Find the moving trihedral and the curvature at any point of R(t) = (In(6t), e²-t,5t). %3D

Q: cot x csc x - 1 csc x + 1 cot x L.S. R.S.

A: We have to prove that cot xcsc x+1=csc x-1cot x.

Q: y = 5/(sin3x +cos3x)

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Q: Our aim is to check whether 179 is a prime number or a composite number. Which among the following…

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Q: Find the matrix A. 13

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Q: The table below shows the bus fare (in rand), including 15% VAT, for a single trip. BUS FARE IN RAND…

A: The fare of a return trip is calculated by multiplying the fare of single trip by 2. The expression:…

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

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Q: Use resolution to show ∀x∀y[p(x,y) → ¬p(y,x)] models ∀x¬p(x,x)

A: Please look into the next step for detailed answer

Q: (c) Use de Moivre's formula to write down a formula for all of the n-th roots of z = rexp(ie). In…

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Q: Find the solution set of x-4y +3z = 1. a. (1, 0, 0) b. (-2, 0, 1) c. (1 - 4s + 3t, s, t) d. (1 + 4s…

A: Solution set of the equation

Q: V= Mm xn (an xn matrix), with standard operation of m addition. 4.

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Q: 3. u, = u, - sin x cos t, 1 >0 В.С.: и(0, г) %3D0, = () 1.С.: «(х, 0) %3D 0, u,(x. 0) = 0

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Q: II. Consider the function g defined by 1 g(r, y) = cos (7x/9) + log3(r – y) Do as indicated. 1.…

A: 2) Given g(x,y) = cos(πxy) +1log3x-y…………………………(1) Differentiate equation(1) partially with respect…

Q: In a particular very small region, the consumer price index, C, depends on the current value of…

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Q: 3. Let f(x) = x(x² + 1)/2. (a) Evaluate fo f(x)dx using integration by parts. (b) Evaluate f, f(x)dx…

A: Solution :-

Q: g. L[cos(3t – 4)] h. L[t³sin(2t)cos(2t)] i. [[te-atsin(at)]

A: As per the company rule, we are supposed to solve the first three sub-parts of a multi-parts…

Q: if was Fife(R)R² Lanearidentifier Teatbxt€ X)= ca,ogb rand father o kert @ EmT

A: We have to find the (1) KerT and (2) ImT

Q: example problem about Area Region Bounded by Different curves. Write the problems and the complete…

A: According to the given question, create an example to show the area between two curves and how to…

Q: Explain how notation in sequence works.

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Q: 1. Solve the differential equation: xy' – y = 2x ln x

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Q: Solve for x when x– 3A + 2B = 0 -4 01 1 21 A = = 1 -5 and B =-2 1 -3 21 4 4] --14 7 -14 -4 4 7 -17…

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Q: Find the solution set of x- 4y + 3z = 1. а. (1, 0, 0) b. (-2, 0, 1) с. (1 — 4s + 3t, s, t) d. (1 +…

A: We have to find the solution set of x-4y+3z=1

Q: 1. Find the smallest distance from the point (0, c, 0) to the surface y = x² + z².

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Q: 1. Write the following function using unit step functions and then find its Laplace transform: e2t 0…

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Q: 5. (a) Give the definition of a group. (b) Show that (Z, +) is an abelian group. (c) Let n e N. Then…

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Q: 1. Use Least Square Regression to fit y - ax to 6 7 8 9 8 10 13 3 4 5 1.5 2 3 4 5 y

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Q: 4 -3 2 1- -8 -7 -6 -5 -4 4. 5 1- (-1,=1) 2 (0, –2) -3 |(1, –4) -4 -5 -6 -7 -8 f (x) =| log (x+

A: We can solve this using given information

Q: Evaluate: , asirnadz using a 3rd level (k=3) Romberg integration. Round off to 6 decimal places.

A: Use the following formulae, to estimate the definite integral ∫abfxdx by the Romberg integration…

Q: if was t:i CR) Linear icdentifier Conversionasfollows PEXJEPICR) Forevery TEPX)=P() grand…

A: We have to find (1) KerT and (2) ImT

Q: A dealer wishes to purchase a number of fans and sewing machines. He has only 5760 ETB to invest and…

A: The profit on Fan is ETB 22 and the profit on Sewing machine is ETB 18 Let the number of fan is ETB…

Q: II. Consider the function g defined by 1 g(x, y) = cos (TLV) + logg(r – y)" Do as indicated. g 1.…

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Q: Find a codomain B such that ƒ: A → B, ƒ(x) = e²´ is surjective. Show that g: B → A, g(x) = Vln x is…

A: As you asked only subpart (C) and (D) So, I answered here only subpart (C) and (D).

Q: The rate of cooling a metal ball can be expressed as dT 3D - k(Т — Та) dt Where T= temperature of…

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Q: ixi + (2 – i)r2 = 4 – 3i (1+ i)x1 – 12 =-3 - i

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Q: A.3 Direction: Let p be "She is not beautiful" and let q be "She is not intelligent." Write…

A: p : she is not beautiful  q : she is not intelligent

Q: Clarify that f :R → R defined by f (x)= 1 is uniformly continuous. 1+x?

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Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Solution:-

Q: Suppose z is a function of a and y, and tan y² + x² = z*e®%. Solve for az az and

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Q: Give the adjacency matrix of the graph below.

A: The entries of the matrix are the number of edges from a vertex to another vertex.

Q: az dz Suppose z is a function of r and y, and tan vy? +x2 3D "e6y. Solve for and

A: If x, y, z are related with the equation  fx,y,z=0then ∂z∂x=-∂f∂x∂f∂zand ∂z∂x=-∂f∂y∂f∂z

Q: [C] Use Newton-Raphson Method to perform thirteen iterations to the equation sin(x) + a? – e + 8 = 0…

A: Find the root of the given equation :-

Q: Determine the cube root of (3 + j4). ound-off the modulus to 3 decimal places, the angle to the…

A: Cube root of (3+4j)

Q: 48. Let f be a function defined on ]0, 1[ by : 0, if x is irrațional f (x) = {1/q, if x=p/q; where p…

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Q: Student Name : Compute the work done by the force along the curve (use defini- tion): F = [3r - y 12…

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Q: 6. Find the rank correlation for the following data: 56 42 72 36 63 47 55 49 38 42 68 60 y 147 125…

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Q: Use Lagrange Multipliers to solve the following: Maximize f(r, Y, z) = 4.x + 2y + z subject to a? +y…

A: Solution

Q: 6. y" + 3y'-2y e-2* [(4+20.x) cos 3x+ (26-32x) sin 3x]

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Q: x - 2 and ao = 0, bo For f(x) Apply the bisection method and calculate bz (right endpoint after 2…

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Q: Let V R°, the vector space over R of dimension 3. (a) Give an example of a subspace of V. (b) Write…

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Q: 1. Six line integrals in no particular order. (a) Evaluate fF dĩ where: F(r, y, 2) = (y²z", 2ryz",…

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Q: Find the Fourier series of the functionf on the given interval. Give the number to which the Fourier…

A: Fourier series of a function f(x) defined in -π,π is given by fx=a02+∑n=1∞an cosnx+∑n=1∞bn sinnxhere…