Take the Laplace transform of the following initial value and solve for Y(s) = L{y(t)}: y" +9y= = = Y(s) Next take the inverse transform of Y(s) to get = Note: (sin(#t), 0

Q: Describe how the graph of the following function can be obtained from one of the basic graphs. 1…

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Q: Prove that 3" +4" ≤5" for all integers n ≥ 2.

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A: It is given that, A is an invertible 2×2 matrix. We have to determine the deductions of Fundamental…

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A: Slope intercept form of line is y=mx+c  Here, m is slope and c is constant.

Q: (GJ-2) Use Gauss-Jordan elimination to find the inverse of the following matrix, and show all…

A: The given matrix is                                       A = 131-1202123 We have to find the…

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A: Given equation of parabola,  y=-x2+3

Q: Assume that 0 0, consider the sequence of sets: A₁ = {\fn-f|> }, n=1,2,... (1) Show that, for every…

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Q: {B].[B]} Vector w expressed in ß is w = Vector v expressed in basis a = = {[]·[3]} Answer: 133 Wa is…

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Q: (c) Let R be a finite commutative ring with identity. Prove that an ideal in R is prime if and only…

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Q: (c) Let G be a group and a, b € G be elements of G each of order 3 such that a² = 6² and prove tha a…

A: Given: A group G, and a,b∈G order of a and b is 3 and a2=b2. To Prove: a=b.

Q: What matrix would the translate by [1, 2, 3] be? 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 1 0 1 0 0 0 0 1 0 0…

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Q: Consider the function G(z) = z¹/². a) Find the regions of analicity of G(z) b) Derive a conservative…

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Q: = (4) Let ER and fn = XAn, where An j+2k = n. Compute fe fn in terms of k and show that (a) the…

A: Pleas find the attached answer

Q: A variable plane lx +my+nz = p (where 1, m, n are direction cosines of normal) intersects the…

A: Given: The equation of a variable plane is lx+my+nz=p. (where l,m,n are the direction cosines of…

Q: 2. y+3y"+4y+2y=0; y(0) = 4; y'(0)=-4; y"(0)=1 a. y=e* (4+sin x) b. y=4e¹ cos x c. y=e*(1+3 cos x) d.…

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Q: Given that f(x) = 3x + 1 and g(x) = x2 - 2x - 4, find (g * f)(6). (g * f)(6) =

A: Composite function value

Q: x/y + 1 - √ x/y x/y + 1 + √ x/y - - 1 1

A: dxdy=xy+1-xy-1xy+1+xy-1      =xy+1-xy-1xy+1-xy-1xy+1+xy-1xy+1-xy-1      =xy+1-2xy2-1+xy-1xy+1-xy+1…

Q: x²=-2x+4y y = -4x-2y wh x(0)=2, y(0) = 8 At=01 9+0 2100 JFF Use the Evien Method with a time step of…

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Q: Q₁. Construct a connected graph with at least 12 vertices such that the minimal dominating set has 6…

A: Please find the attached answer

Q: Ray wishes to determine the optimal order quantity for its best- selling bike in his bike store. Ray…

A: Average daily demand(d) = 31 units Store Annual working days W = 254 Annual demand (D) =d*W = 31*254…

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A: Echelon form of the matrices properties

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Q: Determine if the following sequence converges. If it does, find its limit. 8 √2n! \ (2n)! (n=1 2.…

A: (1) Let, the given sequence is {un}, where un = 2n n!2n!

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Q: A coin is tossed 10 times. Find the probability that the number of heads is exactly five. The…

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Q: lottery

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Q: Use Weiestrass's definition of limit to show that lim (7x - 3)= 32. x-5

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Q: Prove that every minimal dominating set in a graph G is a maximal irredundant set of G.

A: Given that, Every minimal dominating set in a graph G is a maximal irredundant set of G. We have to…

Q: Question #1: A function is given by f(x) = 6e-3. Now Answer the following: 1. 2. 3. 4. Calculate f'…

A: The central difference formula is given by f'x≈fx+h-fx-h2h (1) For x=0.5. h=0.32…

Q: ength of any edge of a regular tetrahedr ar tetrahedron). Show that the angle bet

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Q: Given the differential equation y" + xy = 0 and assume a solution of the form y = Choose All Correct…

A: Given differential equation is y''+xy=0 The solution is determined as shown in the next step.

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Q: Compute the greatest common divisor gcd⁡(1235,455) by hand.

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Q: Can you write more clearly what you did in step 2? It is not clear to me.

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Q: (2) Let fn(x) = X(0,n)(x), x > 0. Find the pointwise limit f of (fn)n and show that (a) the…

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Q: A farmer finds that if she plants 40 trees per acre, each tree will yield 30 bushels of fruit. She…

A: For every additional tree planted, yield decreases by bushels.  Question can be solved by using…

Q: (x - y)y' - 2y + 3x + == 0 ; y(1) = 5 + X² = 0 X

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Q: 3+1 Determine the values of x and y if: 32 = √√96*

A: 3y+1 /32 = (96)^(x/2).

Q: b) Find an integer x such that 37x = 1 (mod 101).

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Q: Multiple Choice о O The probability of a 1 bit is 0.6; hence, the required probability is (6)¹0.06.…

A: Solution:- Option third is correct.

Q: .s) Prove that k = n kn (a) fel(k-n)wot dt = ST = to +00 (b) If x(t) = Σake/kwot and T = 2π ; then…

A: Assuming the series is term by term  integrable

Q: Compute the inverse of f(x) = x³ + 1. f-¹(x) = ³√x-1 Check your answer by showing that ff¯¹(x)) = 3…

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Q: If the price of gold decreases at a monthly rate of 2.2%, by what percentage does it decrease in a…

A: Given  monthly rate of decrease =2.2% Let initially the price be p0 and the price after 12 month is…

Q: Q7. For Theorems below give an example tree T with 15 vertices. Theorem 1. If a tree T is a wounded…

A: Please find the attached answer

Q: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

A: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

Q: Solve equality: (a) 2x² + 3x - 2 = 0 (b) e¹+3e² 10 = 0 (c) ln(x) + ln(x + 1) = ln(12)

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Q: Determine this function from R to R is a bijection. f(x)=2x+4

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