I THINK your supposed to multiply allthe numbers
Answer:
t = 6162 years
Step-by-step explanation:
This equation takes the form of
![N=N_{0}e^{kt}](https://tex.z-dn.net/?f=N%3DN_%7B0%7De%5E%7Bkt%7D)
We are given everything but the amount of C-14 at time t = 0. But we can figure it out from the info we ARE given. We are told that when the spear head is found it contains 54% of its original amount of C-14. Notice we are dealing in percents. If 54% remains when it is found, it started out with 100% of its amount. That's our N value. Filling in:
![100=54e^{.0001t}](https://tex.z-dn.net/?f=100%3D54e%5E%7B.0001t%7D)
Our goal is to get that t down from the exponential position that it is currently in. To do that we will need to eventually take the natural log of both sides, because ln's and e's "undo" each other, much like squaring "undoes" a square, or dividing "undoes" multiplication. So we take the natural log of both sides. On the right side, notice that when we take the natural log, the e disappears; it's "undone", gone. Before that, though, we will simplify by dividing both sides by 54. 100/54 = 1.851851852. So, altogether...
![ln(1.851851852)=.0001t](https://tex.z-dn.net/?f=ln%281.851851852%29%3D.0001t)
Simplifying by plugging the log of that number into our calculator, we get
.6161861395 = .0001t and
t = 6161.8613
Rounding to the nearest year, t = 6162 years
For this case we have the following functions:
![f (x) = 4x + 1\\g (x) = x ^ 2-5](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%204x%20%2B%201%5C%5Cg%20%28x%29%20%3D%20x%20%5E%202-5)
We must find
By definition we have to:
![(f + g) (x) = f (x) + g (x)](https://tex.z-dn.net/?f=%28f%20%2B%20g%29%20%28x%29%20%3D%20f%20%28x%29%20%2B%20g%20%28x%29)
So:
![(f + g) (x) = (4x + 1) + (x ^ 2-5) = 4x + 1 + x ^ 2-5 =](https://tex.z-dn.net/?f=%28f%20%2B%20g%29%20%28x%29%20%3D%20%284x%20%2B%201%29%20%2B%20%28x%20%5E%202-5%29%20%3D%204x%20%2B%201%20%2B%20x%20%5E%202-5%20%3D)
Different signs are subtracted and the major sign is placed.
![(f + g) (x) = x ^ 2 + 4x-4](https://tex.z-dn.net/?f=%28f%20%2B%20g%29%20%28x%29%20%3D%20x%20%5E%202%20%2B%204x-4)
Answer:
![(f + g) (x) = x ^ 2 + 4x-4](https://tex.z-dn.net/?f=%28f%20%2B%20g%29%20%28x%29%20%3D%20x%20%5E%202%20%2B%204x-4)
Answer: go to bitly and type
Step-by-step explanation: 3f3FcEi
Answer:
The answer is is 50
Step-by-step explanation:
If 3/5 if number is 30, then this means that 1/5 of the number must be 10 (i.e. If we divide 3/5 by 3, we get 1/5, so similarly, we can divide 30 by 3 to get 10). So, if 1/5 of the number is 10, this means the original number is 5x10 = 50.
We can also work this out using algebra:
![\frac{3}{5} x = 30\\3x = 150\\x = 50](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B5%7D%20x%20%3D%2030%5C%5C3x%20%3D%20150%5C%5Cx%20%3D%2050)