he complex fourth root

Q: Given: planes II₁: 2x - 5y + z = -1 and II₂ : x + 5y + z = 5 intersecting on a line l (a) Compute…

A: Given: Planes π1:2x-5y+z=-1 and π2:x+5y+z=5 intersecting on a line l.

Q: Question 4 4.1. Find a power series representation for the function 2x-15 sign, 4.2. determine the…

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Q: Problem 25. Find the Laurent expansion of f(2)=1/[2(2-1)(z-2)] in i) 0< < 1 ii) 1 < 2 <2 iii) 2 <…

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Q: Let x and y be two real numbers such that x + y is rational. Prove by contrapositive that if x is…

A: Introduction: Rational and irrational numbers are two very important divisions of real number…

Q: Consider the polar curves C₁:r = 3 (blue) and C₂: r = 2 − 2sin0 (red) and let R be the shaded region…

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Q: Let C be the curve with parametric equations

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Q: u(x, y) and let f and g be twice differentiable functions. The al solution to the equation uy2r + 2y…

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Q: EXAMPLE 2: Find the lower and upper triangular matrix of 9 -3 31 B -3 4 1 1 61 3 using Cholesky…

A: We have B=[9-33-341316] which is real symmetric matrix now checkering if it is positive definite…

Q: Estimate how much the value of the function will change f(x,y,z)= ysinx + 2yz if the point P(x,y,z)…

A: If the input of a multivariable function changes its output also changes. The directional derivative…

Q: Let (R, +,-) ring with properties X.XX, XER Cindempotent properties), show! @a = 0, x ER (b) x. y…

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Q: 4. Evaluate the following integral fel e(-²²-25) dt

A: Note:-  ∫ e-x2 dx=π2 erfx +C   Given integral is ∫0∞ e-t2-254t2 dt

Q: 3. Let 7 and w be vectors such that 7= (2,2, -1), ||w|| = √2, 7-3, and x = (2,-1, 2). a. If u =…

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Q: A company determines that its total cost, in thousands of 3x rands, for producing x items is C =…

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Q: Q5: Consider the following subsets of real plane R² Determine with graph: 1-Arewise connected A=…

A: Follow the steps.

Q: Apply the techniques of Example 7.1.5 to the evaluation of the improper integral 8 dx 1 = (a) Let…

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Q: 2. SOLVING HLDECC USING AUXILIARY EQUATION ²+k²x = 0, k is real number; when t = 0, x = 0,= vo. dt…

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Q: 21. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

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Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

A: We have to solve given problems:

Q: Let FC be the splitting field of x² -2 over and ==e7 Let [F: (=)] = a[F: (√2)] = b then? a) a = b =…

A: Option a is correct i.e. a=b=7.

Q: Let S be the surface with equation 4y² + 4z²x² - 16 = 0. 1. Find an equation of the trace of S on…

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Q: 4. 2x₁ + X₂ X3 3x₂ + x3 -2x3 2x₁ + x₂ + x3 L = Answer X₁ X4 = 7 x4 = -3 = 2 2x4 = 8 x₂ = M U = x3 =…

A: Given,                  2x1 +x2 - x3 - x4 = 73x2 + x3 - x4 = -3         -2x2  = 22x1 + x2 + x3 -2x4…

Q: x² A quadric surface is defined by the equation: + 3y² = 3 + z 3 1. Solve the equation of the traces…

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Q: Show that the three functions: f₁(x) = ex-8f2(x)= ex, f(x) = 4(2x-2) are linearly dependent.

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Q: . Show that the vectors V1=(0, 3, 1, -1); V2=(6, 0, 5, 1); V3=(4, -7, 1, 3) form a linearly…

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Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 cos 0 E³r = g(0) = 1/2 500 € C D: r = 3 the…

A: (1)C : r =f(θ) =3-3cosθ,E : r =g(θ) = 32secθSo,C0 : r =f(θ) + g(θ) =3-3cosθ +32secθ⇒r =3-3cosθ…

Q: Mondo furniture manufacturer, determines that in order to sell x tables, the price per table in…

A: The revenue function is calculated by multiplying the price function by the number of quantities.…

Q: 4. Which of the following subsets of R³ constitute a subspace of R³? [Here, x = (₁, §2, §3).] (a)…

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Q: 2.Evaluate the following integral: fx²cosxdx (a) by solving the integral analytically; by solving…

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Q: Consider the polar curves C₁ r = 2 cos 0 and C₂: r = 2 cos 30, and let R be the shaded region as…

A: Same point can be expressed in polar coordinates in various ways.

