6. a. Solve the differential equation below under the following initial conditions: y (0.5), y (1.0) y' = sin (x) + e-*, 0≤x≤ 1, y(0) = 1

Q: 1. For the matrix A = -2 6 3 -3 7 3 6-12-5, (a) Compute the characteristic polynomial f(x) = det(xI…

A: We have to find the minimal polynomial m(x) of A and then we can proceed further.

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Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

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A: Here we need to find y at x = 218 ft and x = 410 ft.

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Q: (c) Use integration by parts to evaluate the following integrals: √ 2 2 e 3x sin2x. dx

A: We have to evaluate the integral,   ∫012e3xsin2x dx  by using integration by parts.

Q: Evaluate // (1+x² + y2) dV, where E is the region bounded E by the surfaces z = 6y2 - 9x², and z = 6…

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Q: 5. Residue theorem (a) +²+1 Jo° ±1 dt. +4+1 Use the residue theorem to compute

A: We have given integral∫0∞t2+1t4+1 We need  to use residue theorem to compute integral.

Q: Consider the following bivariate linear regression model y = a + 3x + u. Suppose that Cov(x, u) > 0,…

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Q: Batman and Robin caught nine suspects. Their possible crimes were Assault, Bribery, and Homicide.…

A: From given question We can get below statements   Total suspects =9   Possible crimes =3 ( Assault ,…

Q: #2 (Calculator Allowed) Let f(x)=203x and g(x)=Let R be the region in the first quadrant enclosed by…

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Q: Problem 8. When it exists, find the inverse of

A: Given,           M=1aa21bb21cc2

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Q: 3. Suppose y(t) is the inverse Laplace transform of the following function: y(t) = L-1 What is lim…

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Q: Question 12 The temperature T at a point (x,y,z) of a solid is given by the function T(x,y,z) = 2x²…

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A: Given function is y=cosx. We have to evaluate the first derivative of y=cosx at x=π4 using a value…

Q: Let A and B be two matrices innRREF , if they are row equivalent then A=B.

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Q: Suppose S = {1, 2, 3} T = { 1, 3, 5, 7} 28. S = {x|x & S and x & T} = 29. S = {x|x€ S or x ε T} =…

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Q: Find the extreme values of the function f (x,y) = 2 - 4x - - y² on the closed region bounded by the…

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Q: T $ 4 R F √ DII F4 % 5 Use the Venn diagram -X F5 G :9- 6 F6 Y Rh OL I & 7 B U G F8 * 00 8 to sort…

A: A+ will come at the intersection of set A and Rh. B+ will be placed at the intersection of set B and…

Q: Use three-point midpoint formula to evaluate the first derivative of y = cot(x) at x = using a value…

A: We have to evaluate the first derivative of y=cotx at x=π2 using a value of h=π4 by using…

Q: 1. Solve each linear system below. Give a geometric interpretation of each system, by describing the…

A: Given system is 2x+y-z=10-----(1) -4x-2y+2z=-10-----(2) 2x-y+5z=3-----(3) (or)…

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A: Consider the x-intercept of line as a and y-intercept of the line as b.   The intercept form of the…

Q: 13. Find the mass of a thin funnel in the shape of a cone z = √√x² + y²,1 ≤ z ≤ 4, if its density…

A: Here given the shape of a cone  z=x2+y2, 1≤z≤4 , Write it in polar coordinate D=r, θ: 1≤r≤4, 0≤θ≤2π…

Q: Q.2 The train resistance R(lbs/ton) is measured for the following values of its velocity V(km/hr).…

A: to find a, we take the following three Values of V which are in G.P.

Q: Let A be a set. Define a relation over ℘(A) by X ~ Y iff there exists a bijection f: X ⟶Y. Proof…

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Q: Problem 2. If det a1 a2 b₁ b₂ C1 C2 a3 b3 C3) det = 1 4 a₁ b₁ c₁ calculate a2 b2 C2 4a32a2 4b3 - 2b2…

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A: Introduction: The sines law is given by, asinA=bsinB=csinC

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Q: 1. (a) Compute the Fourier sine series expansion of f(x) = 3x - x² on [0,3]. (b) To what value does…

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Q: Solve the given differential equation by separation of variables. dy xy + 6y-x-6 = dx xy-7y+x-7

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Q: procedure Horner(c, ao, a₁, a2, ..., an: real numbers) y := an for i:=1 to n y = y* c + an-i return…

A: Here follow the python code output.

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A: Construct the augmented matrix and check the necessary conditions.

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Q: Solve the initial value problem y + y = g(t), where 1, g(t) ={ 0, The solution should be continuous…

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Q: и, utt =100 и за осхит ли(1,0) с снова И 8x tas lon 1 |4 (30) = со & +6 107 (4 (9,6)= ц(ђt) = 0 x =0

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Q: ii, Find the area under the graph y=5x4 between the limits x= 1 and x=3.

A: Given y = 5x4

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Q: Two colleagues, Alicia and Siyan, are given two vectors b, v € R2 to work with, but they are only…

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