Solve the following set of the differential equation using Laplace Transforms. dx (t) dt dy(t) dt = y(t) + sin(t), = x(t) + 2 cos(t), MMA BMV 128A THE x(0) = 2 y(0) = 0

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A: To find: tan(arctan 25)

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A: f(x)=x-2according to mean value therem f'(c)=f(b)-f(a)b-ad dx(xn)=nxn-1

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Q: 29. Two sides of a triangle are 4 m and 5 m in length and the angle between them is increasing at a…

A: see below the answer and explanation

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Q: If 68 + 5 f(x) + 7x² (ƒ(x))³ = 0 and ƒ(−3) = −1, find ƒ'(−3). f'(-3) = |

A: 68+5f(x)+7x2(f(x))3=0 f(-3)=-1d dx(xn)=nxn-1d dx(a.b)=adbdx+bdadx

Q: i. f(2) ii. iii. iv. V. vi. Given the graph of f(x) at the right, determine the following: lim f(x)…

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Q: 4. Find an antiderivative of the given function. a. f(x) = x³ + √x b. f(x) = 32x c. f(x) = 1 √x

A: (a)  f(x)=x3+xanderivative of f(x) is F(x)∫xndx=xn+1n+1+c

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Q: " 9. Find the equation of the curve for which y = 12x² + 6x - 4 and which passes through (0,1) and…

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Q: A box with a lid has a length two times its width and a volume of 1000 cubic cm. If the minimum…

A: Given : Length of the lid is twice the width, Volume = 1000 cubic cm, Minimum length of one side is…

Q: 35. What is the 6th term in the expansion of (x+)? 8 a. 1792 x-7 b. 16 x5 c. d. 1120 x 1792 x 10

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Q: In the 2000 U.S. Census, a small city had a population of 50,000. By 2010, the population had…

A: In the 2000 U.S. Census, a small city had a population of 50,000. By 2010, the population had…

Q: 21. At noon, ship A is 100 km west of ship B. Ship A is sailing south at 35 km/h and ship B is…

A: At noon, ship A is 100 km west of ship B. Ship A is sailing south at 35 km/h and ship B is sailing…

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Q: O True O False n = 0

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Q: 45. Find all points on the curve x²y² + xy = 2 where the slope of the tangent line is -1. Answer +…

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Q: Find the exact length of the curve. y = ln (1 − x2) , 0 ≤ x ≤ 1/2

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Q: Write the equation of the given sine curve: 8 0,3 0 , 1 3rt, 5 10

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Q: 8) Use the information below about the functions f,g, and k to answer the following questions. 1 2 3…

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Q: For the above function f(x) = 5.0.7², estimate f'(x) using h = 0.001 for the following three values.

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Q: 36. Demography The populations P (in thousands) of Raleigh, North Carolina from 2000 through 2008…

A: Given that population of Raleigh, North Carolina is modeled by P=289.81ekt, where t is the year with…