Q: 3) Find the derivative f(z) = 100 a) f(z) = 400z(z²-1) (2²+1) 100 99 b) f(z)= c) f(z) = d) f(z) = e)…

A: As per the policy of bartleby the provisions is to solve only one question at a time

Q: Consider the vec Ř(e) {{cos (1²₂), c² - 2². ²+/-) t# -1 <-1,4,-27, t = 11. (1.) show that I is…

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Q: 0 -2-4 8 15 1. A = 1 4 1 6

A: We need to find the determinant of the given matrix using raw operations and cofactor method…

Q: List the elements of each set where N= {1,2,3…} a.) A = {x∈ N | 3 < x < 9} b.) B = { x∈ N | x is…

A: Set-builder form The set contains the element that has single property in all Roaster form The set…

Q: Ex: If w = f(x, y, z), x = x(r, 0), y = y(r,0), z = z(r, 0), find wr, we? aw ax aw ay 1 aw

A: Chain rule for total derivative

Q: If R8500 is invested in a saving account offering 5.4% per year, compounded semi-annually, the rate…

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Q: and m' be two R-modules. e set Hom, CM, Mm) is an group under pointwise of morphism

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Q: Consider the stochastic process Y₁ = (1 + y)Bt + (1 + €) (B² – t), where B is a Brownian motion.…

A: For a standard linear Brownian motion {B(t):t≥0}, although at any given time t and for any open set…

Q: Express R² dA as an iterated integral in the order dyda, where R is the region in the xy-plane…

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Q: x"" (t)- 3x"(t) − 4x' (t) + 12x(t) = 12e-t; x(0) = 4, x'(0) = 2, x'(0) = 18

A: The solution is given as

Q: Find the volume generated by revolving the area bounded by x². - 4x - 4y + 4 = 0 and y = 1 about the…

A: We will find point of intersection of curves and line to find region bounded , and then rotate it…

Q: If the graph is Hamiltonian, find a Hamilton cycle; if the graph is Eulerian, find an Euler tour.

A: deg(d)+deg(h) = 4+4 =8 where d and h are not adjacent. Since deg(d)+deg(h) is not greater than the…

Q: Given any two Euclidean spaces E and F, w ension m, for any linear map ƒ: E→F, we have Ker f = Ker…

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Q: 4. Consider the matrix equation Ax = b where, A = a b 1 1 where a, b > 0. (a) When is A strictly…

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Q: Let S be the surface with equation 4y2 + 4z²x² - 16 -0. 1. Find an equation of the trace of S on…

A: Solution:S be the surface with equation 4y2+4z2-x2-16=0⇒4y2+4z2-x2=161)Traces of S in the coordinate…

Q: of the following integral using the Simpson's 1/3 rule will result 0.001. Give the exact answer…

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Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Given,  S is the quadratic with equation 4x2 - (y-3)2 + 4 z2 = 4 Here S is a sphere  whose radius is…

Q: Let C be the parametric curve defined by [x(t)=t²-t-6, [y(t) = 4t³+31²-6t. Determine the point/s…

A: The general form of a parametric equation of the curve in the xy plane is given by xt=ft and yt=gt,…

Q: . SOLVING NHLDECC USING VARIATION OF PARAMETERS (D² + 2D + 1)y = (ex-1)² ANSWER: y = ex(C₁+C₂x -…

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Q: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7-340 0 -7] A = 2 1 -1 14 6 01 0-3 -5

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Q: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7-3 4 0 0 -7] A = 2 1 -1 14 6 010-3-5

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Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.