Answer:
So we have two given angles- 31* and 43*.
First we add those together.
31* + 43* = 74*
Then, we subtract that amount from 180*
180* - 74* = 106*
106* is the missing angle.
x106* - 31* = 75*
x106* + 43* = 149*
~Hope this helps~
Answer:
and ![(500,79)](https://tex.z-dn.net/?f=%28500%2C79%29)
Step-by-step explanation:
Given
See attachment for complete question
Required
Determine the equilibrium solutions
We have:
![\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW](https://tex.z-dn.net/?f=%5Cfrac%7BdR%7D%7Bdt%7D%20%3D%200.09R%281%20-%200.00025R%29%20-%200.001RW)
![\frac{dW}{dt} = -0.02W + 0.00004RW](https://tex.z-dn.net/?f=%5Cfrac%7BdW%7D%7Bdt%7D%20%3D%20-0.02W%20%2B%200.00004RW)
To solve this, we first equate
and
to 0.
So, we have:
![0.09R(1 - 0.00025R) - 0.001RW = 0](https://tex.z-dn.net/?f=0.09R%281%20-%200.00025R%29%20-%200.001RW%20%3D%200)
![-0.02W + 0.00004RW = 0](https://tex.z-dn.net/?f=-0.02W%20%2B%200.00004RW%20%3D%200)
Factor out R in ![0.09R(1 - 0.00025R) - 0.001RW = 0](https://tex.z-dn.net/?f=0.09R%281%20-%200.00025R%29%20-%200.001RW%20%3D%200)
![R(0.09(1 - 0.00025R) - 0.001W) = 0](https://tex.z-dn.net/?f=R%280.09%281%20-%200.00025R%29%20-%200.001W%29%20%3D%200)
Split
or ![0.09(1 - 0.00025R) - 0.001W = 0](https://tex.z-dn.net/?f=0.09%281%20-%200.00025R%29%20-%200.001W%20%3D%200)
or ![0.09 - 2.25 * 10^{-5}R - 0.001W = 0](https://tex.z-dn.net/?f=0.09%20-%202.25%20%2A%2010%5E%7B-5%7DR%20-%200.001W%20%3D%200)
Factor out W in ![-0.02W + 0.00004RW = 0](https://tex.z-dn.net/?f=-0.02W%20%2B%200.00004RW%20%3D%200)
![W(-0.02 + 0.00004R) = 0](https://tex.z-dn.net/?f=W%28-0.02%20%2B%200.00004R%29%20%3D%200)
Split
or ![-0.02 + 0.00004R = 0](https://tex.z-dn.net/?f=-0.02%20%2B%200.00004R%20%3D%200)
Solve for R
![-0.02 + 0.00004R = 0](https://tex.z-dn.net/?f=-0.02%20%2B%200.00004R%20%3D%200)
![0.00004R = 0.02](https://tex.z-dn.net/?f=0.00004R%20%3D%200.02)
Make R the subject
![R = \frac{0.02}{0.00004}](https://tex.z-dn.net/?f=R%20%3D%20%5Cfrac%7B0.02%7D%7B0.00004%7D)
![R = 500](https://tex.z-dn.net/?f=R%20%3D%20500)
When
, we have:
![0.09 - 2.25 * 10^{-5}R - 0.001W = 0](https://tex.z-dn.net/?f=0.09%20-%202.25%20%2A%2010%5E%7B-5%7DR%20-%200.001W%20%3D%200)
![0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0](https://tex.z-dn.net/?f=0.09%20-2.25%20%2A%2010%5E%7B-5%7D%20%2A%20500%20-%200.001W%20%3D%200)
![0.09 -0.01125 - 0.001W = 0](https://tex.z-dn.net/?f=0.09%20-0.01125%20-%200.001W%20%3D%200)
![0.07875 - 0.001W = 0](https://tex.z-dn.net/?f=0.07875%20-%200.001W%20%3D%200)
Collect like terms
![- 0.001W = -0.07875](https://tex.z-dn.net/?f=-%200.001W%20%3D%20-0.07875)
Solve for W
![W = \frac{-0.07875}{ - 0.001}](https://tex.z-dn.net/?f=W%20%3D%20%5Cfrac%7B-0.07875%7D%7B%20-%200.001%7D)
![W = 78.75](https://tex.z-dn.net/?f=W%20%3D%2078.75)
![W \approx 79](https://tex.z-dn.net/?f=W%20%5Capprox%2079)
![(R,W) \to (500,79)](https://tex.z-dn.net/?f=%28R%2CW%29%20%5Cto%20%28500%2C79%29)
When
, we have:
![0.09 - 2.25 * 10^{-5}R - 0.001W = 0](https://tex.z-dn.net/?f=0.09%20-%202.25%20%2A%2010%5E%7B-5%7DR%20-%200.001W%20%3D%200)
![0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0](https://tex.z-dn.net/?f=0.09%20-%202.25%20%2A%2010%5E%7B-5%7DR%20-%200.001%2A0%20%3D%200)
![0.09 - 2.25 * 10^{-5}R = 0](https://tex.z-dn.net/?f=0.09%20-%202.25%20%2A%2010%5E%7B-5%7DR%20%3D%200)
Collect like terms
![- 2.25 * 10^{-5}R = -0.09](https://tex.z-dn.net/?f=-%202.25%20%2A%2010%5E%7B-5%7DR%20%3D%20-0.09)
Solve for R
![R = \frac{-0.09}{- 2.25 * 10^{-5}}](https://tex.z-dn.net/?f=R%20%3D%20%5Cfrac%7B-0.09%7D%7B-%202.25%20%2A%2010%5E%7B-5%7D%7D)
![R = 4000](https://tex.z-dn.net/?f=R%20%3D%204000)
So, we have:
![(R,W) \to (4000,0)](https://tex.z-dn.net/?f=%28R%2CW%29%20%5Cto%20%284000%2C0%29)
When
, we have:
![-0.02W + 0.00004RW = 0](https://tex.z-dn.net/?f=-0.02W%20%2B%200.00004RW%20%3D%200)
![-0.02W + 0.00004W*0 = 0](https://tex.z-dn.net/?f=-0.02W%20%2B%200.00004W%2A0%20%3D%200)
![-0.02W + 0 = 0](https://tex.z-dn.net/?f=-0.02W%20%2B%200%20%3D%200)
![-0.02W = 0](https://tex.z-dn.net/?f=-0.02W%20%3D%200)
![W=0](https://tex.z-dn.net/?f=W%3D0)
So, we have:
![(R,W) \to (0,0)](https://tex.z-dn.net/?f=%28R%2CW%29%20%5Cto%20%280%2C0%29)
Hence, the points of equilibrium are:
and ![(500,79)](https://tex.z-dn.net/?f=%28500%2C79%29)
Answer:
the center is (-2,2) and the radius is 5
The midpoint between the two points are (0,1/2)
Answer:
Step-by-step explanation:
hypotenuse=2*AB
where AB is the smallest side.
Take AB as the base .
Draw a perpendicular at B.
A as the center and cut an arc AC=2 AB
Join AC.
CAB is the reqd. triangle.