Webb(a) The plane y + z = 3 intersects the cylinder x 2 +y 2 = 5 in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1.2, 1). (b) Graph the cylinder, the plane, and the tangent line on the same screen. WebbThe plane 4x-3y+8z=5 intersects the cone z^2=x^2+y^2 in an ellipse. Graph the cone, the plane, and the ellipse. Use Lagrange multipliers to prove that the triangle with maximum …
Solved The plane 4x - 3y + 8z = 5 intersects the cone z^2
Webbdownward orientation at the upper tip of the ellipse (0;0;5), thus we pick the negative sign. The scalar area element is dS= jdS~j= 1 4 p 3z2 + 18z 11r2drd and therefore the surface area is just the integral of this over the parameterization, A(S) = Z Z S 1dS= Z 2ˇ 0 Z 5 1 1 4 p 3z2 + 18z 11 dzd = 2ˇ 1 4 Z 5 1 q 16 3(z 3)2dz: Now do the ... Webb17 jan. 2016 · 06.(11%) The plane 4x - 3y - z = 5 intersects the cone x^2 + y^2 = z^2 in an ellipse. Find the highest and the lowest points on the ellipse. -- 這題是否有誤？實際上該平面無法與橢球體交出橢圓，而僅能交出雙 曲線。 greenwoods fresh catch
Name: SOLUTIONS Date: 10/06/2016
Webb3.Find a point on the surface z= x2 y3 where the tangent plane is parallel to the plane x+ 3y+ z= 0. Solution: First, rewrite z= x2 y3 into the level surface F(x;y;z) = z x2 +y3 = ... On this boundary, we have y2 = 16 4x2 and 2 x 2. So, we get z = Name: SOLUTIONS Date: 10/06/2016 4x2 2(16 4x) + 1 = 8x2 15 for 2 x 2. The critical number here ... Webb> The plane 4x - 3y + 8z = 5 intersects the cone z2 = x2 + y2 in an ellipse. (a). Graph the cone and the plane, and observe the elliptical intersection. (b). Use Lagrange multipliers to find the highest and lowest points on the ellipse. > A lamina occupies the part of the disk x2 + y2 < 1 in the first quadrant. WebbThe plane 4x – 3y + 8z = 5 intersects the cone z 2 = x 2 + y 2 in an ellipse. (a) Graph the cone and the plane, and observe the elliptical intersection. (b) Use Lagrange multipliers … foam roofing icc number