Answer:
see explanation
Step-by-step explanation:
the exterior angle of a triangle equals the sum of the 2 opposite interior angles, that is
2x + 4 = x + 60 ( subtract x from both sides )
x + 4 = 60 ( subtract 4 from both sides )
x = 56
exterior angle = 2x + 4 = (2 × 56) + 4 = 112 + 4 = 116°
Answer:
x = -5
Step-by-step explanation:
Angles "50" and "x+55" are alternate interior angles which means that they are the same.
So 50 = x + 55
That leaves you with x = -5
Firstly, the height increased.
Before restoration the height was 56.84*cos(5.5°).
After restoration : <span>56.84*cos(3.99°).
The difference is :
</span>56.84*cos(3.99°)-56.84*cos(5.5°)=56.84(cos(3.99°)-cos(5.5°))=56.84*0.0022=0.1239≈0.124 - the answer
Answer:
Part 1 : ![I_A = 5.77 e^{0.01055t}](https://tex.z-dn.net/?f=I_A%20%3D%205.77%20e%5E%7B0.01055t%7D)
Part 2 : In 2069 the population would be 12 millions.
Step-by-step explanation:
Part 1 : Given function that shows the population( in millions ) of Israel after t years since 2000,
![I_A = A_0 e^{kt}](https://tex.z-dn.net/?f=I_A%20%3D%20A_0%20e%5E%7Bkt%7D)
If t = 0,
![I_A = 5.77](https://tex.z-dn.net/?f=I_A%20%3D%205.77)
![\implies 5.77 = A_0 e^{0}\implies A_0 = 5.77](https://tex.z-dn.net/?f=%5Cimplies%205.77%20%3D%20A_0%20e%5E%7B0%7D%5Cimplies%20A_0%20%3D%205.77)
If t = 77 years,
The population in 2077,
![I_A = A_0 e^{77k}=5.77 e^{77k}](https://tex.z-dn.net/?f=I_A%20%3D%20A_0%20e%5E%7B77k%7D%3D5.77%20e%5E%7B77k%7D)
According to the question,
Population in 2077 = 13 millions
![13 = 5.77 e^{77k}](https://tex.z-dn.net/?f=13%20%3D%205.77%20e%5E%7B77k%7D)
![\frac{13}{5.77} = e^{77k}](https://tex.z-dn.net/?f=%5Cfrac%7B13%7D%7B5.77%7D%20%3D%20e%5E%7B77k%7D)
Taking ln both sides,
![\ln(\frac{13}{5.77}) = \ln(e^{77k})](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B13%7D%7B5.77%7D%29%20%3D%20%5Cln%28e%5E%7B77k%7D%29)
![\ln(\frac{13}{5.77}) = 77k](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B13%7D%7B5.77%7D%29%20%3D%2077k)
![\implies k = 0.010549\approx 0.01055](https://tex.z-dn.net/?f=%5Cimplies%20k%20%3D%200.010549%5Capprox%200.01055)
Hence, the required function would be,
![I_A = 5.77 e^{0.01055t}](https://tex.z-dn.net/?f=I_A%20%3D%205.77%20e%5E%7B0.01055t%7D)
Part 2 : If ![I_A = 12](https://tex.z-dn.net/?f=I_A%20%3D%2012)
![12 = 5.77 e^{0.01055t}](https://tex.z-dn.net/?f=12%20%3D%205.77%20e%5E%7B0.01055t%7D)
![\frac{12}{5.77} = e^{0.01055t}](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B5.77%7D%20%3D%20e%5E%7B0.01055t%7D)
Taking ln both sides,
![\ln(\frac{12}{5.77}) = \ln(e^{0.01055t})](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B12%7D%7B5.77%7D%29%20%3D%20%5Cln%28e%5E%7B0.01055t%7D%29)
![\ln(\frac{12}{5.77}) =0.01055t](https://tex.z-dn.net/?f=%5Cln%28%5Cfrac%7B12%7D%7B5.77%7D%29%20%3D0.01055t)
![\implies t\approx 69](https://tex.z-dn.net/?f=%5Cimplies%20t%5Capprox%2069)
∵ 2000 + 69 = 2069
Hence, in 2069 the population would be 12 millions.