Problem 3: Consider the functional: I = /1+yr2 dx. y a) Find the Euler-Lagrange equation, which minimizes that functional. b) Solve the Euler-Lagrange and show that the curve is a circle. c) Find the radius and the center of the circle.

Q: is not an endpoint of any of the intervals (e) Prove that eC but in any of the sets A (k e N),

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Q: Q1-Find S sin 3x e4* dx

A: let I=∫sin3x e4xdx using by parts I=e4x∫sin3x-∫ddxe4x∫sin3xdxdx simplify I=e4x∫sin3x-∫12e4xcos3xdx a...

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A: Introduction: The incenter of a triangle is the point at which the triangle's three interior angle b...

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Q: 1. Complete the following table by placing ticks (V) to show which of the number sets N, Z, Q, R the...

A: claim- to complete the table by placing tick to show that which of the number sets these number belo...

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A: Introduction: An equation of the form y=mx+c always represents a straight line. The slope of the lin...

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Q: V = \ + 855-t Prove that act) = 32

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Q: (g) –3x +4x-8=0 (h) 3x² +8x+4= 0

A: g Given equation is −3x2+4x−8=0. We have to determine the number and nature if the roots by first ca...

Q: Exercise 5.27 Find the Green functions on the following regions in R a) the semi-ball B(0, R) n {{z,...

A: We will use basic knowledge of functions and PDE to answer both the parts of this question.

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A: Given fx=sinx and h=1 and h=0.5

Q: 16. There is a very quick way to compute £-, 2'(-1)ª-' (); do use it. l=D0

A: Introduction: The binomial theorem is very important in mathematics. For any real numbers a,b with p...

Q: Directions: Solve the derivatives of the given functions, Encirele the correct anawer. You can also ...

A: According to our guidelines we can answer only three sub-parts and rest can be reposted. 

Q: into the ancient grounds of the Acropolis, 3D XYZ left this not. Z stole stone oolumns from the Part...

A: Introduction: The formula of a right triangular prism is given by, V=12bhl The formula of a cylinder...

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Q: Let R be the relation on the set of ordered pairs of positive integers such that  ((?, ?), (?, ?)) ∈...

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Q: Write the inequality of the graph below. Use a forward slash (i.e. "/") for all fractions (e.q. 1/2 ...

A: First identify the line in the graph. The line passes through the points 0,-2 and 5,4.

Q: esent value of the income c (in dollars) over t1 years at the given annual inflation rate r. (Round ...

A: Introduction: The formula for the present value of the cost function is given by, Present value=∫t0t...

Q: Write -4 -3i in polar form A) 5 38.87° B) 5 <216.87° 51 323.13° D 51 <143.13°

A: The given problem is to convert the given complex expression in rectangular form to polar form. Give...

Q: -1, 4, -2 >. Find ( A) 0.BO

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Q: 1 2 *) Let ū : and i Find a vector w not in span {u, i}. 10 || 13

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Q: Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 4x – 2y subject to the ...

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Q: Let ( A) D = and BD= . Find the angle between BD and A D* O [cos] 2/N(30(21)) O [cos] (-1) 2/(30(21...

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Q: Find y as a function of t if 5184y" – 1584y + 121y = 0, - y(0) = 6, y'(0) = 3. y =

A: We have to find the general solution of the given problem.

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2) abo...

A: Solution

Q: Find y as a function of t if y" + y' – 2y = 0, y(0) = 8, y(1) = 8. y(t) = Remark: The initial condit...

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Q: 1. Consider the following system of linear equations: T1 + kr2 = 2 kri + x2 + 13 =1 X1+ x2 + x3 =k F...

A: Here the given matrices are                                      A=abcd and B=dcba We have to show t...

Q: Determine whether or not the relation R on the set of all people is reflexive,  symmetric, antisymme...

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Q: Newjet, Inc. manufactures Inkjet printers and laser printers. and 3 hours

A: Given, Newjet, Inc. manufactures inkjet printers and laser printers. The company has the capacity to...

Q: Four coins are tossed. Let Y be the random variable representing the number of tails that occur. fin...

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Q: a. Graph the domain of the function, and the z = 0,1,2 level curves. b. Find all the partial second ...

A: This is a problem of multi variable calculus.

Q: Consider the relation ? = {(a, b), (a, d), (b, a), (c, d)} on the set {a, b, c, d}.  a.  Find the re...

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Q: Use the exponential equation below to answer part A, part B, in part c 35^x=8 Part A: explain the ...

A: Let us consider the equation ax=b Taking logarithmic on both sides  Using the property of logarithm...

Q: Find y as a function of t if y" + 8y' + 41y = 0, y(0) = 2, y' (0) = 8. y = Note: This problem cannot...

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Q: The monthly rent for the first house is S1, 190, and the Bainters can expect it to increase 1.7% eve...

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Q: (x, y, Z) = è + xlny + ylnx find fz fx fxx fy 5) fxy Fyx

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Q: Consider the axiomatic system below with cat, scratch, and pole as undefined terms. Any two cats scr...

A: Let us solve the given problem in the next steps.

Q: y borrows $79,500 for

A: Introduction: The formula of the simple interest rate is given by, S.I.=P×R×T100 Where P is the prin...

Q: 2. Find a 3 x 4 matrix R for which the null space of R is spanned by the vectors -- -E 0. v = u = Hi...

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Q: A system of equations for the variables x, y and z reduces to following matrix: 1 2 1 5 0 1 -2 7 0 0...

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Q: rs. Wha

A: Formula used, where, P(t)=Population at time t Po=Initial Population k=Growth rate t=time e=Euler's...

Q: Evaluate the following integrat«

A: Given,               ∫cos4xdx

Q: 1. Which one of the following facts supports the formula for the circumference of a circle? A. The d...

A: We will use basic knowledge of geometry and arithmetic to answer this question.

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Q: - cos²(x) + cos²) cos²G) .2 cos³ (x) . dx 3

A: let I=∫cos2x+cos2x2cos3xdx this can be written as  I=∫cos2xcos3xdx+∫cos2x2cos3xdx =∫1cosxdx+∫cos2x2c...