be a linear operator on a vector space V(F). If = 0, t ce oft and null space of t. Also given an example of a line

Q: b) Solve: P(4)=4-5t + tetsint

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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: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

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Q: Find the orthogonal matrix and upper triangular matrix in matrix A using QR method

A: The given matrix is                           A=20-40-204-26

Q: 3. Consider the points K (-1,0,7) and M(1, -2,5), the vector MN = (1,4, -3) and the li symmetric…

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Q: dy Find the complete solution of 2e2¹ cosx- dx Note: fe"du=e" + c sin²x = 0.

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Q: Village C (he is at Village A): A → Bk → C for k Marvin is deciding a path from three (3) routes to…

A: Solution : Conditional probability: probability of A given that B already happened. P(AB)=P(A∩B)P(B)…

Q: Given the following observations, determine an 3 ^ 1 5 66 7 8 8

A: Given,         3, 4, 4, 5, 6, 6, 7, 8, 8, 9

Q: Consider the vector-valued function R (t) = ( 8/3 t 3− t, 2t2 , 2 − 2t2 ) - Find II R(t) II…

A: We are given R(t)=(83t3− t, 2t2, 2 − 2t2) to find II R(t) II and distance traveled by a particle…

Q: (b) Show that k-1 (k+1) n n+1 for every n ≥ 1.

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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: let Co then 허 the ㅗ of gotattin angle tant (승) fant h of axey

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Q: You are given u and a span of vectors. In the first box, enter 1, 2, or 3 to describe which of the…

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Q: Solve dy/dx = yx²-1.2y with the initial condition y(0) = 1 over the interval [0, 2] using Heun's…

A: Let us start solving the problem step by step...HEUNS METHOD ALSO KNOWN AS SECO D DERIVATIVE RUNGE…

Q: In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

A: Solution: Let N be the number of bacteria present at any time t.  The rate of growth of the bacteria…

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: We can solve this using given information

Q: 3. Magkano ang nominal wage? Real wage = P10,200.00 CPI = P180.20

A: Here given  Real wage =10,200.00 CPI =180.20

Q: Consider the following payoff Table Decision Alternative D₁ D₂ The State of Nature 0.79 1-0.79- $1…

A: ED1 = 0.79(5)+ 0.21(8)ED1 = 3.95+1.68E(D1) = 5.63ED2 = 0.79(4)+ 0.21(8)ED2 = 3.16+1.68E(D2) =…

Q: Q. If B = {e, = the usual basis R2. Determine its dual basis. ?? ده رده را( = (D, 1)} is

A:

Q: 5. The von Bertalanffy equation is defined by the ODE W'(t) = aw (t)-BW (t) where is a constant…

A: The von Bertalanffy equation is defined by ODE as follows W'(T) = αW(t)2-βW(t)Let  y(t) = W1-λdWdt =…

Q: Let S be the surface with equation 4y2 + 4z2 - x2 - 16 = 0 1) Find an equation of a generating…

A: Solution

Q: c) There are three train tracks from village X to village Y and four train tracks from village Y to…

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Q: Solve the nonhomogeneous system ty' = 3-2 2 -2 Y + -2t ¹-1

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Q: (h) Let u(x, t) be given by u(x, t) = a, cos(3nt) cos(2nx). [ an n=1 If u(x, 0) = cos(4x), 0≤x≤/2.…

A: This is a problem of Fourier analysis.

Q: 3. Solve the linear system using Gauss-Jordan method I 2x+y+z=2 y+z+w=2 x+y-z=0 x + 2z-w=1

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Q: Let M be a matrix a M-[b] = c d Matrix M is non-singular if and only if O ad + bc #0 O ad - bc #0

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Q: - (² homogeneous system ty' = 2 -2 Y +

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Q: dy Find the complete solution of 2e2¹ cosx- dx Note: fe"du = e" + C - sin² x = 0.

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Q: 2- Study the integrability in the Lebesgue sense of the following functions. Calculate the integral…

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Q: f(x) = 3 - 2x and g(x) = ln (x - 1) then (image attached) = 1. -2 2. None of these 3. 3 4. 1

A: Composite rule is used

Q: For each problem below, use algebra to answer the questions. You may find it helpful to draw and…

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Q: -42 20 00 2 3 10 3 102 303 Evaluate D.

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Q: 2. Find the inverse of A = 1 1 1 1 2 -1 3 1 -1 2 3 H2H2 1 using Gauss-Jordan method.

A: The solution is given as

Q: Let S be the surface with equation 4y² + 4z²x² - 16 = 0. +4√3 1. Find an equation of the trace of S…

A: Solution

Q: 3. Solve the linear system using Gauss-Jordan method I 2x+y+z=2 y+z+w=2 x+y=z=0 x + 2z-w = 1

A:

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

A: 4x2 - (y-3)2 + 4z2 = 4 (C) The quadric S can also be identified as a surface of revolution.

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bound by…

A: Sketch the region bounded by given curve and line and then rotate it about given line to generate…

Q: sforms in finding the solution to the giver +4y= 4e²t. v(0) = -1.v'(0) = -4

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Q: Let A be an n x n symmetric matrix, R be an n xm matrix such that with m ≤n), and let B = R¹ AR (an…

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Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: we will use relation between cartesian and cylindrical/spherical co ordinate to convert equation…

Q: 2. Consider the polar curves C₁: r = 4 + ³² cos 0 and C₂:r = 2 - cos as shown in the figure on the…

A: Given,C1 : r = 4+322cosθC2 : r =2-22cosθand  r > 0 , θ∈ [ 0, 2π ]

Q: Let s in G, s is not equal to 1.

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Q: (a) Solve the first order linear ordinary differential equation dy x sin x- + (sin x + x cos x) y =…

A: The solution is given as

Q: 0 -2 2 -1 B = 1 4 -1 3 4

A: We have to solve given problems:

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral…

A: Let  I= ∫π4π2ln(tanx)dx Here, a=π4 , b=π2 , f(x) =ln(tanx) Step size h=b-1n=π2-π410=π410=π40 Then…

Q: (b) One of the following is NOT a second order PDE: (A) Uz Uyy + Uzy=0 (C) (U₂)² -Uz Uy = 0 (B)…

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Q: Find the volume of the solid generated by the region bounded by -x + y² = 8, x = -2y and y = -2…

A: Frist we graph identify region bounded by given curves Now we know volume of the solid formed by…

Q: (2) If c(z) ≥ 0 for all z = [0, 1], then a function minimizes J(v), that is, J(u) = inf J(v), with…

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Q: II Find the maximum value M of f(x, y) = x4y5 for x ≥ 0, y ≥ 0 on the line x + y = 3. (Use symbolic…

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Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. (a)…

A: