Evaluate the surface integral fof the scalar feld 1-62+4 where S is the surface parametrised by (u, r) - (u con, usin n, w) with 0
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- Find the surface area of the "Coolio McSchoolio" surface shown below using the formula: SA = integral, integral D, ||ru * rv||dA %3D The parameterization of the surface is: r(u,v) = vector brackets (uv, u + v, u - v) where u^2 + v^2 <= 1 A.) (pi/3)(6squareroot(6) - 8) B.) (pi/3)(6squareroot(6) - 2squareroot(2)) C.) (pi/6)(2squareroot(3) - squareroot(2)) D.) (pi/6)(squareroot(6) - squareroot(2)) E.) (5pi/6)(6 - squareroot(2))Sketch or describe the surfaces in R³ determined by the equa- tions in Exercises 40–46. z = y² +2'99 '37 37 XCOS Z Evaluate dzdydx. and the sphere
- let G be the part of the sphere x^2 + y^2 +z^2 = 9 that lies below the plane z=1 oriented with outward facing normal vectors. Let F(x,y,z) =<x,y,z>. find the flux of del x F through G clearly state theorems usedEvaluate the surface integral. (x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u - v, z = 1 + 2u + v, 0Find F dr where C is a circe of radius 2 in the plane z+y+z= 9, centered at (2, 2, 5) and ariented clockwise when viewed from the origin, F- 2yi2rj + 3(y 2)kA trace of the surface + - z = 0 on the xy- plane is: O Point at (3, 2, O) O Circle Ellipse Point at (0, 0, 0)Given F=yi-zj+0k and parametric surface (u,v) = ui + v²j+(u-v) for 0A and B can do a piece of work in 12 days; B and C can do it in 15 days while C and A can finish it in 20 days. In how many days will A,B,C finish it, working togeteher? In hpw many days will each one of them finish it, working alone?Question 16 Suppose that you have downloaded data on the daily share prices for a company for the period from the start of 2020 to the end of 2020 from the website of Yahoo Finance UK. You have also calculated the daily rates of return for the company's shares as (closing price - opening price)/opening price. By using the knowledge that you have gained from descriptive statistics, how can you obtain useful information about the company's share performance in terms of risk and return using a range of alternative indicators? Note that you should give necessary formulas for the technical concepts wherever they may apply.Let S be the surface parametrized by R(u, v) = (2u sin v, 2u cos v, -v), where 0 ≤ u ≤ 2 and 0 ≤ ≤. Evaluate f4yz² do. SFind a parametrization of the line in which the planes x-2y • 22 = 2 and - 3x + 3y - 3z = 0 intersect. Find the parametrization of the line. Use a point with z =0 on the line to determine the parametrization. x-.y=0z=D- 0Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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