Find an algebraic integer a in a Trace(a) = 17. quadratic field with N(a) 31 and

Q: A clamped beam of length 3 is modeled by: y(4) = 24, y(0) = y'(0) = 0, y(3) = y'(3) = 0. Solve the p...

A: The given differential equation is y4=24, with y0=y'0=0 and y3=y'3=0 Now we integrate the given equa...

Q: Evaluate: 2sin(3i)cos(3i)

A: Given  2sin(3i)cos(3i) To solve we use following properties: 2sin(θ)cos(θ) = sin(2θ) sin(iθ) = isin...

Q: Give McLaurin Series of Cimmon function for sinh x

A: We have to find the Maclurins series of function for fx=sinhx. The Maclurins series of function fx i...

Q: Let f(x)= e* be approximated by Taylor's 1 polynomial of degree nat the point x = and on the entire ...

A: taylor s polynomial   f(x) = e^x entire interval [0,1]  

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does...

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Q: C01. Verify that for all n>1, the Sum the first 2n positive of the squares of hitegeis is giveń baf ...

A: Disclaimer: Since you have asked multiple questions we will solve the first question for you. If you...

Q: If F = 2ui – (-u³ + 4)j – u²k and G = t?i – 3tj + tk at u = 1 , t = -1. Calculate: a) F×G ze d) :(Fx...

A: Since you have posted a question with multiple sub-parts , we will solve first three sub-parts for y...

Q: 0. 1 E1. Using the methods of the proof of the theorem about the existence of the SVD, find an SVD f...

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w ...

A: This is the problem of vector algebra.

Q: 5. Determine the roots of the complex numbers studied in class. z³ = 2 – 3i

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Q: Given points P (4, -2, 5), Q (3, 5, 5), and R (0, 2, 6) find the parametric equation of the line PQ ...

A: Here given point  P (4, -2, 5), Q (3, 5, 5), and R (0, 2, 6) So  PQ=2-4, 5--2, 5-5=-1, 7, 0 PR=0-4, ...

Q: Find gcd(2,3+5i) in Z[i], ii. Show that 3 + 4i and 4-3i are associates in Z[i] iii.Determine the spl...

A: (i)

Q: 5. Find the highest power of 2 that divides each of the following integers. a) (101111110)2 b) (1010...

A: Given: (101111110)2 (1010000011)2 (111000000)2 (1011011101)2 Which of these is divisible by 3

Q: 2a) Find the area of triangle PQR where P is (4, 2, 5), Q is (3, -1, 6) and R is (1, 4, 2) [1 2 31 2...

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Q: Test for exactness. If exact, solve. If not, use an integrating factor as given or obtained by inspe...

A: we have given the differential equation x2+y2dx-2xydy=0 we have to test the exactness of the given d...

Q: (3) Every baby that eats will make a mess and drool. Every baby that drools will smile. There is a b...

A: Solution:-

Q: Q1. Solve the recurrence relation x, = 6xn-1 – 9 xn-2 with initial condition x, = 1,x1 = 4

A: We have given recurrence relation ,  xn = 6xn-1 - 9xn-2   with  x0 = 1 , x1 = 4. Take all the term t...

Q: PPROBLEM SOLVING Directions: Read carefully and write your answers on the black provided after each ...

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Q: 2. + 2y = cos(x) 3. y cos(x)dx + 3sin(x)dy = 0 dy 4. dx 1-2у-4х 1+y+2x

A: We will identify type of differential equation and then solve it accordingly  Note :According to gui...

Q: 1. Calculate the Laplace transform L {(t² – 4) sin(t)}.

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Q: 1. Show that x^2 - y^2 = (x – y)(x + y) for all x, y in a ring R if and only if R is commutative. %3...

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Q: Evaluate, sin(4 – 3i) O 10.04240.68° 10.04Z – 139.32° O 9.71Z – 137.52° 10.04Z139.32°

A: We evaluate sin(4-3i)

Q: 2 Consider the IVP (x + 1)²y" – 2y = 0, y(0) = 1, y'(0) = -1. Determine all ordinary points of the d...

