Answer:
See verification below
Step-by-step explanation:
We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that
![1-P=1-\frac{ce^t}{1+ce^t}=\frac{1+ce^t-ce^t}{1+ce^t}=\frac{1}{1+ce^t}](https://tex.z-dn.net/?f=1-P%3D1-%5Cfrac%7Bce%5Et%7D%7B1%2Bce%5Et%7D%3D%5Cfrac%7B1%2Bce%5Et-ce%5Et%7D%7B1%2Bce%5Et%7D%3D%5Cfrac%7B1%7D%7B1%2Bce%5Et%7D)
Now, differentiate to obtain
![\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%3D%28%5Cfrac%7Bce%5Et%7D%7B1%2Bce%5Et%7D%29%27%3D%5Cfrac%7B%28ce%5Et%29%27%281%2Bce%5Et%29-%28ce%5Et%29%281%2Bce%5Et%29%27%7D%7B%281%2Bce%5Et%29%5E2%7D)
![=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%28ce%5Et%29%281%2Bce%5Et%29-%28ce%5Et%29%28ce%5Et%29%7D%7B%281%2Bce%5Et%29%5E2%7D%3D%5Cfrac%7Bce%5Et%2Bce%5E%7B2t%7D-ce%5E%7B2t%7D%7D%7B%281%2Bce%5Et%29%5E2%7D%3D%5Cfrac%7Bce%5Et%7D%7B%281%2Bce%5Et%29%5E2%7D)
To obtain the required form, extract a factor in both the numerator and denominator:
![\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)](https://tex.z-dn.net/?f=%5Cfrac%7BdP%7D%7Bdt%7D%3D%5Cfrac%7Bce%5Et%7D%7B1%2Bce%5Et%7D%5Cfrac%7B1%7D%7B1%2Bce%5Et%7D%3DP%281-P%29)
First you find the circumference:
C=2
![\pi](https://tex.z-dn.net/?f=%20%5Cpi%20)
r=2(3.14)15=94.2 cm
Then you figure out the ratio of 150 to the entire circle:
150/360=5/12.
Then multiply:
5/12*94.2= 39.25 cm.
Therefore, the length of the arc if about 39.25cm.
Answer:
202.3 ounces of real silver
Step-by-step explanation:
Another example would be like pizza. If there are 6 slices of pizza in each box, then 2 boxes of pizza would have 6 + 6 slices = 12 slices. It is 6 slices each * 2 boxes = 12 slices total. The same applies to the coin situation, for every additional coin, multiply 0.85 by the number of coins to get the total weight of real silver.
If there are 238 silver coins, then you have 238 0.85 ounces of real silver. Multiplying 238 by 0.85 to simplify gives you 202.3 ounces of real silver.
Answer:
it was rough it the beginning but I got it its B: