THREE submissions are allowed for each question part, except for True/False and
ID: 2862867 • Letter: T
Question
THREE submissions are allowed for each question part, except for True/False and 2-option multiple-choice questions. For these types of problems, only ONE submission is allowed Exact answers are required unless the question specifically asks for a rounded answer. The types of questions that require rounded answers display the StgFig icon beside the answer box Half credit will be given on these types of problems only, for answers that are numerically correct but do not have the correct number of significant digits. If a problem requires an exact answer, an approximated (rounded) answer will not be accepted The MathPad or Calc Pad tool that pops up will assist you on questions that require a correctly formatted mathematical expression (le. expressions involving squareroots. Euler's number, greek symbols, trig functions, etc Note that variables (letters and symbols) are case sensitive. The message, "Your answer cannot be understood or graded" will appear when a syntax error (le. missing operands, incorrect grouping operators, misspelled units, symbols with no meaning in response) has been made You will not lose submissions for syntax errors Please see the topic, Answering Math and Science Questions, under the Web Assign Student Help System for detailed information and examples. Let F(x, y, z) = z tan^-1(y^2)i + z^2 ln(x^2 + 1)j + zk. Find the flux of F across S, the part of the paraboloid x^2 + y^2 + z = 12 that lies above the plane z = 4 and is oriented upward integral integral_S F dS =Explanation / Answer
Let S = the surface of the paraboloid as specified.
Surface int_S F dot dS
= triple int div F dV
dot F = 0+0+1=1
Thus, triple int div F dV
= triple int dV
= triple int rdrdtdz, r=0 to rt(29-z), t=0 to 2pi, z=4 to 29
= double int [(1/2) r^2, r=0 to rt(29-z)] dtdz
= double int (1/2)(29-z) dtdz
= int pi(29-z) dz
= pi[29z - (1/2)z^2], z=4 to 29
= pi(841-841/2-116-+16/2)
= 625 pi / 2
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