what that guy said ddddddddddddddddd
Angle 1 and angle 2 are what are called alternate angles. Two opposite angles between parallel lines. this means they are equal to each other.
So we have an equation: 2x + 20 = 3x + 10
Subtract 2x and 10 from each side
We now have 10 = x, so we know what x is
now plug in x to angle 1: (2 x 10) + 20 = 40, so angle 1 = 40.
Answer:
10%
Step-by-step explanation:
80-10%= 72
Hope this helps!
Answer:
The doomsday is 146 days
<em></em>
Step-by-step explanation:
Given
![\frac{dy}{dt} = ky^{1 +c}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20ky%5E%7B1%20%2Bc%7D)
First, we calculate the solution that satisfies the initial solution
Multiply both sides by
![\frac{dt}{y^{1+c}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdt%7D%7By%5E%7B1%2Bc%7D%7D)
![\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}](https://tex.z-dn.net/?f=%5Cfrac%7Bdt%7D%7By%5E%7B1%2Bc%7D%7D%20%2A%20%5Cfrac%7Bdy%7D%7Bdt%7D%20%3D%20ky%5E%7B1%20%2Bc%7D%20%2A%20%5Cfrac%7Bdt%7D%7By%5E%7B1%2Bc%7D%7D)
![\frac{dy}{y^{1+c}} = k\ dt](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7By%5E%7B1%2Bc%7D%7D%20%20%3D%20k%5C%20dt)
Take integral of both sides
![\int \frac{dy}{y^{1+c}} = \int k\ dt](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7Bdy%7D%7By%5E%7B1%2Bc%7D%7D%20%20%3D%20%5Cint%20k%5C%20dt)
![\int y^{-1-c}\ dy = \int k\ dt](https://tex.z-dn.net/?f=%5Cint%20y%5E%7B-1-c%7D%5C%20dy%20%20%3D%20%5Cint%20k%5C%20dt)
![\int y^{-1-c}\ dy = k\int\ dt](https://tex.z-dn.net/?f=%5Cint%20y%5E%7B-1-c%7D%5C%20dy%20%20%3D%20k%5Cint%5C%20dt)
Integrate
![\frac{y^{-1-c+1}}{-1-c+1} = kt+C](https://tex.z-dn.net/?f=%5Cfrac%7By%5E%7B-1-c%2B1%7D%7D%7B-1-c%2B1%7D%20%3D%20kt%2BC)
![-\frac{y^{-c}}{c} = kt+C](https://tex.z-dn.net/?f=-%5Cfrac%7By%5E%7B-c%7D%7D%7Bc%7D%20%3D%20kt%2BC)
To find c; let t= 0
![-\frac{y_0^{-c}}{c} = k*0+C](https://tex.z-dn.net/?f=-%5Cfrac%7By_0%5E%7B-c%7D%7D%7Bc%7D%20%3D%20k%2A0%2BC)
![-\frac{y_0^{-c}}{c} = C](https://tex.z-dn.net/?f=-%5Cfrac%7By_0%5E%7B-c%7D%7D%7Bc%7D%20%3D%20C)
![C =-\frac{y_0^{-c}}{c}](https://tex.z-dn.net/?f=C%20%3D-%5Cfrac%7By_0%5E%7B-c%7D%7D%7Bc%7D)
Substitute
in ![-\frac{y^{-c}}{c} = kt+C](https://tex.z-dn.net/?f=-%5Cfrac%7By%5E%7B-c%7D%7D%7Bc%7D%20%3D%20kt%2BC)
![-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}](https://tex.z-dn.net/?f=-%5Cfrac%7By%5E%7B-c%7D%7D%7Bc%7D%20%3D%20kt-%5Cfrac%7By_0%5E%7B-c%7D%7D%7Bc%7D)
Multiply through by -c
![y^{-c} = -ckt+y_0^{-c}](https://tex.z-dn.net/?f=y%5E%7B-c%7D%20%3D%20-ckt%2By_0%5E%7B-c%7D)
Take exponents of ![-c^{-1](https://tex.z-dn.net/?f=-c%5E%7B-1)
![y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}](https://tex.z-dn.net/?f=y%5E%7B-c%2A-c%5E%7B-1%7D%7D%20%3D%20%5B-ckt%2By_0%5E%7B-c%7D%5D%5E%7B-c%5E%7B-1%7D)
![y = [-ckt+y_0^{-c}]^{-c^{-1}](https://tex.z-dn.net/?f=y%20%3D%20%5B-ckt%2By_0%5E%7B-c%7D%5D%5E%7B-c%5E%7B-1%7D)
![y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}](https://tex.z-dn.net/?f=y%20%3D%20%5B-ckt%2By_0%5E%7B-c%7D%5D%5E%7B-%5Cfrac%7B1%7D%7Bc%7D%7D)
i.e.