A: Since you have asked multiple questions, we will solve the first question along with its subparts fo...

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize...

A: We can solve using lagranges multiplier 

Q: Find the root of the function using newton’s method.

A: Note:- In given problem, you mentioned Newton's Method but didn't mention exact equation or function...

Q: Q3 Evaluate the integral fei sin e dz, where Cis a circle |z| = 1.

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Q: cercise 1.10. (a). Let V = R² = {(x,y)| x, y 2 0} with usual addition and scalar multiplication. Is ...

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Q: Let X be a random variable with p.d.f f(x) = c+ 1.2x2,0<x< 1. Find a constant c if E(X) = ! 0.6 0.4 ...

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Q: Question 3. Given the formula y(s) – y(s – k) y'(s) use the Taylor series y(s + k) = y(s) + ky'(s) +...

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Q: 4. sin (4x – y)dy dx 2

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Q: (c) Calculate the population of a spherical cloud of locusts which lies in the ball x2 + y?+ (z – 1)...

A: By our guidelines we are supposed to solve only one question. For the solution of the first question...

Q: What is L! if 2 1 +. s s-4] 4r A. -2t +e В. -t+ 2e¬7! 3t +e" D. -2t+e" C. 47 3r E. 4t - 2e"

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Q: If n 2 1, then the Fermat number Fn 22" +1 is prime if and only if %3D 3(F.-1)/2 = -1 mod (Fn).

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Q: 1. Find when the function is increasing and when it is decreasing. x2 – 9 f(x) = x2 – 16

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Q: Solve for a root/roots of the functions x² – 3 sin x + 2 In(x + 1) = 3.5 Applying the following meth...

A: Newton Raphson Method:-

Q: 2(s+1) What is L¯' s- using Completing the Square? + 2s +10 А. 2e cos 3t 4 -e sin3t 3 В. 2е сos 3t 8...

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Q: Solve for a root/roots of the functions 1. f(x) = e¯* – tan x Applying the following methods a) Fixe...

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Q: a piccewise Snction. Cleasly label bounday values. Make Sue the Shape of each seqmert.is corsect. Gr...

A: Given function is fx=−x2+4,   x≤02x+4,     0&lt;x≤2x−33,   x&gt;2. We have to graph the given piecew...

Q: Re-write. the.ethar.five.iterated.nt.eg.ral.s. 2 Fang, z)dydzdx -I x2 d

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

Q: B: Represent the region shown in figure (2) by double integrals of order dydx, dxdy and rdrde. y = V...

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Q: Complex Numbers: Find the roots. z = -2

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Q: In Exercises 1-4, use the comparison test to confirm the statement. In Exercises 15-21, use the rati...

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Q: What is 1-1] 2s – 3 2s +2 A. -2 cos 2t-3 sin 2t В. sin 3t V3 cos 3t 3 cost--sint 2 C. D. -2cosh 2t +...

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Q: (2) Let - {b ] E [2 3] A- Is A linearly independent? Justify your answer.

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Q: Given vectors: A(7,4,2), B(2,4,6) and C(6,1,2) forms a triangle. Find the unit vector in the plane ...

A: Cross product of two vector gives a vector perpendicular to both of them i.e. perpendicular to the p...

Q: (5х — у 28 1. у <-3

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Q: 2. Find the optimal solution of the following linear programming (LP) problem using the dual simplex...

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Q: Find the radii of curvature and torsion at a point of the curve r? + y2 = a², x² – y? = az. %3D %3D

A: Given curve is x2+y2=a2x2-y2=az

Q: Given points P(4, -2, 5), Q ( 3, 2, 7), and R(-3, 2, 4)  makes up a triangle. Determine the magnitud...

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Q: Show an example that the scalar multiple of a diagonal matrix is also a diagonal matrix. Put brief e...

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