Given the vector function (1) = (e+→¹², 2√³+1, 4 arctan(1-1)), find the speed and the equation of the tangent line to this curve at t = 2, then graph the tangent line. Speed= i(t) =

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: (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: 1- Define degree of freedom

A: We have to define the degree of freedom

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: A forest has a population of lynx and a population of rabbits. Let a represent the number of lynx…

A: Solution: x'=dxdt=-0.25x+y  .....1y'=dydt=-x+4y  .....2B.C.S: x0=0 and  y0=1From equation 1  and 2…

Q: Polar curves C1: r = 2 cos 0 and C2: r = 2cos 30 and let R (shaded region). 2π The Cartesian…

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

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Q: B. SOLUTION OF HOMOGENEOUS SYSTEM GIVEN: 1 -13 -1 4 0 2 -2 1 100 10-20 1 0 A= 0011-10

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Q: E be a Euclidean space of dimension (E(1, f)) = dim(Ker (f- id)), then s minimal.

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

A: The trace of the surface: f(x,y,z)=0 on any plane is the projection of the surface on that plane.

Q: Find the equations of

A: Side view of S

Q: a. Find -R(t), . give the parametric equations of the tangent line to the graph of -R(t) at t=0: 1…

A: Given that R't=4e2t,11+t2,2cosht R0=1,−2,3 To find: R(t) Parametric equation of the tangent line…

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: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7 -3 4 0 0-7 A-2 1-1 4 6 010-3 0-3-5 1.1 TRANSFORM TO…

A: A=7-340-721-146010-3-5

Q: please could someone solve this for x -415000 =8.314* 1073* ln x

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Q: Solve the nonhomogeneous system tY': = - (²-2) ₂ Y+ (1-2₁).

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Q: Suppose you have an mxn matrix A and its Singular Value Decomposition (SVD): A = UEVT Pick all of…

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Q: (i) At x = 1, the Fourier Series of f(x) = converges to: (A) 0 (B) 1 (2-2x, -1<x<0 0< x≤1 (C) 2 (D)…

A: At x=1 , the function value is 0. i.e. f(1)=0 Therefore, at x=1, the Fourier series for f(x)…

Q: Consider the vector-valued function Ŕ(t) = a. Find the domain of R. b. Determine if R is continuous…

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Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

A: To find the volume of the solid generated by revolving the region: y-x2=3, x+y=3 about y=-5

Q: Q3: Use finite difference method to solve Laplace equation in the red domain illustrated below. Ax =…

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Q: 1. Find the inverse of A = 1 1 1 2 3 01 1 using the Gauss-Jordan method.

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Q: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7 -3 4 0 -71 A-2 1-1 4 6 010-3 -5 3. SOLVE THE SYSTEM…

A: A=7-340-721-146010-3-5 WE HAVE TO FIND LU FACTORIZATION.

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

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Q: Let C be the parametric curve defined by fa(t)=t²-t-6, y(t) = 4t³ + 3t² - 6t. Determine the point/s…

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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: 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: Find an analytic function whose real part is u(x, y) = x³y - y³x 7²+1

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

Q: Show that in an n-dimensional vector space X, the representation of any x as a linear combination of…

A: The given problem is related with linear algebra. We have to show that in an n-dimensional vector…

Q: : R³ → R², find its dual map, where (i) 1(x, y, z)=(x-y, y+z), (ii) t(x, y, z) = (x + y + 2z, 2x+y),…

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Q: Using the data in the table below and the best combination of trapezoidal and Simpson's rules,…

A: Solution: Solution using Trapezoidal rule, The value of table for x and y x 1 2 3.25 4.5 6 7 8 9…

Q: Provide all answers to four (4) decimal places. Applying the Gauss-Seidel method in solving the…

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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: Sketch f(t) and find the Laplace Transformation of the following functions t, 0 < t < 1 i) f(t) =…

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

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Q: Identify and sketch the graph of the following SURFACES. x² + y² = sin²z, z = [0, π]

A: Any point on the 3D plane is represented using the ordered pair: x, y, z. A graphing utility can be…

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

A: given total cost C=500e3x8 and production function x=5t6+1

Q: Consider a curve given by Ř(t) = (2 cos t, 12t + 3, -2 sin t). Let f(t) be a function such that f(1)…

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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: 2. Sketch the function and write in terms of unit step function. Hence find the Laplace…

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Q: The marginal cost of manufacturing a certain product is dC/dX = 17 + 0.005x .  If the cost of…

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Q: 5. Consider the following function: f(t)= Find the Laplace transform of this function. Lis odd -1 is…

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Q: Solve this problem. Show your complete answer with a graph in a given-required-solution format…

A: Here follow the graph of the region bounded.

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: 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: 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 moment with respect to the y-axis of the area bounded by the parabola x = 9y - y² and y =…

A: It first moment about y-axis.

Q: Put I, in equ (1) 80 = 61 + 6( 1² + 1) 12 3 -- I = 7amp.

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Q: 8x Show that the three functions: f₁(x) = ex-8, f₂(x) = e³x, f(x) = 4(2x-2) are linearly dependent.

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Q: Finding the Determinants Using Combined Methods (row operations and cofactor method) -2 -4 A = 1 4 8…

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