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Q: (b) Solve the given IVP x'= :)x , Xt) = ()

A: 1b

Q: 1- 3s Find the Inverse Laplace Transform of G (s) = s2+ 8s + 21 -4i sinh (/51) 13 8 (t) = – 3e…

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Q: A constant field vector is given by E = -5a_p + 10a_0 + 3a_z. Calculate the vector component of E at…

A: The problem is related to vector. The topic is multidimensional geometry. We find the component of…

Q: A certain simple economy has two sectors: work and play. To produce $1 of work requires $0.7 of work…

A: Let us take x as the production of work and y as the production of the play. Now we can form two…

Q: A small boat leaves the dock at Camp DuNuthin and heads across the Nessie River at 23 miles per…

A: The side with touches the angle is given by rcosθ. The another side is given by rsinθ. Magnitude of…

Q: Find the equation of the tangent plane at the point a = xo = 4, y= yo = 1 of the surface z = f(x, y)…

A: Given z = f(x, y) = xyex+y

Q: 2. Use Newton-Raphson Method to find the root of x'-2x²-5 = 0 between [1, 4] accurate to five…

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Q: Let K be a field. Consider the following set {(: :)e R:= a 0 a2 a1 (a) Show that (R, +) with the…

A: Let K be a field. R = a10a2a1 ∈ K2×2  : a1 , a2 ∈ K We need to show that , R , + with matrix…

Q: 2. For a, b e R, show that r3+ ax +b= 0 has three real roots iff 4a3 + 2762 < 0. Remark: This is a…

A: We have to show that, x3 + ax +b =0 has three real roots iff 4a3 +27b2 &lt;0   for any real numbers…

Q: Connider the Legendre's litterential equation Cl-x²) Y" - 2xy Any soluhion tuis" equation is…

A: Solve Legendre differential equation by series solution.

Q: Beginning January 1, 1982, Mr. Cruz's salary is increased by 30.01% every two years. When counting…

A: Let the beginning salary = x, rate of increment, r=30.01% every two years. To find the time when his…

Q: 6. (The fractional residue theorem) Show that sin(ar) L r(r² + 1) tz = 5(1 – e~“), a>0. iaz [Hint:…

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Q: Solve the following recurrence relations. а) а, 4an-2, n > 2; ao = 0 and a1 = 4.

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

Q: If A = 3a_0 + 2a_0 - 5a_z and B = -2a_p + 3a_0- a_z are given at points P(3,T1/6,5) and Q(4,T1/3,3)…

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Q: Consider the following problem: Find two numbers whose sum is 23 and whose product is a maximum. (a)…

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Q: Given: A = 0.6 – j0.4 B = 0.5 + j0.8 С 3 0.6 — 30.8 D = 0.5+ j0.4 %3D Evaluate: C+2 log, (3B)2(cos…

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Q: Use the information provided to write the standard form equation of the hyperbola. a2 - y? + 14x 6y…

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Q: Show that a commutative ring R with unity is a field if and only if its only two ideals are (0) and…

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Q: 1 Find the inverse transform: F(s) s2+4s+4

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Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent. (-1)"…

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Q: B) Find a solution to the BVP: z'y"-5zy' + 8y = 0, y(1) = -2, y'(-1) = 4.

A: B.

Q: 2 (a) Define a Dirichlet function. (b) Assume that f(z) is a function of the form -x-1; when -n<I<0…

A: Given function is  fx=-x-1;       when -π&lt;x≤0x;                 when 0≤x&lt;π

Q: 1 , Evaluate (i) L-1 (s2 + 1) (s + 9)

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Q: 2. lim f(x) = x²– 4x +4 х 2 Use the domain [-9,6] to draw the graph. X X -2

A: Firstly, See the graph of (x² -4x +4)/(x-2) , -9≤x≤6

Q: Given: A = 0.6 – j0.4 B = 0.5 + j0.8 C = 0.6 – j0.8 D = 0.5+ j0.4 %3D %3D Evaluate: log. (3B)]²(cos…

