Find T(t), N(t), aT, and an answer is undefined, enter UNDEFINED.) at the given time t for the space curve r(t). [Hint: Find a(t), T(t), aT, and aN. Solve for N in the equation a(t) = aT + aNN.] (If an Function Time t = 0 r(t) = e sin(t)i + e° cos(t)j + e'k %3D T(0) = %3D N(0) = %3D aT %3D aN %3D

Q: prove that E be an elliptic curve over F„2 with #E(F,2) = p² +p + 1. Then j(E) = 0

A: As per the question we are given a special elliptic curve over the field Fp² , such that : #E(Fp²) =…

Q: Let I = f x*cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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Q: - Determine the largest interval in which the unique solution of (t – 3)y +tan t y =t, y(n) =0 is…

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Q: 2. Consider the generalized initial value problem Ut + cuz = 0, u(t, at) = f(t) where a and c+0 are…

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Q: (5) (--) A particle is traveling with acceleration d(t) particle was at the origin, (0) =(0,0,0),…

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Q: 1. At z = 0, the function f(z) = z ez has O a. A non-isolated singularity O b. An essential…

A: The function f(z) = ze^1/z has the only singular point at z=0 .  We will use the Laurent series of…

Q: 1. If the parametric curve $x=f(t), y=g(t)$ satisfies $g^{\prime}(1)=0,$ then it has a horizontal…

A: TRUE Slope of the curve, when in parametric form = dy/dx = g'(t) / f'(t)

Q: 12 sin°(z) dr: C is any closed curve -dz enclosing 7/6 (a) Ic 6z – T -

A:

Q: 1. Consider the equation u +Uy = 1, with the initial condition u(x, 0) = sin(x). (a) What are the…

A: From the given information. The given equation is as follows. The initial condition is as follows.

Q: Can you help with 17  and 20 please?

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Q: The position of a particle moving along the x– axis at time t is given by x(t) = ecos2t, 0stS T. For…

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Q: 7. Given the space curve er(t) = (4 sin t ,4 cos t , 10t), Find T, N, B, and t (torsion)

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Q: 9. let C G TR? be Simple Close d curve bounding the positively orierned a reyi'on D. IF Area cO)=|…

A: Given that, Area(D)=∫Cx2+2xy+2y+eydx+∫CAx+x2+xeydy

Q: Determine the largest interval (a,b) for which Theorem 1 guarantees the existence of a unique…

A:

Q: 4. Find f such that F = Vf and use it to evaluate SF. dr. (a) F(x, y) = (3 + 2xy²) î+ 2x²y ĵ, C is…

A: (4) To find: f such that F→=∇f and To Evaluate: ∫CF→·dr→. For the following Functions: (a)…

Q: 6. Find F' and dF[a; h] where: In ¤1 (a) F(x1,x2) and hence show that if v is tangent to the curve…

A: (a.) Given: Fx1,x2=lnx1x2e2x1x22cosx1 To find: F' and dFa;h To show: If v is tangent to the curve…

Q: Let z(t) = 5 cos (t) and y(t) = 3 sin(t) ELLIPSE 2- At t = 3, x(3) = -495 -1- y(3) = 0.42 -2- dz…

A:

Q: 5. True or False: suppose that for any simple, closed curve C, ſF · dr = 0 where F(x, y) = (f(x, y),…

A:

Q: Find and classify the singularities of the following functions: 1. 4 1- cos(6z) i) ii) ii) 6 z4 + 26…

A: z=r is a pole of f(z) if and only if 1/f(r)=0.

Q: 6. At time t, a particle moving in the xy – plane is at position (x(t), y(t)) where the x(t)and y(t)…

A:

Q: 5. Show the variable ellipsoide sec(t +++ +7)+'csc(t + +)+cos(21)=1 is a possible form for the…

A: Given: x2a2etsect+π4+y2b2e-tcsct+π4+z2c2cos2t=1 To prove that the equation of continuity is…

Q: 1) Solve the Laplace equation for the function f(x,y,z) = (ax+by+cz)^n, where n is a given positive…

A: Part (1):   Given that f(x, y, z) = (ax + by + c z )n   Where, n is a positive integer and a, b, c…

Q: prove that E be an elliptic curve over F„2 with #E(F,) = p² +p + 1. Then %3D j(E) = 0

A: As per the question we have to prove that the given elliptic curve E over the field Fp² is…

Q: An object is moving along a path defined by the graph   x2+y2=2   Compute dy/dy, if dx/dt=2,x=−1,…

A: Differentiation application

Q: (1) Vf (f is a scalar function) 2) ř(t) and r(s), t is time and s is arch length.

A: This is a problem of vector calculus.

Q: 15. What is the correct piecewise parametrization of a path C created by starting from C₁ of…

A: Given Path C is C1:  y=x+3,     0≤x≤4C2:  y=x2,         y=7 to y=0C3:  line connecting C1 and C2…

Q: B- Solve the Laplace equation for steady heat conduction in the semi-infinite region 0 < y< 1, x 2…

A: The given problem is to solve the given Laplace equation for steady heat conduction in the given…

Q: 3. Sketch the space curve, r(t) = 8 cos ti +8 sin t j+tk , and find its length over the interval []…

A: Given: r(t)=8cost+8sint+tk    [0,pi/2]

Q: EXAMPLE 4 Find the arc length for the curve y = 2x2 In(x) taking Po(1, 2) as the starting point. 16…

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Q: (2) Solve the Laplace equation with the following boundary condi- tions. Uzr + Uyy = 0, 0 < « < a,0…

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Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Mathematical modeling is the real-life application of the differential equation. One such important…

Q: Consider the 1-D Burgers' equation in [-1,1] ди a?u дии + at The initial condition is: u(x, t = 0) =…

A: Solution is below

Q: A particle moves in the r(t) = (t- sin t, 1- cos t) Find the maximum and minimum speeds of the…

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Q: The two-dimensional Laplace equation, f(x,y)= -9x-6y +4 2²f ax 2²f Find for the given function. 2²4…

A: The given function,  f(x,y)=-9x-6y+4

Q: c) to the left of z = -2.46 and to the right of z = 1.72. Gaussian Curve

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Q: Consider the following initial value problem. Determine the coordinates tm and ym of the maximum…

A: To Find: The coordinates tm&amp; ym of maximum points of the solution of y''+9y'+20y=0, y(0)=7,…

Q: Exercise 1. Find the residues at z = 0 of the functions ez sinh(z²) 1 1 26 Z + z3 ' 25 and also find…

A: As per Bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: (b) Find the solution of Laplace's equation outside a unit circle a?u 1 du 1 a2u 0, (r>1,0<0 < 2x),…

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Q: Find T(t), N(t), a-, and a, at the given time t for the space curve r(t)- Function Time r(t) = 4- j…

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Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A:

Q: Suppose water is leaking from a tank through a circular hole of area A, at its bottom. When water…

A: Given: Water is leaking from a circular hole(in the bottom) whose area is Ah. When water leaks…

Q: 28. Suppose you follow the spiral path C: x = cos t, y= sin t, and z= t, for t20, through the domain…

A: NOTE: You have posted a question with multiple subpart, we have given answers to the first three…

Q: 1. Solve Laplace's equation inside a rectangle 0 0 and H > 0), with the following boundary…

A: Given, Laplace's equation                    ∂2u∂x2+∂2u∂y2=0                   ...(1) (0≤x≤L,…

Q: The two-dimensional Laplace equation, f(x,y)=-4x+2y-7 Find 2x² 22²4 for the given function. 2²1 2²²…

A: Given function f(x,y)=-4x+2y-7

Q: 1. (a) Consider the equation e'un+2ayury +2e"u- sin(y) u =0, where a is a real constant. Determine…

A: We will use basic knowledge of PDEs to solve this question.

Q: 4. (a) Evaluate limit of the two variable funcllon. x- y + 5Vx + 5/y lim V + Vy (x.y)-(0,0) (h) The…

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Q: Let {X(t)} be a BM with parameter o = 2 and X(0) = 0. Find P(T-1 < T, <T_2). BM means Brownian…

A: It is known that X(t)-XS~Nμt-s,σ2t-s Here μ=3,σ2=?,t=2,s=0 so it follows:…

Q: Sketch the space curve. Function r(t) = (5 sin t, 3t, 5 cos t) 1.0 0.5 0.0 0.0 -0.5 -1.0 -5 N 0.5…

A: Please see the below picture for detailed solution.

Q: Using Runge-Kuta thod of order Four to approximate the solution for the following problem with step…

A: Given:- y'=y3cosx+y2ex, 0≤x≤3, y(0)=1

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.