![y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20%5B-ckt%2By_0%5E%7B-c%7D%5D%5E%7B-%5Cfrac%7B1%7D%7Bc%7D%7D)
Next:
i.e. 3 months
--- initial number of breeds
So, we have:
![y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}](https://tex.z-dn.net/?f=y%283%29%20%3D%20%5B-ck%20%2A%203%2B2%5E%7B-c%7D%5D%5E%7B-%5Cfrac%7B1%7D%7Bc%7D%7D)
-----------------------------------------------------------------------------
We have the growth term to be: ![ky^{1.01}](https://tex.z-dn.net/?f=ky%5E%7B1.01%7D)
This implies that:
![ky^{1.01} = ky^{1+c}](https://tex.z-dn.net/?f=ky%5E%7B1.01%7D%20%3D%20ky%5E%7B1%2Bc%7D)
By comparison:
![1.01 = 1 + c](https://tex.z-dn.net/?f=1.01%20%3D%201%20%2B%20c)
![c = 1.01 - 1 = 0.01](https://tex.z-dn.net/?f=c%20%3D%201.01%20-%201%20%3D%200.01)
--- 16 rabbits after 3 months:
-----------------------------------------------------------------------------
![y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}](https://tex.z-dn.net/?f=y%283%29%20%3D%20%5B-ck%20%2A%203%2B2%5E%7B-c%7D%5D%5E%7B-%5Cfrac%7B1%7D%7Bc%7D%7D)
![16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}](https://tex.z-dn.net/?f=16%20%3D%20%5B-0.01%20%2A%203%20%2A%20k%20%2B%202%5E%7B-0.01%7D%5D%5E%7B%5Cfrac%7B-1%7D%7B0.01%7D%7D)
![16 = [-0.03 * k + 2^{-0.01}]^{-100}](https://tex.z-dn.net/?f=16%20%3D%20%5B-0.03%20%2A%20k%20%2B%202%5E%7B-0.01%7D%5D%5E%7B-100%7D)
![16 = [-0.03 k + 0.9931]^{-100}](https://tex.z-dn.net/?f=16%20%3D%20%5B-0.03%20k%20%2B%200.9931%5D%5E%7B-100%7D)
Take -1/100th root of both sides
![16^{-1/100} = -0.03k + 0.9931](https://tex.z-dn.net/?f=16%5E%7B-1%2F100%7D%20%3D%20-0.03k%20%2B%200.9931)
![0.9727 = -0.03k + 0.9931](https://tex.z-dn.net/?f=0.9727%20%3D%20-0.03k%20%2B%200.9931)
![0.03k= - 0.9727 + 0.9931](https://tex.z-dn.net/?f=0.03k%3D%20-%200.9727%20%2B%200.9931)
![0.03k= 0.0204](https://tex.z-dn.net/?f=0.03k%3D%200.0204)
![k= \frac{0.0204}{0.03}](https://tex.z-dn.net/?f=k%3D%20%5Cfrac%7B0.0204%7D%7B0.03%7D)
![k= 0.68](https://tex.z-dn.net/?f=k%3D%200.68)
Recall that:
![-\frac{y^{-c}}{c} = kt+C](https://tex.z-dn.net/?f=-%5Cfrac%7By%5E%7B-c%7D%7D%7Bc%7D%20%3D%20kt%2BC)
This implies that:
![\frac{y_0^{-c}}{c} = kT](https://tex.z-dn.net/?f=%5Cfrac%7By_0%5E%7B-c%7D%7D%7Bc%7D%20%3D%20kT)
Make T the subject
![T = \frac{y_0^{-c}}{kc}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7By_0%5E%7B-c%7D%7D%7Bkc%7D)
Substitute:
,
and ![y_0 = 2](https://tex.z-dn.net/?f=y_0%20%3D%202)
![T = \frac{2^{-0.01}}{0.68 * 0.01}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5E%7B-0.01%7D%7D%7B0.68%20%2A%200.01%7D)
![T = \frac{2^{-0.01}}{0.0068}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B2%5E%7B-0.01%7D%7D%7B0.0068%7D)
![T = \frac{0.9931}{0.0068}](https://tex.z-dn.net/?f=T%20%3D%20%5Cfrac%7B0.9931%7D%7B0.0068%7D)
![T = 146.04](https://tex.z-dn.net/?f=T%20%3D%20146.04)
<em>The doomsday is 146 days</em>