7 because you do 27/27 and that cancels out and then you do 189/27 and you get 7 as your final answer which is equal to six. Easy peasy!
Answer:
sorry I cant really see with what. I recomend checking out some toturing servesices
Step-by-step explanation:
The initial population is P₀ = 650,000.
Growth rate, r = 5% per year, or r = 0.05.
Let t = years.
The proposed model is
![P(t)= P_{0}e^{rt}](https://tex.z-dn.net/?f=P%28t%29%3D%20P_%7B0%7De%5E%7Brt%7D%20)
or
![P(t)=650000e^{0.05t}](https://tex.z-dn.net/?f=P%28t%29%3D650000e%5E%7B0.05t%7D)
Therefore
![\frac{P}{650000} =e^{0.05t}](https://tex.z-dn.net/?f=%20%5Cfrac%7BP%7D%7B650000%7D%20%3De%5E%7B0.05t%7D)
ln(P/650000) = 0.05t
When P = 1,000,000
0.05t = ln(1000000/650000) = 0.4308
t = 8.6157 years = 2 years (approx)
Answer: 2 years (approx)
Answer:
50.285
Step-by-step explanation:
Find out the radius of the circle first.
8 ÷ 2 = 4 (radius)
Formula:
pi x radius x radius
22/7 x 4 x 4 = 50.285
Answer:
![AX = 1084.20](https://tex.z-dn.net/?f=AX%20%3D%201084.20)
![BX = 1270.69](https://tex.z-dn.net/?f=BX%20%3D%201270.69)
Step-by-step explanation:
See attachment for complete question
Let the position of the submarine be represented with X
Given
![AB = 1425](https://tex.z-dn.net/?f=AB%20%3D%201425)
![\angle A = 59^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20A%20%3D%2059%5E%7B%5Ccirc%7D)
![\angle B = 47^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20B%20%3D%2047%5E%7B%5Ccirc%7D)
First, we calculate angle at X.
![\angle X + \angle A + \angle B = 180](https://tex.z-dn.net/?f=%5Cangle%20X%20%2B%20%5Cangle%20A%20%2B%20%5Cangle%20B%20%3D%20180)
![\angle X + 59^{\circ} + 47^{\circ}= 180^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20X%20%2B%2059%5E%7B%5Ccirc%7D%20%2B%2047%5E%7B%5Ccirc%7D%3D%20180%5E%7B%5Ccirc%7D)
![\angle X = 180^{\circ} -59^{\circ} - 47^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20X%20%3D%20180%5E%7B%5Ccirc%7D%20-59%5E%7B%5Ccirc%7D%20-%2047%5E%7B%5Ccirc%7D)
![\angle X = 74^{\circ}](https://tex.z-dn.net/?f=%5Cangle%20X%20%3D%2074%5E%7B%5Ccirc%7D)
Solving (a): Distance AX: The distance between ship A and the submarine
To do this, we apply sine formula which states
![\frac{a}{sin\ A} = \frac{b}{sin\ B} = \frac{c}{sin\ C}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%5C%20A%7D%20%3D%20%5Cfrac%7Bb%7D%7Bsin%5C%20B%7D%20%3D%20%5Cfrac%7Bc%7D%7Bsin%5C%20C%7D)
In this case:
![\frac{AB}{sin\ X} = \frac{AX}{sin\ B}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7Bsin%5C%20X%7D%20%3D%20%5Cfrac%7BAX%7D%7Bsin%5C%20B%7D)
Substitute values for AB,
and ![\angle B](https://tex.z-dn.net/?f=%5Cangle%20B)
![\frac{1425}{sin(74^{\circ})} = \frac{AX}{sin(47^{\circ})}](https://tex.z-dn.net/?f=%5Cfrac%7B1425%7D%7Bsin%2874%5E%7B%5Ccirc%7D%29%7D%20%3D%20%5Cfrac%7BAX%7D%7Bsin%2847%5E%7B%5Ccirc%7D%29%7D)
Make AX the subject
![AX = \frac{1425}{sin(74^{\circ})} * sin(47^{\circ})](https://tex.z-dn.net/?f=AX%20%3D%20%5Cfrac%7B1425%7D%7Bsin%2874%5E%7B%5Ccirc%7D%29%7D%20%2A%20sin%2847%5E%7B%5Ccirc%7D%29)
![AX = \frac{1425}{0.9613} * 0.7314](https://tex.z-dn.net/?f=AX%20%3D%20%5Cfrac%7B1425%7D%7B0.9613%7D%20%2A%200.7314)
![AX = \frac{1425 * 0.7314}{0.9613}](https://tex.z-dn.net/?f=AX%20%3D%20%5Cfrac%7B1425%20%2A%200.7314%7D%7B0.9613%7D)
![AX = \frac{1042.245}{0.9613}](https://tex.z-dn.net/?f=AX%20%3D%20%5Cfrac%7B1042.245%7D%7B0.9613%7D)
![AX = 1084.20](https://tex.z-dn.net/?f=AX%20%3D%201084.20)
Solving (b): Distance BX: The distance between ship B and the submarine
To do this, we apply sine formula which states
In this case:
![\frac{AB}{sin\ X} = \frac{BX}{sin\ A}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7Bsin%5C%20X%7D%20%3D%20%5Cfrac%7BBX%7D%7Bsin%5C%20A%7D)
Substitute values for AB,
and ![\angle A](https://tex.z-dn.net/?f=%5Cangle%20A)
![\frac{1425}{sin(74^{\circ})} = \frac{BX}{sin(59^{\circ})}](https://tex.z-dn.net/?f=%5Cfrac%7B1425%7D%7Bsin%2874%5E%7B%5Ccirc%7D%29%7D%20%3D%20%5Cfrac%7BBX%7D%7Bsin%2859%5E%7B%5Ccirc%7D%29%7D)
Make BX the subject
![BX = \frac{1425}{sin(74^{\circ})} * sin(59^{\circ})](https://tex.z-dn.net/?f=BX%20%3D%20%5Cfrac%7B1425%7D%7Bsin%2874%5E%7B%5Ccirc%7D%29%7D%20%2A%20sin%2859%5E%7B%5Ccirc%7D%29)
![BX = \frac{1425}{0.9613} * 0.8572](https://tex.z-dn.net/?f=BX%20%3D%20%5Cfrac%7B1425%7D%7B0.9613%7D%20%2A%200.8572)
![BX = \frac{1425* 0.8572}{0.9613}](https://tex.z-dn.net/?f=BX%20%3D%20%5Cfrac%7B1425%2A%200.8572%7D%7B0.9613%7D)
![BX = \frac{1221.51}{0.9613}](https://tex.z-dn.net/?f=BX%20%3D%20%5Cfrac%7B1221.51%7D%7B0.9613%7D)
![BX = 1270.69](https://tex.z-dn.net/?f=BX%20%3D%201270.69)