Homework Answers
1 3. (10 points) Let S be the quadratic surface given by 22-2-y (a) Classify S...
1 3. (10 points) Let S be the quadratic surface given by 22-2-y (a) Classify S (B) S is a hyperboloid of one sheet (E) S is an (A) S is an (D) S is an (b) Find the equation of the tangent plane to S at the point (1,1, v3) (C) S is a hyperboloid of two sheets ellipsoid elliptic cone elliptic paraboloid point P(ro.Mo, 20) on S where the tangent plane to S at the point P contains...
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first oct...
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
2) (27 points) Let D be the region bounded from below by the plane : 0, from above by the plane z-2J3 and laterally by the hyperboloid of one sheet x2 + y2-1-24. a) (3 points) Draw the region...
2) (27 points) Let D be the region bounded from below by the plane : 0, from above by the plane z-2J3 and laterally by the hyperboloid of one sheet x2 + y2-1-24. a) (3 points) Draw the region D. b) (12 points) Set up triple integrals representing the volume of D in spherical coordinates according to the order of integration dp do de c) (12 points) Set up triple integrals representing the volume of D in cylindrical coordinates according...
Can someone help me understand part c, I'm not quire how to do it. The answer is (0,0, plus/minus root(10)) and I d...
Can someone help me understand part c, I'm not quire how to do
it. The answer is (0,0, plus/minus root(10)) and I don't know how
to get there.
3. (9 points) Let S be the quadratic surface given by 2y22 (a) Classify S 10 elliptic paraboloid (B) S is a hyperboloid of one sheet (A) S is an (C) S is a hyperboloid of two Answer (Letter): (D) S is an elliptic cone sheets (E) S is an ellipsoid (b)...
Consider the vector field F(x, y, z) = (z arctan(y2), 22 In(22 +1), 32) Let the...
Consider the vector field F(x, y, z) = (z arctan(y2), 22 In(22 +1), 32) Let the surface S be the part of the sphere x2 + y2 + x2 = 4 that lies above the plane 2=1 and be oriented downwards. (a) Find the divergence of F. (b) Compute the flux integral SS. F . ñ ds.
question #6 1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1...
question #6
1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
Let P = (Px, Py) be the point on the unit circle (given by x2+y2=1) in...
Let P = (Px, Py) be the point on the unit circle (given by x2+y2=1) in the first quadrant which maximizes the function f(x,y) = 4x+ y. Find Py?. Pick one of the choices O 1/5 O 1/9 O 1/13 O 1/17
22 + y2 with (1 point) The region W lies between the spheres x2 + y2...
22 + y2 with (1 point) The region W lies between the spheres x2 + y2 + z2 = 1 and 22 + y2 + x2 = 4 and within the cone z = z > 0; its boundary is the closed surface, S, oriented outward. Find the flux of F=ri+y +z3k Out of S. flux =
9. (a) Let P1(21, 91, zı), P2 (22, 42, z2),P3 (13, 93, 23) be three non-collinear...
9. (a) Let P1(21, 91, zı), P2 (22, 42, z2),P3 (13, 93, 23) be three non-collinear points in R, that is, three points which do not all lie on a straight line. Then the equations of the plane through these three points is: 2 y 21 1 = 0 22 Y2 22 1 2 1 2141 I3 Y3 23 1 Page 1 (b) Find the equation of the plane through P1(1,2,2), P2(1, 2, -1), P3(0,1,2)
3. Let E be the elliptic curve y2-x3+x 6 over ZI1 1) Find all points on E by calculating the quad...
3. Let E be the elliptic curve y2-x3+x 6 over ZI1 1) Find all points on E by calculating the quadratic residues like the one demonstrated in the lecture 2) What is the order of the group? [Do not forget the identity element 0] 3) Given a point P - (2, 7), what is 2P? [point doubling] 4) Given another point Q (3, 6), what is PQ? [point addition]
3. Let E be the elliptic curve y2-x3+x 6 over ZI1...
1 3. (10 points) Let S be the quadratic surface given by 22-2-y (a) Classify S (B) S is a hyperboloid of one sheet (E) S is an (A) S is an (D) S is an (b) Find the equation of the tangent plane to S at the point (1,1, v3) (C) S is a hyperboloid of two sheets ellipsoid elliptic cone elliptic paraboloid point P(ro.Mo, 20) on S where the tangent plane to S at the point P contains...
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
9. Find the parametric representation of each surface. a. The part of the hyperboloid 2 -xy-1 that lies above the rectangle [-2,2]*[-5,5]. b. The part of the sphere x2 +y2 +22-16 in the first octant that lies above the cone
2) (27 points) Let D be the region bounded from below by the plane : 0, from above by the plane z-2J3 and laterally by the hyperboloid of one sheet x2 + y2-1-24. a) (3 points) Draw the region D. b) (12 points) Set up triple integrals representing the volume of D in spherical coordinates according to the order of integration dp do de c) (12 points) Set up triple integrals representing the volume of D in cylindrical coordinates according...
Can someone help me understand part c, I'm not quire how to do
it. The answer is (0,0, plus/minus root(10)) and I don't know how
to get there.
3. (9 points) Let S be the quadratic surface given by 2y22 (a) Classify S 10 elliptic paraboloid (B) S is a hyperboloid of one sheet (A) S is an (C) S is a hyperboloid of two Answer (Letter): (D) S is an elliptic cone sheets (E) S is an ellipsoid (b)...
Consider the vector field F(x, y, z) = (z arctan(y2), 22 In(22 +1), 32) Let the surface S be the part of the sphere x2 + y2 + x2 = 4 that lies above the plane 2=1 and be oriented downwards. (a) Find the divergence of F. (b) Compute the flux integral SS. F . ñ ds.
question #6
1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
Let P = (Px, Py) be the point on the unit circle (given by x2+y2=1) in the first quadrant which maximizes the function f(x,y) = 4x+ y. Find Py?. Pick one of the choices O 1/5 O 1/9 O 1/13 O 1/17
22 + y2 with (1 point) The region W lies between the spheres x2 + y2 + z2 = 1 and 22 + y2 + x2 = 4 and within the cone z = z > 0; its boundary is the closed surface, S, oriented outward. Find the flux of F=ri+y +z3k Out of S. flux =
9. (a) Let P1(21, 91, zı), P2 (22, 42, z2),P3 (13, 93, 23) be three non-collinear points in R, that is, three points which do not all lie on a straight line. Then the equations of the plane through these three points is: 2 y 21 1 = 0 22 Y2 22 1 2 1 2141 I3 Y3 23 1 Page 1 (b) Find the equation of the plane through P1(1,2,2), P2(1, 2, -1), P3(0,1,2)
3. Let E be the elliptic curve y2-x3+x 6 over ZI1 1) Find all points on E by calculating the quadratic residues like the one demonstrated in the lecture 2) What is the order of the group? [Do not forget the identity element 0] 3) Given a point P - (2, 7), what is 2P? [point doubling] 4) Given another point Q (3, 6), what is PQ? [point addition]
3. Let E be the elliptic curve y2-x3+x 6 over ZI1...
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