Answer each of the following question about the given the 3-dimensional surfaces x + y² +22...
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...
1. 2. Which vector function represents the curve of intersection of the surfaces x = y2 and y² + x2 25 ? = Find a vector that is parallel to both of the planes 2 – y + 2z = 2 and x + y + 3z = 13.
Consider the following. z = x2 + y2, z = 36 − y, (6, -1, 37) (a) Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the given point. x − 6 12 = y + 1 −2 = z − 37 −1 x − 6 1 = y + 1 12 = z − 37 −12 x − 6 = y + 1 = z − 37 x − 6 12 =...
1) Consider the surface x2 + 3y2-2z2-1 (a) What are the cross sections(traces) in x k,y k, z k Sketch for (b) Sketch the surface in space. 2) Draw the quadric surface whose equation is described by z2 +y2 - 221 (a) What are the cross sections(traces) inx-k,y k,z k Sketch for (b) Sketch the surface in space. a) Sketch the region bounded by the paraboloids z-22 + y2 and z - 3) 2 b) Draw the xy, xz, yz...
The surfaces z = x/y and z = x*y intersect each other at a space curve. The space curve is passing through a point (1, 1, 1). Define the tangent vector of the shear curve at this point (1,1,1). %3D
The graphs of the surfaces z=(x²+y²)² and z=3-2 x²-2 y² intersect in 3D-Space. Find an equation for the projection of this intersection in the x y-plane.
Question 3 3 pts Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The cone z = V x2 + y2 and the plane z =6+y 12 1 12 a. r= 1 (61,42 – 36,42 +36) b. 1) = 1 (12t,t2 + 36,42 +36) +(12t,– 12,42 +12) ${12t,t2 – 36,2 +36) P(8) = 1 / 2 C. d. (6) 2 1
Suppose a point in three-dimensional Cartesian space, (X, Y, Z) , is equally likely to fall anywhere on the surface of the hemisphere defined by X2+y2+2 -1 and Z20. (a) Find the PDF of Z. zz) (b) Find the joint PDF of X and Y. JK.ужд) Suppose a point in three-dimensional Cartesian space, (X, Y, Z) , is equally likely to fall anywhere on the surface of the hemisphere defined by X2+y2+2 -1 and Z20. (a) Find the PDF of...
Let F(x, y, z) be the gradient vector field of f(x, y, z) = exyz , let C be the curve of the intersection of the plane y + z = 2 and the cylinder x2 + y2 = 1, oriented counterclockwise, evaluate Sc F. dr. OT O -TT O None of the above. 00
3. Find the points of intersection of the pairs of curves a. y = x² +3; y = 3x +1 b. 2x² +2 y2 = 5; xy = 1 4. Identify and sketch the curve represented by the given equation. x? - + y2 = 1 a. 4 (y+1) 4 b. (x - 1)? + 4 c. x² - y2 =-1