Question 8 (20 points) Parts (a) and (b) are distinct from e…
Question 8 (20 points) Parts (a) and (b) are distinct from each other. State any theorems or formulas used. (a) Use Stokes’ Theorem to evaluate \(\displaystyle \int_C \vec{F} \cdot d\vec{r}\), where \(\vec{F}(x,y,z)= \langle z^2, y^2, xy \rangle\) and \(C\) is the triangle with vertices (1,0,0), (0,1,0) and (0,0,2) oriented counterclockwise as viewed from above. (b) Let \(\vec{F}(x,y,z)=\langle x^3+e^{y^2+z^2}, \,2xz^2, \, 3y^2z \rangle\) be a vector field on \(\mathbb{R^3}\), \(E\) be the part of the solid bounded above by the paraboloid \(z=4-x^2-y^2\) and below by the xy-plane , and \(S\) be the boundary of \(E\) oriented outward. Using the Divergence Theorem find the total flux, \(\displaystyle \iint_S \vec{F} \cdot d\vec{S}\), of \(\vec{F}\) through \(S\).
Read DetailsDo you believe that the Federal Reserve has too much influen…
Do you believe that the Federal Reserve has too much influence on monetary policy, not enough influence on monetary policy, or just the right amount of influence on foreign policy? Your answer should be at least 150 words and should be your original work.
Read DetailsPick one: What influence did John Locke have on the drafting…
Pick one: What influence did John Locke have on the drafting of the US Constitution? orWhat influence did the Articles of Confederation have on the drafting of the US Constitution?Your answer should be at least 150 words and should be your original work.
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