. SOLVING NHLDECC USING VARIATION OF PARAMETERS (D² + 2D + 1)y = (ex-1)² ANSWER: y = ex(C₁+C₂x - In|1 - e-*|)

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

A: Here we are given a 3d surface S by the following equation : 4x2 - (y-3)2 + 4z2 = 4 And we have to…

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: 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: 36. Sin(xy) + cos(yz) = 1. Compute z and az at P = (2, п/12,4). дх ду

A: Let us consider the given function z=f(x,y) The partial derivative of the function is obtained as…

Q: 5. || x+y cosx 1+sin x

A: Solution

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

A: Follow the steps

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: EV and V' be vector spaces over a field I xists a unique linear transformation, t: V at

A:

Q: 3. Provide a hand-drawn sketch of S using the traces obtained in (1). Label all important points…

A: As per the question we are given a 3d surface S as : 4y2 + 4z2 - x2 - 16 = 0 And we have to find :…

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: Inverse of a Matrix II. Solve the following 1. Find (1,3) entry of G-¹. 2. Find (3,2) entry of G-¹.…

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Q: Consider the following ODE system: = x² + xy³ =zy subject to the initial conditions x(0) = 2 and…

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Q: Write down the time measurements on the following analogue stop watches. Give your answe correct to…

A: Given,

Q: Lett: V→ V' be a linear transformation. Then (1) Ker (t) is a vector sub space of V, and (ii) im (1)…

A: The solution is given as

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

A: Here the lower limit is π4 and upper limit is π2

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

A:

Q: Thando furniture manufacturer, determines that in order to sell x chairs, the price per chair in…

A:

Q: Toss a coin repeatedly, and let X, be the number of heads after n coin tosses, n ≥ 1. Suppose now…

A: Given: Xn|P=P∈Binn,p with P∈U0,1 To find: Distribution of Xn

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: 10x + 2y — z = 27 -3x - 6y + 2z = -61.5 x + y + 5z = -21.5 L == Answer x = y = U = N ||

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Q: 1. Evaluate the following iterated triple integrals: pa+ay (a) f f f xy dz dy dx 1 (6) L L L (x² +…

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Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: we are given a solid and we need to find The Centroid or center of mass.   About the solid in…

Q: B. SOLUTION OF HOMOGENEOUS SYSTEM GIVEN: [1 -1 -13-14 0 2-2 1 10 0 A= 10 0-2 0 0 0011-10

A: Let us solve the system of homogenous linear equations in the next step using LU FACTORIZATION(row…

Q: ) Using each graph of y = f(x), sketch th [(x) and g(x).

A: (a) Given,

Q: Consider the point P(1,-1, -3), the vector u = (2, 1, 0) and the line l : 1- x z+3 = y + 1 = 3 2…

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Q: 2. Given the figure below, find a single vector that is equivalent to C B tw b) 10 14 וד --(A-F+C) G…

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Q: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7 -34 0 0 -7] A = 2 1 -1 146 010-3 0-3 -5 1.2 TRANSFORM…

A: Let us determine the Lower Triangular matrix using Gaussian Elimination method in the next step.

Q: Provide a hand-drawn sketch of S using the traces obtained in (1). Label all important points found…

A: As per the question we are given a 3d surface S defined as : 4y2 + 4z2 - x2 - 16 = 0 And we have to…

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: Find a power series representation for the function 8 using summation 2x-15 sign, determine the…

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Q: 1-x Consider the point P(1,-1, -3), the vector u = (2, 1, 0) and the line l : z+3 = y + 1 = 3 2 Find…

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Q: Let C be the curve with parametric equations

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

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

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Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

A: As per the question we are given an invertible function f such that f(-1) = 2 And Q is the surface…

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 = 0 -2 12 4 −1 -1 3 4

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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 &gt; 0 , θ∈ [ 0, 2π ]

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: Tell whether each statement is True or False. Explain your answer. a.) {o,n,e} = {n,e,o} b.)…

A: Equal Set : Two sets are said to be equivalent if both the sets have the same number of elements.…

Q: f(x) = x3 - 2x2 - 15x + 36 = (3 - x)(12 - x - x2) Find the (a)  intervals on which f  is…

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Q: 8. Time to explain: a) why does the vector equation of a plane have two parameters, while the vector…

A: Part (a) A line is a defined in one dimension, whereas, a plane is defined in 2 dimensions. So, for…

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: 9. xy(1+xy2) = 1 Ans: + y² -2 =

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

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Q: (k) The solution of the following problem for the heat equation with nonhomge- neous boundary…

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Q: Find a set of parametric equations for the curve of intersection of the given paraboloid and plane:…

A: Solution:-

Q: 1-x Consider the point P(1,-1, -3), the vector u = (2, 1, 0) and the line : 2+3 =y+1= 3 2 Find the…

A: Introduction: A plane is a three dimensional Euclidean figure. At least three points are needed to…

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.…