(2) Use the Laplace transform to solve the given initial-value problem. (a) 2y + y=0; s(0) = -3, (b) s-y-2 cos(5t); y(0) = 0,

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A: f(x)=7-2x+x2The formula is given by,Average =(f(b)-f(a))/(b-a)

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A: Given four times a certain number plus one-third is equal to three times the number plus twenty.

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A: A writer earns $2 per word. The writer's total expenses per projectis $10. The project pays up to a…

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A: A city's initial population is 25000 and it has a growth factor of 1.19Using exponential…

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A:

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A: Since you have posted a question with multiple sub parts. As per guidelines we are supposed to…

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A: To find the annual growth rate, we can use the formula for compound annual growth rate (CAGR) which…

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A:

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A: f(x)=8x2+12x2+7x−4

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Q: Suppose that the augmented matrix of a system of linear equations for unknowns x, y, and z is 16 13…

A: The given augmented matrix

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Q: find the standard deviation for the group of data items   stem 1 = 6,7,7,6,5,6 stem 2 = 0,3,2,0

A: The objective of this question is to calculate the standard deviation of a group of data items. The…

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A:

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A: The given matrix is

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A:

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A: We solve the given problem by using the substitution method.

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A: As we can see from the graph,The function is not defined at x=-1 and x=1So the domain is

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Q: x -3 -2 -1 0 1 2 3 4 V -5 -4 -3 -2 -2 -2 -1 0

A: xy−3−5−2−4−1−30−21−22−23−140

Q: Prove the given statement by using mathematical induction. 1 1 1 n ++++)-¹-(-)* = =1- 4 n

A: use mathematical induction

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Q: 1. Simplify the fraction: 1 3√x X - √x 3x-1 3x √ ! No, that's not the correct answer.

A:

Q: For f(x) = 5x + 7 and g(x)=x², find the following composite functions and state the domain of each.…

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A: we need to find out the value of

Q: Se 0.031 =10

A: 5e−0.03t=10

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A: The given system of equations

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A: Formula

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Q: Simplify each expression a. √50 b. √√6xx√3x² * C. d. e. 121 9 √150x² √√3x m

A: Since you have posted withmultiple sub parts. As per guidelines we are supposed to answer only first…

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Q: log,(6x - 8) = log,(3x + 6)

A: log7⁡(6x−8)=log7⁡(3x+6)

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A: A club with five members is to choose three officers: president, vice-president…

Q: Solve the the exact answer. logarithmic equation. log₂ (x + 1) = 3

A: log2⁡(x+1)=3

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A: 5ex=10

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A: To factor the trinomial completely.

Q: figure. The volume is (Simplify your answer.) Ional 8 in. 7 in. 2 in. 13 in. 2 in. 13 in.

A: Height of Trapezium = 2 inLength of  Trapezium base1 a= 13 inLength of trapezium base2  b=7 inHeight…

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A: