Consider the space curve r(t) = (sin(t), 3t, cos(t)). a. Find the arc length function for F(t). s(t) = b. Find the arc length parameterization for r(t). T(s) =

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A: The number of students at a school increases at a rate proportional to its current size. In 2005,…

Q: Let an be a recursively defined sequence: a₁ = 1 and exists, then a = 0 or a = = 1/3. an+1 = 3a.…

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Q: with T(X)= S x sintdt a) Find the derivative of f(x) b) Find the limit: lim x-0 f((x)) x²

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Q: Solve the initial value problem: x²y" + 5xy' + 3y = 1+x³, y(2) = 0 and y' (2) = 0.

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Q: Sally plots (-4, π) on the polar plane. How does she proceed? Drag a phrase to each box to correctly…

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Q: Evaluate 9 €₂ N d da (2-1) (2³8) ²

A: Using,  Cauchy integral theorem we can solve above integral.

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A: To find the volume of the solid S generated by rotating region R around the given axis, we can use…

Q: Given F=xy¹i+x²yj. A) Find a potential function for F. B) Evaluate F dr where C is parametrized by…

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Q: A poll asked respondents if they agreed with the statement that colleges should reserve a certain…

A: The given Venn diagram,Using the Venn diagram to find the number of respondents agree the statement.

Q: 1. Find a discretization scheme for the heat equation with insulating boundary conditions PDE IC BC…

A: Let the solution be in the form We shall consider the three cases as follow,

Q: Reduce the equation to a canonical form and solve it. Sh yzxx + (x + y)2xy + XZyy = 0 Text

A: The characteristics integrals:

Q: The function f(x) = −6 sin (x + ¹) − 5 models the average rate of change in temperature of a…

A: Function :

Q: Write a general formula to describe the variation. y varies inversely with √x; y = 2 when x = 4

A: Given that, varies inversely with , when .To find the equation of the variation.

Q: x₁ = x2 = X3 Solve the following initial value problem: -4 1 +6:9--0 = -3 -8 -2 , (0) = -1 -1 -11,…

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Q: (a) Use the Mean Value Theorem to show that, if smals x+1 x² +1' then there is a point c in (-1, 1)…

A: (a). To prove that if  then there is a point in such that

Q: 2-3 [84] 5 -2 - [ ² - 3] · B = [$ 3]), and C = [; } 2. Verify that -4 6 55 3 - Let A = AB = AC and…

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Q: Here are the meanings of some of the symbols that appear in the statements below. . E means "is a…

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Q: Suppose I have a curve with derivative function r' (t) = (t + 1, t³, sin(t)). 2 (a) Calculate f² r'…

A: We have

Q: 6. Given the following ad for an apartment, what are the upfront costs? BR/1 BA, Bright & Beautiful…

A: From the data what is upfront cost?Expense's that are payed for the source thing at at the beginning…

Q: Find the inverse of matrix, if possible, by applying the Gauss-Jordan Method (3³),

A: We have to find the inverse of the matrix using gauss jordan method.

Q: Consider the following function. Find the following derivatives. fx(x, y) = f(x, y) = x² + xy + y² +…

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Q: Find the absolute maximum and minimum values off on the set D. f(x, y) = x + y - xy, D is the closed…

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Q: IV. Let B= 000 Let [x] = 123 110 100 and A= -1080 Find [x]. be bases for 9³

A: First off all we find the vector  x from the given conditions . Details solution is given in step 2.

Q: find two power series solutions of the given differential equation about the ordinary point x = 0.

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Q: Find the Volume V(S) of the solid S generated by given R: R is the region bounded by y=x², and…

A: The region R:

Q: Solve the separable differential equation. dy/dx = sec y / y^2 (x^2 - 3x^2 + x - 3)

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Q: Calculate the area of the polygon given the vertices

A: The area of the polygon is the area of smaller polygons that when joined create the original…

Q: 19) Using Newton Raphson method find the root of equation f(x) = x³ + 2x²+x-1.

A: Find: The root of the equation.

Q: Reduce the equation yzxx + (x + y)2xy + XZyy = 0 to a canonical form and solve it.

A: The characteristics integrals:

Q: Express J5(x) in terms of Jo(x) and J₁(x). Answer: J₁(x) = = ( 384 72²-1) J, (x) + (1¹2_192) √ ₁ (x)…

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Q: 5) A. Define the dihedral group D, and write the elements. Find the order of element yx³ and compute…

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Q: For the first order model 4* + x = u, (t) with initial condition (0) = 2, what is the value of a(t)…

A: Given: The first-order model subjected to the initial condition of ,To find:  after one time…

Q: Given that f [a, b] → R is a bounded function. (a) Explain the definition of Riemann integrability…

A: Let is  a  bounded function.Now, f  is  integrable  iff

Q: Original Equation: 4+ (1+x) = 1 First Step:

A: The first step of a solution to an algebraic equation is given.

Q: Consider the following second order differential equation: y''(t) + 4y'(t)+ 3y(t) = 3t + 2. (i)…

A: “Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

Q: Consider the graph of the function g(x) given below. g(x) -4- 2

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Q: The differential equation y"" +9y' = xsin x + x²e²x is given. Which of the followin is definitely…

A: Given differential equation

Q: Please resolve/reanswer items "a, b and c". Upvote will be given.

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Q: Find the power series solution in powers x (about zo = 0) the differential equation y" + xy…

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Q: In how many ways can you be given 44 cards where order is Not important? In how many ways can you be…

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Q: Suppose the cost of an object appreciates at a rate inversely proportional to the sum of its squared…

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Q: 5.4. u = 3122 -1 2 V = -5 0 -1 3 and w = Are the vectors u, v, w linearly inde- pendent in R4? If…

A: The vectors are:.To Do: We have to check whether the given vectors are linearly independent or not.

Q: workout the commutators of poincare group. I need full derivation so please do the full derivation

A: The Poincaré group is the group of symmetries of Minkowski spacetime, which includes translations,…

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A: To find that how many six-digit numbers with a possible leading zero, but no repeated numbers are…

Q: Problem Find the initial solution for the following transportation problem, by using 1- North-west…

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Q: 5.12. Give a basis find its dimension. elements). for the vector space of all 3 x 3 matrices of…

A: We want to give the vector space of all  of trace 0 and…

Q: Determine the general solution of the differential equation y' = x²/y(1 + x³) and the solution of…

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