Answer:
2x-z=0 is the equation of the plane.
Step-by-step explanation:
Given that the plane passes through the points (1,0,2) and (-1,1,-2)
and also origin.
Hence equation of the plane passing through three points we can use
Any plane passing through 3 given points is given as
![\left[\begin{array}{ccc}x-x_1&y-y_1&z-z_1\\x_2-x_1&y_2-y_1&z_2-z_1\\x_3-x_1&y_3-y_1&z_3-z_1\end{array}\right] =0](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx-x_1%26y-y_1%26z-z_1%5C%5Cx_2-x_1%26y_2-y_1%26z_2-z_1%5C%5Cx_3-x_1%26y_3-y_1%26z_3-z_1%5Cend%7Barray%7D%5Cright%5D%20%3D0)
Substitute the three points to get
![\left[\begin{array}{ccc}x-1&y&z-2\\-1-1&1&-2-2\\0-1&0&0-2\end{array}\right] \\=0\\(x-1)(-2) -y(4-4)+(z-2)(1) =0\\-2x+z=0\\2x-z-=0](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx-1%26y%26z-2%5C%5C-1-1%261%26-2-2%5C%5C0-1%260%260-2%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%3D0%5C%5C%28x-1%29%28-2%29%20-y%284-4%29%2B%28z-2%29%281%29%20%3D0%5C%5C-2x%2Bz%3D0%5C%5C2x-z-%3D0)
2x-z=0 is the equation of the plane.
Answer:
The top tree correctly represents the sample space
Step-by-step explanation:
At the "root" of our tree, we can either have three branches for each of the flavors, or two branches for each of the types of crust. Here's how each of those branches continue:
- If we start with the <em>three branches for flavors</em>, each branch will have <em>two more branches for the types of crust</em>. Working down the tree, I could start by choosing the pepperoni branch, and then continue to choose either thin or hand-tossed crust.
- If we start with the <em>two branches for crusts</em>, each branch will have <em>three more branches for the flavors</em>. This option is represented as the first tree in the image, and in this case would be the correct choice.
<span>A complex number is a number of the form a + bi, where i = and a and b are real numbers. For example, 5 + 3i, - + 4i, 4.2 - 12i, and - - i are all complex numbers. a is called the real part of the complex number and bi is called the imaginary part of the complex number.</span>
Answer:56.57
Step-by-step explanation:
πr2
2
=
22
7
⋅(6)2
2
=56.57
