For this assignment, you submit answers by quesion parts. The nun submissions re

Question

For this assignment, you submit answers by quesion parts. The nun submissions remaining for each question part only changes if you s change the answer Your best submission for each question part is used for your score. only ONE submission is allowed. Exact answers are required uniess the question specitcally asks for a rounded answer. The types of questions hat require rounded answers display the SigFig icon beside the answer box Haif credit will be given on these types of problems only, for answers frounded) answer wil not be accepted. The MathPad or CakcPad tool that pops up will assist you on symbols) are case sensitive. The message,"Yolr answer cannot be understood or graded" wll appear when a syntax emor e missing operands, errors. Please see the topic, Answering Math and Science Questions, under the WebAssign Student Hep System tor detailed intormation and cormect but do not have the correct number of significant digts. If a probiem requires an exadt answer, an approximated hat require a correctly formatted involving roots, Euler's number, greek symbols, trig functions, etc.).Note that variabies (eters and for syntax Evaluate the surface integralF ds for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) F(x, y, z) = yi + (z-y)1+xk S is the surface of the tetrahedron with vertices (o, 0, 0), (2, o, o), (o, 2, 0), and (0, o, 2) 0 ALIENWARE

Explanation / Answer

Note that S has equation x + y + z = 2 (in the first octant).
==> z = 2 - x - y.

So, s F · dS
= <y, z-y, z> · <-z_x, -z_y, 1> dA
= <y, z-y, z> · <1, 1, 1> dA
= 2z dA
= (x = 0 to 2) (y = 0 to 2 - x) 2(2 - x - y) dy dx
= (x = 0 to 2) [2y(2 - x) - y^2] {for y = 0 to 2 - x} dx
= (x = 0 to 2) (2 - x)^2 dx
= -(2 - x)^3/3 {for x = 0 to 2}
= -8 /3.

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