#4: ConsiderSSC(V x F).ndSwhereF = 9x²¹²₁ + 8e²²³₁+ ln(+5)xos, kand S is the top half (20) of the ellipsoid 16x² + 16y² +21=² = a².By Stoke's Theorem, this is equivalent to2TT[p(a) sin 0+q(a) cos 0] deEnter the functions p(a) and q(a) (in that order) into the answer box below, separated with a comma. Yourexpressions should involve a, integers, fractions and exp() only.

For F and ellipsoid S we have to find p(a) and q(a).

Answered: #4: Consider SSC (V x F).ndS where F =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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An environmental engineer wants to evaluate three different methods for disposing of nonhazardous chemical waste: land application, fluidized-bed incineration, and private disposal contract. Use the estimates below to help her determine which has the least cost at /= 15.00% per year on the basis of an annual worth evaluation. First Cost AOC per Year Salvage Value Life Land $-145000 $-86000 $23000 4 years Incineration $-760000 $-70000 $260000 6 years Contract O $-132000 O 2 years
Express the circle specified by x = 2 cos(0) y = 1 + 2 sin(0) in Cartesian coordinates and find the point where 0 = r/3. a. (x – 0)? + (y – 1)? = 22, (1, 1 + V3) b. (x – 0)2 + (y – 1)? = 2, (1, 1 – V3) %3D c. (x – 0)? + (y – 1)? = 2, (1, 1 + V3) d. (x – 0)? + (y – 1)? = 4, (1 + V3, 1)
Compute the surface area of the surface generated by revolving the astroid with the parametrization c(t) (9 cos (t), 9 sin (t) about the x-axis for 0 <1 < 5. (Use symbolic notation and fractions where needed.) S =
(a) Consider the change of variable from cartesian coordinates (x, y, z) to coordi- nates (r, y, 0) in R². x = exp(r) cos y cos 0, y = exp(r) sin 0, We will assume that y = [0, 2π) and 0 € [-π/2, π/2]. (i) Show that exp(r) = √x² + y² + z². (ii) Compute the Jacobian of this transformation. I.e. find the determinant of the matrix 'дх др ах ах до до ду z = exp(r) sin cos 0. до до əz əz əz др др до до (iii) For y € (0, π) and 0 € (−π/2, π/2), express r, 4 and 0 in terms of x, y and z. (b) Consider a box with square base and no lid which has width x > 0 and height h> 0. It has area a(x, h) = x² + 4hx and volume v(x, h) = hx². (i) What is the maximum volume of such a box when it has fixed area A? (ii) Is it also possible to minimise the volume of the box, keeping the area fixed? Explain your answer.
1. (a) Consider the equation e'ux+2ayuy +2eu,- sin(y) u =0, where a is a real constant. Determine the value(s) of a when this equation is elliptic everywhere in the xy-plane, in which case find the canonical variables and reduce the equation to its canonical form. (b) Find the solution of Laplace's equation outside a unit circle a?u 1 du 0, (r>1,0<0 < 2x), zee e subject to the boundary condition u(1,0) = 2 sin 30, having in mind the requirements that the solution must satisfy in an unbounded domain.
Q.No 05: Find the expressions for the spherical harmonics Y30 (0, 9) and Y3,+1(0, 9), Y30 (0, 9) = /7/16x (5 cos³ 0 – 3 cos 0), Y3,41 (0, 9) = F/21/64x sin 0(5 cos 0-1)e*io, in terms of the Cartesian coordinates x, y,z.
Let F = (x'e* +2xy – 2 y)i+(cos y +x² +3x) j and let C be the ellipse with equation (2x – 2 y)² + (x+ y)² = 9 . Find the work (circulation) associated with F along the curve C traversed counterclockwise. [Hint: You may have to invoke two important theorems to complete this problem.]
Bracket Manufacturing uses a Kanban system for a component. Daily demand is 1,100 units. Each container has a combined waiting and processing time of 0.65 days. If the container size is 100 and the alpha value (a) is 12%, how many Kanban card sets should be authorized? Round your answer up to the whole number. Kanban card set(s) What is the maximum authorized inventory? Use the rounded value from the previous question. Round your answer to the nearest whole number. unit(s)
A particle moves such that its velocity at time t is given by: v = 3t2i + 2 cos(4t)j + t2k If its position x at time t = 0 is given by x(0) = 2i what is the position of the particle at time t? The position is...

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