Q3 6 Points Let F be the vector field represented in the figure: P(-1,1) toyIX Q3.1...
6 Points Let F be the vector field represented in the figure: P(-1,1) 1907/1X X Q3.1 3 Points O2d-Curl F(0,0) > 0 O2d-Curl F(0,0) = 0 O2d-Curl F(0,0) < 0 Q3.2 3 Points OV.F(0,0) > 0 OV.F(0,0) = 0 OV.F(0,0) < 0
Let F be the vector field represented in the figure: y X 1Q0Y, 1X P(-1, 1) X Q3.1 3 Points 2d-Curl F(0,0) > 0 O 2d-Curl F(0,0) = 0 2d-Curl F(0,0) < 0 Q3.2 3 Points OV: F(0,0) > 0 OV: F(0,0) = 0 OV: F(0,0) < 0
4. Stoke's Theorem: Consider a vector field F = (1,1)+(1,0) + (0,0). tyle +rin the unit square bordered by (0,0) + (0,1) ► (a) What is the curl of the vector field F? [2 points) (b) What is the path integral of the vector field around the unit square? [5 points) (c) Show your answers to the previous parts are consistent with Stoke's Theorem. HINT: consider the right-hand rule. (3 points]
Let F = (P,Q) be the vector field defined by P(x,y) ity, (1, y) = (0,0) 10, (x,y) = (0,0) Q(x, y) = -Ity. (x, y) = (0,0) 10, (x, y) = (0,0). (a) (3 points) Show that F is a gradient vector field in RP \ {y = 0}. (b) (4 points) Letting D = {2:2020 + y2020 < 1}, compute the line integral Sap P dx +Qdy in the counter-clockwise direction. (c) (1 point) Does your calculation in...
Q3 Grinding Distributions 10 Points Let the joint probability density function of X and Y be fxy(x,y) (24ry, r,y> 0 and 0 < x+y<1 otherwise Q3.1 1 Point What is P[X >0.75 Y > 0.5]? Enter your answer here I have entered my answer as specified in the Vitamin Policy at the beginning of this Vitamin. Save Answer Q3.2 2 Points Are X and Y independent? O No Yes Save Answer Q3.3 2 Points Are X and Y identically distributed?...
6. Let f be a scalar function and F be a vector field. Label each quantity as a Scalar, Vector or Nonsense. Scalar Vector Nonsense Scalar Vector Nonsense curl F div F curl(curl F) div(curl F) Vf DO000 DDDDD D0000 V:(V F) VF div(div F) div(curl VF) curl (div F) 00000 DDDDD 00000
5. Let F (y”, 2xy + €35, 3yes-). Find the curl V F. Is the vector field F conservative? If so, find a potential function, and use the Fundamental Theorem of Line Integrals (FTLI) to evaluate the vector line integral ScF. dr along any path from (0,0,0) to (1,1,1). 6. Compute the Curl x F = Q. - P, of the vector field F = (x4, xy), and use Green's theorem to evaluate the circulation (flow, work) $ex* dx +...
3.4 Only please! Q3 Grinding Distributions 10 Points Let the joint probability density function of X and Y be fxy(x,y) (24ry, r,y> 0 and 0 < x+y<1 otherwise Q3.1 1 Point What is P[X >0.75 Y > 0.5]? Enter your answer here I have entered my answer as specified in the Vitamin Policy at the beginning of this Vitamin. Save Answer Q3.2 2 Points Are X and Y independent? O No Yes Save Answer Q3.3 2 Points Are X and...
Let F = (P,Q) be the vector field defined by -x+y . P(x,y) = 22, (x, y) + (0,0) 0, (x, y) = (0,0) Q(x,y) = (x, y) + (0,0) x2+y2; 10,(x, y) = (0,0). (a) Show that F is a gradient vector field in R2 \ {y = 0}. (b) Letting D = {2:2020 + y2020 < 1}, compute the line integral Sap P dx + Q dy in the counter-clockwise direction. (c) Does your calculation in part (b)...
Q3 14 Points Consider the vector space P2(R). Let T1, T2, T3 be 3 distinct real numbers and 21, 22, az be three strictly positive real numbers. Define (p(x), q(x)) = Li_1 Qip(ri)q(ri) Q3.1 5 Points Show that this P2 (R) together with (-:-) is an inner product space. Please select file(s) Select file(s) Save Answer Q3.2 2 Points Give a counter example that (-, - ) is not an inner product when T1, 12, 13 are still distinct real...