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Let P = (Px, Py) be the point on the unit circle (given by x2+y2=1) in...
1. Consider the unit circle: (x,y) : x2 y2 = 1. T. Let f R2 ->R be defined by f(x,y) = x2-y, and let F : R2 -> R be defined by F(x, y) Compute the integral of f and F around the unit circle. For the integral of F, proceed in the standard (anticlockwise) direction
let: y=14+2x1+x2-0.12x1-0.08x2+0.12x1x2 given: Py= $5/unit Px1=$1/unit Px2=$2/unit Fixed cost= $200 find a. the amount of (x1) and (x2) that maximizes profit b. the amount of (y) at maximum profits c. the amount of profit d. the maximum amount of (y) that can be produced
A) Find fY1 and show that the area under this is one B) Find P(Y1 > 1/2) Let (Y1, Y2) denote the coordinates of a point chosen at random inside a unit circle whose center is at the origin. That is, Y1 and Y2 have a joint density function given by 1 yiy f(y, y2) 0, - elsewhere Let (Y1, Y2) denote the coordinates of a point chosen at random inside a unit circle whose center is at the origin....
(1 point) (a) Show that each of the vector fields F-4yi + 4x j, G-i ЗУ x2+y2 x?+yi J, and j are gradient vector fields on some domain (not necessarily the whole plane) x2+y2 by finding a potential function for each. For F, a potential function is f(x, y) - For G, a potential function is g(x, y) - For H, a potential function is h(x, y) (b) Find the line integrals of F, G, H around the curve C...
1.2 (10 mks each). In parts a) and b) below, assume px = $1, py = $5, I = income = $21. Solve the U-max problem for each of the following two utility functions: (a) U = xy?, x, y = 0; (b) U=x1/3y2/3, x, y 2 0; (c) now, let px = p, Py = $5, 1 = $21, find the u-max solution for U = xy?, x, y = 0; (d) let px = 1, Py = p,...
F(x,y) =<2xy,x^2+y^2> the part of the unit circle in the first quadrant oriented counter clockwise 37. F(x, y) = (2.xy, x2+y2), quadrant oriented counterclockwise the part of the unit circle in the first 37. F(x, y) = (2.xy, x2+y2), quadrant oriented counterclockwise the part of the unit circle in the first
Let MM be the capped cylindrical surface which is the union of two surfaces, a cylinder given by x2+y2=81, 0≤z≤1x2+y2=81, 0≤z≤1, and a hemispherical cap defined by x2+y2+(z−1)2=81, z≥1x2+y2+(z−1)2=81, z≥1. For the vector field F=(zx+z2y+4y, z3yx+4x, z4x2)F=(zx+z2y+4y, z3yx+4x, z4x2), compute ∬M(∇×F)⋅dS∬M(∇×F)⋅dS in any way you like (1 point) Let M be the capped cylindrical surface which is the union of two surfaces, a cylinder given by X2 + y2-81, 0 < ž < 1, and a hemispherical cap defined by...
(a) 1.2 (10 mks each). In parts a) and b) below, assume px = $1, Py = $5, I = income = $21. Solve the U-max problem for each of the following two utility functions: U= xy?, x, y 2 0; (b) U = x1/3y2/3, x, y = 0; now, let px = P, Py = $5, I = $21, find the u-max solution for U = xy?, x, y 2 0; let px = 1, Py =p, I =...
12 1. (2 points) The point P(x, y) is on the unit circle in Quadrant IV with x = 19 Find the value for y. 57 2. (2 points) Find the terminal point P(x, y) on the unit circle with t 3
s2, and (1 point) Let p be the joint density function such that px, y)- n R, the rectangle O s xs4,0 sy p(x,y0 outside R. Find the fraction of the population satisfying the constraint x 2 y fraction-