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Problem 3 i) Let D be the polygon in R2 with vertices, in a counter-clockwise order, given by (zı, y), (x2,U2), , (Tm%)...
Problem 3 i) Let D be the polygon in R2 with vertices, in a counter-clockwise order, given by (zı, y), (x2,U2), , (Tm%). Use Green's Theorem to shows that the area of D is given by the formula ny...
Problem 3 i) Let D be the polygon in R2 with vertices, in a counter-clockwise order, given by (zı, y), (x2,U2), , (Tm%). Use Green's Theorem to shows that the area of D is given by the formula nyn-1 7 marks (i) Using the formula from (i) to derive the area of triangle with a base of width w 1 and a height of h 3 marks]
Problem 3 i) Let D be the polygon in R2 with vertices, in...
Let A be the inside and boundary of the triangle in R2 whose vertices are (0,0), (1,0) and (0,1). Let C be the curve obtained by proceeding around the boundary of A in an anti- clockwise direction. P...
Let A be the inside and boundary of the triangle in R2 whose vertices are (0,0), (1,0) and (0,1). Let C be the curve obtained by proceeding around the boundary of A in an anti- clockwise direction. Prove İ}!").lx (ly İ)(2 dr dy. Pdr+Qdy That is, prove Green's Theorem for the triangle A. [Hint: the lecture notes have a proof for when A is a rectangle. So, the idea is is to give a similar proof where we have this...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
i need help with number 3&4 and the answer is in red i just need to know how to work the problem (a) y (b) y=-x3 + 6x2-9x + 3 2. The sum of two nonnegative numbers is 36 (a) Find the two numbe...
i need help with number 3&4 and the answer is in red i
just need to know how to work the problem
(a) y (b) y=-x3 + 6x2-9x + 3 2. The sum of two nonnegative numbers is 36 (a) Find the two numbers if the differ ence of their square roots is to be as large as possible. 0 and 36 (b) Find the two numbers if the sum of their square roots is to be as large as...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
Problem 3 i) Let D be the polygon in R2 with vertices, in a counter-clockwise order, given by (zı, y), (x2,U2), , (Tm%). Use Green's Theorem to shows that the area of D is given by the formula nyn-1 7 marks (i) Using the formula from (i) to derive the area of triangle with a base of width w 1 and a height of h 3 marks]
Problem 3 i) Let D be the polygon in R2 with vertices, in...
Let A be the inside and boundary of the triangle in R2 whose vertices are (0,0), (1,0) and (0,1). Let C be the curve obtained by proceeding around the boundary of A in an anti- clockwise direction. Prove İ}!").lx (ly İ)(2 dr dy. Pdr+Qdy That is, prove Green's Theorem for the triangle A. [Hint: the lecture notes have a proof for when A is a rectangle. So, the idea is is to give a similar proof where we have this...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
i need help with number 3&4 and the answer is in red i
just need to know how to work the problem
(a) y (b) y=-x3 + 6x2-9x + 3 2. The sum of two nonnegative numbers is 36 (a) Find the two numbers if the differ ence of their square roots is to be as large as possible. 0 and 36 (b) Find the two numbers if the sum of their square roots is to be as large as...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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