Question 1 Find a polynomial q(x) of minimal degree in F,[x] such that q = x+2 (modx' +1) ; q = x +x (modx'+2x+1) : Find then all solutions of this system of congruences.

Q: Vrite the equation in spherical coordir (a) 5z2 = 8x2 + 8y? %3D

A: In this question, the cartesian coordinate system is transformed into the spherical coordinate…

Q: , Find the antiderivati 4x3/2 –1

A: Introduction: We know that the antiderivative of some functions is as follows:…

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Q: Problem (1): Let r, s E Q with s t2 .r for all t e Q and let E = QIVr, Vs). Prove that Gal (E/Q) =…

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Q: Hew y If the directiond derivative Valne ( Duf) ef the function f(x,4) = x²-3xy +uy3 at Paint (-2,0)…

A: From the given statements, we have to find the unit vector. Then, we can proceed further.

Q: Find the area of the shaded region. f(x) =x - 8x° +21x2, g(x)= 20x+50

A: INTRODUCTION: If the straight line is above the curve in the bounded region, the straight line's…

Q: PROBLEM 2. Let X(t) be a Brownian motion t > 0. Use the definition of the stochastic integral to…

A: Dear student I've started working into your question. I assure you that I will perform my best and…

Q: Thelma and David built a recycling bin that is 6 feet wide 12 feet long and 14 feet high. How much…

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Q: Consider the given vector equation. r(t) = e16t i + e8t j (a) Find r'(t).

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Q: у" — бу' — 7у %3D 8e7x

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Q: 3 1 4 1 5 1 1- Show that the series is convergent. | 2 4 3 42 4 43

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Q: The function P(t) = t² (2t + 3)5, can ONLY be differentiated by using the product rule. Select one:…

A: The product rule of the differentiation can be stated as f·g'=fg'+gf'.

Q: 15. Evaluate SLL:(z+1)dV where E is the solid enclosed by the paraboloid y = x2 + z² and the plane y…

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Q: The network and communication systems attached to the smart grid, including the routers and…

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Q: Evaluate the integral below by changing to spherical coordinates. 81 - y V 81 – x2 - y2 (x²z + y?z +…

A: We have to solve the given intregal

Q: wo Eigen values of the matrix e a ratio of 3:1 for p = 2. What e of p for which the Figen valu

A: Introduction:   Eigenvalues are a subset of scalars that are associated with a system of linear…

Q: Identify any misrepresentation issues in the given graph, Select all that apply.. 100 80 60 40 20 0…

A: To identify the misrepresentation .

Q: -2 4 For the matrix B = what is the value of |B|? 3 7 3. A. 8 В. — 2 С. 4 D. -5 Select one: O D O C…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: For each of the questions a), b), c) and d) find the volume of the solid generated by revolving the…

A: Using disc and cylindrical shell method.

Q: Al is at the point (0,6) and Bob is at the point (8,0). They are both running towards the origin. Al…

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Q: A palr of parametric equations is given. x = t2, y =t- 2, 2 sts 4 (a) Sketch the curve represented…

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Q: [t +3 If A = -1 6. t- 3 -6 one of the following must be true? 1 t+ 4] A) The rank is 3 ift#-4, B)…

A: Rank of the Matrix, and it's properties

Q: lution of the linea dz + pqz = 0

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Q: Solve the inequality |4x + 6| 2 18 A. x 3 С. х2 3 B. 3<x<6 D. -6 <x<3 Select one: O A о в ос O D

A: We have to solve the inequality.

Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 8t – t³, In(t))

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Q: and f p5

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Q: The diagram below will be used to answer the following questions: f(x) 8 -7- -6 -5 -3 -2 3 4 8. 9 10…

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Q: The natural numbers are N= {1,2,3,..}. The prime numbers are P = {2,3,5,7...}. True or false? ØSN…

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Q: 1. Consider the separable differential equation y' = x²y³. a. Plot the slope field of this…

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Q: The Nicols are buying a house selling for $345,000. They pay a down payment of $45,000 from the sale…

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Q: Find T(0)

A: Introduction: The tangent vector of a vector valued function rt is represented as r't. The necessary…

Q: Find the following antiderivatives. 49 – 2y dy 49 +1 (a)

A: Introduction: Evaluation of anti derivative is the main aim of indefinite integral. An anti…

Q: Find the sum of the series (-1)*n2k 42k (2k)! k=0

A: We have to find the sum of the given series

Q: Given two functions h(t) and g(t), is h'g (t) = (hg)' (t). Select one: O True O False

A: We want to find given statement is true or false.

Q: Prove that x? – 34y? = -1 has no integer solutions. (Hint: First find the minimal positive integer…

A: As per the question we have to prove that the equation : x2 - 34y2 = -1 Has no integer solution, bu…

Q: In the 1930's LF. Richardson proposed that an arms race between two countries could be modeled by a…

A: given  dxdt=-0.45x+10.5dydt=8.2x-0.8y-142 (a) find the equilibrium points for equilibrium points put…

Q: Consider laurent Series expanSions around Zzo of the following f(2) = 2?-3Z+2

A: Given:  f(z) = z/(z²-3z+2) To find laurent series expansion around z = 0.

Q: Suppose A is a symmetric nxn matrix and B is any nxm matrix Show that B'AB, B'B, and BB' are…

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Q: lim x" = a" %3D for any positive integer n, is an example of a Lof limits.

A: We have limx→axn=an We have that whenever x tends to a, we see that xn tends to an

Q: 1. Use the midpoint rule with n = 6 to estimate the value of the integral (x³ + x) dx.

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Q: Find term 4, term 6 and term 8 given by the formula: n2 +n+6 a n ;n2 1. n +7 Determine whether the…

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Q: A. Ē = -VV if V(r, p, z) = 10z sin o B. Divergence ủ ifů = (r cos² 0)f = (r cos 0 sin 0)êê + 3r@ C.…

A: As per the question we are given some scaler and vector fields in spherical &amp; cylindrical…

Q: Solve the following Integer Programming problem Maximize z = 2x1 + 3x2 subject to 5x1 + 7x2 \leq35…

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Q: 1. Evaluate 4x³ds, where C ie the line segment trom -2,-1,QL,4). らt Xz xlt)= (1-t)(-2) + t(1) E) :…

A: Introduction: A line integral is an integral that determines the function to be integrated along a…

Q: Let 1 2 2 1 3 00 3 S = 1 3 2 2 1 1 1 1 Find a rank one matrix R so that the matrix T the same…

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Q: Question 1 f(x) = e²* – x,xo = 0, x1 = 1.25 and x2 = 1.6. %3! %3D a. Construct the interpolating…

A: (a) We can use Lagrange interpolating polynomial method to find P2(x) using given nodes.

Q: Solve the initial value problem: 1 y" + 2x(y')² = 0; y(1) = 5; y'(1) 3 II

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Q: Let D be the region bounded by the curves y= 42-x², x=0, and y= x a) Draw the enclosed region b)…

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Q: A tank initially contains 100L of brine in which there dissolved 20kg of salt. Pure water flows into…

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