Answer:
<C = 133 degrees
Step-by-step explanation:
<B = 90 - 43
<B = 47
<C = 180 - 47
<C = 133 degrees
Answer:
(a) 100 fishes
(b) t = 10: 483 fishes
t = 20: 999 fishes
t = 30: 1168 fishes
(c)
![P(\infty) = 1200](https://tex.z-dn.net/?f=P%28%5Cinfty%29%20%3D%201200)
Step-by-step explanation:
Given
![P(t) =\frac{d}{1+ke^-{ct}}](https://tex.z-dn.net/?f=P%28t%29%20%3D%5Cfrac%7Bd%7D%7B1%2Bke%5E-%7Bct%7D%7D)
![d = 1200\\k = 11\\c=0.2](https://tex.z-dn.net/?f=d%20%3D%201200%5C%5Ck%20%3D%2011%5C%5Cc%3D0.2)
Solving (a): Fishes at t = 0
This gives:
![P(0) =\frac{1200}{1+11*e^-{0.2*0}}](https://tex.z-dn.net/?f=P%280%29%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2Ae%5E-%7B0.2%2A0%7D%7D)
![P(0) =\frac{1200}{1+11*e^-{0}}](https://tex.z-dn.net/?f=P%280%29%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2Ae%5E-%7B0%7D%7D)
![P(0) =\frac{1200}{1+11*1}](https://tex.z-dn.net/?f=P%280%29%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2A1%7D)
![P(0) =\frac{1200}{1+11}](https://tex.z-dn.net/?f=P%280%29%20%3D%5Cfrac%7B1200%7D%7B1%2B11%7D)
![P(0) =\frac{1200}{12}](https://tex.z-dn.net/?f=P%280%29%20%3D%5Cfrac%7B1200%7D%7B12%7D)
![P(0) = 100](https://tex.z-dn.net/?f=P%280%29%20%3D%20100)
Solving (a): Fishes at t = 10, 20, 30
![t = 10](https://tex.z-dn.net/?f=t%20%3D%2010)
![P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483](https://tex.z-dn.net/?f=P%2810%29%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2Ae%5E-%7B0.2%2A10%7D%7D%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2Ae%5E-%7B2%7D%7D%5C%5C%5C%5CP%2810%29%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2A0.135%7D%3D%5Cfrac%7B1200%7D%7B2.485%7D%5C%5C%5C%5CP%2810%29%20%3D483)
![t = 20](https://tex.z-dn.net/?f=t%20%3D%2020)
![P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999](https://tex.z-dn.net/?f=P%2820%29%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2Ae%5E-%7B0.2%2A20%7D%7D%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2Ae%5E-%7B4%7D%7D%5C%5C%5C%5CP%2820%29%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2A0.0183%7D%3D%5Cfrac%7B1200%7D%7B1.2013%7D%5C%5C%5C%5CP%2820%29%20%3D999)
![t = 30](https://tex.z-dn.net/?f=t%20%3D%2030)
![P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168](https://tex.z-dn.net/?f=P%2830%29%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2Ae%5E-%7B0.2%2A30%7D%7D%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2Ae%5E-%7B6%7D%7D%5C%5C%5C%5CP%2830%29%20%3D%5Cfrac%7B1200%7D%7B1%2B11%2A0.00247%7D%3D%5Cfrac%7B1200%7D%7B1.0273%7D%5C%5C%5C%5CP%2830%29%20%3D1168)
Solving (c): ![\lim_{t \to \infty} P(t)](https://tex.z-dn.net/?f=%5Clim_%7Bt%20%5Cto%20%5Cinfty%7D%20P%28t%29)
In (b) above.
Notice that as t increases from 10 to 20 to 30, the values of
decreases
This implies that:
![{t \to \infty} = {e^{-ct} \to 0}](https://tex.z-dn.net/?f=%7Bt%20%5Cto%20%5Cinfty%7D%20%3D%20%7Be%5E%7B-ct%7D%20%5Cto%200%7D)
So:
The value of P(t) for large values is:
![P(\infty) = \frac{1200}{1 + 11 * 0}](https://tex.z-dn.net/?f=P%28%5Cinfty%29%20%3D%20%5Cfrac%7B1200%7D%7B1%20%2B%2011%20%2A%200%7D)
![P(\infty) = \frac{1200}{1 + 0}](https://tex.z-dn.net/?f=P%28%5Cinfty%29%20%3D%20%5Cfrac%7B1200%7D%7B1%20%2B%200%7D)
![P(\infty) = \frac{1200}{1}](https://tex.z-dn.net/?f=P%28%5Cinfty%29%20%3D%20%5Cfrac%7B1200%7D%7B1%7D)
![P(\infty) = 1200](https://tex.z-dn.net/?f=P%28%5Cinfty%29%20%3D%201200)
Answer:
The answer would be 49 I think hehe
Step-by-step explanation:
Answer:
1/5
Step-by-step explanation:
There are 3 numbers of less than 4 (1, 2 and 3) and there are 2 multiples of 9 (9 and 18). So there are 5 favourable outcomes and 25 possible outcomes. So you put 5/25 and cancel down, which makes 1/5. I hope this helps!
Square root 50 does not belong....all of the other numbers are rational numbers. square root 50 is irrational.