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Q: Osx<1 If f(x) = * then L{f(x)}= %3D X21 1 1 e O 1 e s2 1 1 e 1 s2 s2

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Q: 3. Show that the Fourier series of the function g(x) = |x| on the interval [-7,7] is 4 5 - 1 cos(2n…

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Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

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Q: Find the Laplace Transform of the following functions 4) f(1) =t sinh(at) 5) f(t)= 2te' 6) f(1) = e"…

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Q: Find the Laplace Transform of the following functions 1) f(t)=tcos(@t) 2) f(t)=t sin(@t) 3) f(t)=t…

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Q: 21. The product of the ages of four friends is shown by the expression x* – 10x2 + 9. If the sum of…

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Q: |I E with [d] Let L be the set of all E R ()() In-1 Show that Lis a subspace of R2n is, calculate…

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Q: The function f(x, y) = r° – 3x – 2xy – y – 2y + 4 Has two stationary points. Find and classify then.…

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Q: 1. (Power series expansions) (a) Determine the radius of convergence of the series E n" when: (n!)3…

A: 1.a.(i) The given series ∑n=1∞anzn where an=ln n2 We have to find the radius of convergence. Here we…

Q: 4. Is y' = sin (ty) separable a) not separable c) separable %3D b) for y =, yes d) with a proper…

A: We have to check whether the given differential equation is variable separable or not.

Q: Given: A = 0.6 – j0.4 B = 0.5 + j0.8 C = 0.6 – j0.8 D = 0.5 + j0.4 Evaluate: (c+)/ log. (3B) (cos…

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Q: Using the Cauchy-Hadamard Theorem, find the radius of convergence and disk of convergence of Συ 1.…

A: Given series is ∑n=0∞3nz2n

Q: Solve the value of x in the given equation _by Jacobi and Gauss-Seidel Method. 13x2 + 4x3 = 111 4x1…

A: Given the equation system  19x1-13x2+4x3=1114x1+22x2-13x3=-1288x1+8x2+17x3=10 We have to solve the…

Q: y(exy + y)dx + x(exy + 2y)dy = 0

A: Exact differential equation and it's solution

Q: Any soluhon äf thuis equation is called Legendre's clifterential equation Considir the (1-x²) Y" -…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 12, (1, 3, 4) 12x…

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Q: 4. The tank shown below is full of water. Find the work required to pump the water out of the spout.…

A: Work is the product of force and distance, W=Fd. Force is the product of mass and acceleration, F=ma…

Q: the general solution * the given fystem Find (i dx at -을x + 29 dy dt zy 2. (u) x'= 10 (u) x'= :)x -2

A: Use the matrix associated with the given system to obtain eigen values eigen vectors and then…

Q: study compare with

A: Introduction: When the integrand is discontinuous at any of the two limits or both at the limits,…

Q: Can a graph have 17 vertices where every vertex has either degree 1 or degree 3 or degree 5? Yes or…

A: Given  A graph with17 vertices  we have to prove that can a graph have 17 vertices where every…

Q: (8) Suppose a license plate contains two letters followed by three digits with the first digit not…

A: We can find how many different licence plates can be printed (Repetition is allowed).

Q: Given: A = 0.6 – j0.4 B = 0.5 + j0.8 C = 0.6 – j0.8 D = 0.5 + j0.4 %3D Evaluate: (c+B)/ log.…

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Q: ILW. Find the solution of the integration using trapezoids and Simpson's 1/3 rule and compare the…

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Q: Segment congruence theorem. Segment congruence is an equivalence relation. In other words, if PQ, RS…

A: If PQ≅RS then by definition, d(P,Q)=d(R,S)...(equation 1) and if RS≅UV then by definition,…

Q: Consider the vector field F (x+ y)i + (x² + y²)j What is the downward flux across the line segment…

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