Answer:
Linear pair postulate
Step-by-step explanation:
Linear pair postulate states that if two angles adjacent to each other form a line, then they are a linear pair and are supplementary.
Step-by-step explanation:
if the vertex A is (-2;5), vertex B is (1;3) and the vertex C is (-1;0), then
1) the lengths are (note, the side AC should be hypotenuse):
![|AB|=\sqrt{(1+2)^2+(3-5)^2}=\sqrt{13};](https://tex.z-dn.net/?f=%7CAB%7C%3D%5Csqrt%7B%281%2B2%29%5E2%2B%283-5%29%5E2%7D%3D%5Csqrt%7B13%7D%3B)
![|BC|=\sqrt(1+1)^2+(3-0)^2}=\sqrt{13};](https://tex.z-dn.net/?f=%7CBC%7C%3D%5Csqrt%281%2B1%29%5E2%2B%283-0%29%5E2%7D%3D%5Csqrt%7B13%7D%3B)
![|AC|=\sqrt{(-1+2)^2+(0-5)^2}=\sqrt{26}.](https://tex.z-dn.net/?f=%7CAC%7C%3D%5Csqrt%7B%28-1%2B2%29%5E2%2B%280-5%29%5E2%7D%3D%5Csqrt%7B26%7D.)
2) if to check the equation AB²+BC²=AC², then
13+13=26 - it is true.
It means, the triangle ΔABC is right triangle.
P.S. all the details are in the attachment.
Answer:
![\frac{\partial w}{\partial t} = y(e^t) +(x+z)*(cos(t)) - 3y*sin(3t)](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20w%7D%7B%5Cpartial%20t%7D%20%20%3D%20y%28e%5Et%29%20%2B%28x%2Bz%29%2A%28cos%28t%29%29%20%20-%203y%2Asin%283t%29)
Step-by-step explanation:
First, note that
![\frac{\partial x}{\partial t} = e^{t} \\\frac{\partial y}{\partial t} = cos(t)\\](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20x%7D%7B%5Cpartial%20t%7D%20%20%3D%20e%5E%7Bt%7D%20%5C%5C%5Cfrac%7B%5Cpartial%20y%7D%7B%5Cpartial%20t%7D%20%20%3D%20cos%28t%29%5C%5C)
And using the chain rule in one variable
![\frac{\partial z}{\partial t} = -3sin(3t)](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20t%7D%20%20%3D%20-3sin%283t%29)
Now remember that the chain rule in several variables sates that
![\frac{\partial w}{\partial t} = \frac{\partial w}{\partial x} * \frac{\partial x}{\partial t} + \frac{\partial w}{\partial y} * \frac{\partial y}{\partial t} + \frac{\partial w}{\partial z} * \frac{\partial z}{\partial t}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20w%7D%7B%5Cpartial%20t%7D%20%20%3D%20%5Cfrac%7B%5Cpartial%20w%7D%7B%5Cpartial%20x%7D%20%2A%20%5Cfrac%7B%5Cpartial%20x%7D%7B%5Cpartial%20t%7D%20%2B%20%5Cfrac%7B%5Cpartial%20w%7D%7B%5Cpartial%20y%7D%20%2A%20%5Cfrac%7B%5Cpartial%20y%7D%7B%5Cpartial%20t%7D%20%2B%20%5Cfrac%7B%5Cpartial%20w%7D%7B%5Cpartial%20z%7D%20%2A%20%5Cfrac%7B%5Cpartial%20z%7D%7B%5Cpartial%20t%7D)
Therefore the chain rule in several variables would look like this.
![\frac{\partial w}{\partial t} = y(e^t) +(x+z)*(cos(t)) - 3y*sin(3t)](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20w%7D%7B%5Cpartial%20t%7D%20%20%3D%20y%28e%5Et%29%20%2B%28x%2Bz%29%2A%28cos%28t%29%29%20%20-%203y%2Asin%283t%29)
Answer:
19,725
Step-by-step explanation:
Answer:
im pretty sure its B becuase Richard owes more
Step-by-step explanation:
is that Florida vertual school? it looks like what i used to do