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Cristiano Sears

Answered 2021-05-14
Author has **28671** answers

content_user

Answered 2021-09-29
Author has **11829** answers

Vertices are \(A(-3,0),\ B(-1,6),\ C(8,5)\) and \(D(6,-1)\)

So

\(\vec{AB}=<-1-(-3),6-0>=<2,6>\)

\(\vec{AD}=<6-(-3),-1-0>=<9,-1>\)

Hence area of parallelogram

\(=|\vec{AB}\times\vec{AD}|\)

\(\vec{AB}\times\vec{AD}=\begin{bmatrix}i&j&k\\2&6&0\\9&-1&0\end{bmatrix}\)

\(=i(0-0)+j(0-0)+k(-2-54)\)

\(=-56k\)

Hence

Area \(=|\vec{AB}\times\vec{AD}|\)

\(=\sqrt{(-56)^2}=56\)

asked 2021-06-11

Find the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4), and D(5, -1).

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 2021-06-04

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 2021-06-08

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

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 2021-08-21

asked 2021-08-16

Is it true that the equations r=8, \(\displaystyle{x}^{{2}}+{y}^{{2}}={64}\), and \(\displaystyle{x}={8}{\sin{{\left({3}{t}\right)}}},{y}={8}{\cos{{\left({3}{t}\right)}}}{\left({0}\le{t}\le{2}\pi\right)}\) all have the same graph.