un4t5o4v

Answered 2021-06-12
Author has **5066** answers

content_user

Answered 2021-09-28
Author has **2252** answers

Consider the parallelogram A=(-3;0), B(-1,5), C(7;4) and D=(5;-1)

The objective is to find the area of parallelogram

Find the are as follows:

The area of the parallelogram is the magnitude of the cross product of the adjacent edges.

That is, \(Area=|\overline{AB}\times\overline{AD}|\)

Find the adjacent edges \(\overline{AB}\) and \(\overline{AD}\) as follows

\(\overline{AB}=B-A\)

\(=(-1;5)-(-3;0)\)

\(=(-1+3;5-0)\)

\(=(2;5)\)

\(\overline{AD}=D-A\)

\(=(5;-1)-(-3;0)\)

\(=(8;1)\)

Find \(\overline{AB}\times\overline{AD}\) as,

\(\overline{AB}\times\overline{AD}=\begin{bmatrix}i&j&k\\2&5&0\\8&-1&0\end{bmatrix}\)

\(=5(0)-0(-1)i-(2(0)-0(8))j+(2(-1)-5(8))k\)

\(=0i+0j-42k\)

The area of the parallelogram is,

Area \(=|AB\times AD|\)

\(=|(0i+0j-42k|\)

\(=\sqrt{(0)^2+(0)^2+(-42)^2}\)

\(=\sqrt{(42)^2}\)

= 42 square unit

Hence, the area of parallelogram is 42

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 2021-06-09

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 2021-06-08

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

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 2021-06-04

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 2021-09-14

asked 2021-05-13

Find a basis for the eigenspace corresponding to the eigenvalue of A given below.

\(A=\begin{bmatrix}4 & 0&2&0 \\4 & 2&10&0\\3&-4&17&0\\2&-2&8&3 \end{bmatrix} , \lambda=3\)

\(A=\begin{bmatrix}4 & 0&2&0 \\4 & 2&10&0\\3&-4&17&0\\2&-2&8&3 \end{bmatrix} , \lambda=3\)

asked 2021-08-30