asked 2021-09-25

Find an equation of the plane.

The plane through the points (4, 1, 4), (5, -8, 6), and (-4, -5, 1)

The plane through the points (4, 1, 4), (5, -8, 6), and (-4, -5, 1)

asked 2021-08-30

asked 2021-06-03

Find an equation of the plane.

The plane through the points (2,1,2), (3,-8,6), and (-2,-3,1)

The plane through the points (2,1,2), (3,-8,6), and (-2,-3,1)

asked 2021-05-13

Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1)

asked 2021-06-08

\(4x + 3y + z = 12\)

that lies in the first octant.

2) Use polar coordinates to find the volume of the given solid.

Bounded by the paraboloid \(z = 5 + 2x^2 + 2y^2\) and the plane z = 11 in the first octant

asked 2021-06-09

Change from rectangular to cylindrical coordinates. (Let \(r\geq0\) and \(0\leq\theta\leq2\pi\).)

a) \((-2, 2, 2)\)

b) \((-9,9\sqrt{3,6})\)

c) Use cylindrical coordinates.

Evaluate

\(\int\int\int_{E}xdV\)

where E is enclosed by the planes \(z=0\) and

\(z=x+y+10\)

and by the cylinders

\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)

d) Use cylindrical coordinates.

Find the volume of the solid that is enclosed by the cone

\(z=\sqrt{x^{2}+y^{2}}\)

and the sphere

\(x^{2}+y^{2}+z^{2}=8\).

a) \((-2, 2, 2)\)

b) \((-9,9\sqrt{3,6})\)

c) Use cylindrical coordinates.

Evaluate

\(\int\int\int_{E}xdV\)

where E is enclosed by the planes \(z=0\) and

\(z=x+y+10\)

and by the cylinders

\(x^{2}+y^{2}=16\) and \(x^{2}+y^{2}=36\)

d) Use cylindrical coordinates.

Find the volume of the solid that is enclosed by the cone

\(z=\sqrt{x^{2}+y^{2}}\)

and the sphere

\(x^{2}+y^{2}+z^{2}=8\).

asked 2021-09-06

Find a parametric vector equation for the given plane: