Answer:
<h3>numbers of
Ostrich he keep =
725</h3>
<u>Step-by-step explanation:</u>
- Area of field = 30 × 155 + 90 × 45
- Area of field = 4650 + 4050
- Area of field = 8700 m²
numbers of Ostrich = 8700 ÷ 12
numbers of Ostrich = 725
To find the decimal form, you have to manually divide 1 by 8. Since 8 is greater than 1, the quotient would then start with 0., then you add a 0 next to 1, to make it 10. This time, divide 10 by 8. The nearest answer would be 1, because 1 *8 = 8. Subtracting this from 10, you get 2. Add another 0 to 2, to make it 20. Do the cycle all over again. The complete solution is as follows:
0.125
---------------------------
8 | 10
- 8
------------------------
20
-16
-------------
40
- 40
-------------
0
<em>Hence, the decimal form of 1/8 is 0.125.</em>
Solution: Let x be the height of a student in Marta's class.
The mean height of 18 students in Marta's class is 60 inches
We know that:
![Mean = \frac{\sum x_{i}}{n}](https://tex.z-dn.net/?f=Mean%20%3D%20%5Cfrac%7B%5Csum%20x_%7Bi%7D%7D%7Bn%7D)
![60 = \frac{\sum x_{i}}{18}](https://tex.z-dn.net/?f=60%20%3D%20%5Cfrac%7B%5Csum%20x_%7Bi%7D%7D%7B18%7D)
![60 \times 18 = \sum x_{i}](https://tex.z-dn.net/?f=60%20%5Ctimes%2018%20%3D%20%5Csum%20x_%7Bi%7D)
![\sum x_{i} = 1080](https://tex.z-dn.net/?f=%5Csum%20x_%7Bi%7D%20%3D%201080)
Therefore, the total measure of all 18 student's heights is 1080 inches
Answer:
The population when t = 3 is 10.
Step-by-step explanation:
Suppose a certain population satisfies the logistic equation given by
![\frac{dP}{dt}=10P-P^2](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%3D10P-P%5E2)
with P(0)=1. We need to find the population when t=3.
Using variable separable method we get
![\frac{dP}{10P-P^2}=dt](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7B10P-P%5E2%7D%3Ddt)
Integrate both sides.
.... (1)
Using partial fraction
![\frac{1}{P(10-P)}=\frac{A}{P}+\frac{B}{(10-P)}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7BP%2810-P%29%7D%3D%5Cfrac%7BA%7D%7BP%7D%2B%5Cfrac%7BB%7D%7B%2810-P%29%7D)
![A=\frac{1}{10},B=\frac{1}{10}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B10%7D%2CB%3D%5Cfrac%7B1%7D%7B10%7D)
Using these values the equation (1) can be written as
![\int (\frac{1}{10P}+\frac{1}{10(10-P)})dP=\int dt](https://tex.z-dn.net/?f=%5Cint%20%28%5Cfrac%7B1%7D%7B10P%7D%2B%5Cfrac%7B1%7D%7B10%2810-P%29%7D%29dP%3D%5Cint%20dt)
![\int \frac{dP}{10P}+\int \frac{dP}{10(10-P)}=\int dt](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7BdP%7D%7B10P%7D%2B%5Cint%20%5Cfrac%7BdP%7D%7B10%2810-P%29%7D%3D%5Cint%20dt)
On simplification we get
![\frac{1}{10}\ln P-\frac{1}{10}\ln (10-P)=t+C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%5Cln%20P-%5Cfrac%7B1%7D%7B10%7D%5Cln%20%2810-P%29%3Dt%2BC)
![\frac{1}{10}(\ln \frac{P}{10-P})=t+C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%28%5Cln%20%5Cfrac%7BP%7D%7B10-P%7D%29%3Dt%2BC)
We have P(0)=1
Substitute t=0 and P=1 in above equation.
![\frac{1}{10}(\ln \frac{1}{10-1})=0+C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%28%5Cln%20%5Cfrac%7B1%7D%7B10-1%7D%29%3D0%2BC)
![\frac{1}{10}(\ln \frac{1}{9})=C](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%28%5Cln%20%5Cfrac%7B1%7D%7B9%7D%29%3DC)
The required equation is
![\frac{1}{10}(\ln \frac{P}{10-P})=t+\frac{1}{10}(\ln \frac{1}{9})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D%28%5Cln%20%5Cfrac%7BP%7D%7B10-P%7D%29%3Dt%2B%5Cfrac%7B1%7D%7B10%7D%28%5Cln%20%5Cfrac%7B1%7D%7B9%7D%29)
Multiply both sides by 10.
![\ln \frac{P}{10-P}=10t+\ln \frac{1}{9}](https://tex.z-dn.net/?f=%5Cln%20%5Cfrac%7BP%7D%7B10-P%7D%3D10t%2B%5Cln%20%5Cfrac%7B1%7D%7B9%7D)
![e^{\ln \frac{P}{10-P}}=e^{10t+\ln \frac{1}{9}}](https://tex.z-dn.net/?f=e%5E%7B%5Cln%20%5Cfrac%7BP%7D%7B10-P%7D%7D%3De%5E%7B10t%2B%5Cln%20%5Cfrac%7B1%7D%7B9%7D%7D)
![\frac{P}{10-P}=\frac{1}{9}e^{10t}](https://tex.z-dn.net/?f=%5Cfrac%7BP%7D%7B10-P%7D%3D%5Cfrac%7B1%7D%7B9%7De%5E%7B10t%7D)
Reciprocal it
![\dfrac{10-P}{P}=9e^{-10t}](https://tex.z-dn.net/?f=%5Cdfrac%7B10-P%7D%7BP%7D%3D9e%5E%7B-10t%7D)
![P(t)=\dfrac{10}{1+9e^{-10t}}](https://tex.z-dn.net/?f=P%28t%29%3D%5Cdfrac%7B10%7D%7B1%2B9e%5E%7B-10t%7D%7D)
The population when t = 3 is
![P(3)=\dfrac{10}{1+9e^{-10\cdot 3}}](https://tex.z-dn.net/?f=P%283%29%3D%5Cdfrac%7B10%7D%7B1%2B9e%5E%7B-10%5Ccdot%203%7D%7D)
Using calculator,
![P=9.999\approx 10](https://tex.z-dn.net/?f=P%3D9.999%5Capprox%2010)
Therefore, the population when t = 3 is 10.