…

A: L{e4tsin(8t)−t4+e6t}=(s−4)2+648​−s524​+s−61​​Explanation:Step 1:To find the Laplace transform of the…

Q: 5.41 through 5.43 Determine by direct integration the centroid of e area shown. Express your answer…

A: We have to find the centroid of the mass in terms of  and

Q: (7) Find the general solution of the ordinary differential equation x²y" + xy' - y = 8x²e²x.

A: See l solution in image Explanation:

Q: Find all solution to: sinh(z)=i/2

A:

Q: Theorem 1.21 Let (X,T) be a topological space and Y₁, Y2,,Yk, be a family of path connected…

A: