Well, we are told that in the beginning, it has traveled 30km vertically, so do not forget to add that on at the end.
Next it says that it traveled 40km 30 degrees from vertical, so we set up a sin equation to solve for the missing side, n:
sin(angle)= opposite/hypotenuse:
sin(30) = n/40
40sin30=n
n=20km
Then it says at an angle of 45 degrees, it goes 100km. This means that we are given the hypotenuse of a right triangle, and we need to find the side that goes up and down. We shall call this length x.
We know that the angle opposite x is 45 degrees.
So, we will use sin to solve for x:
sin(angle)= opposite/hypotenuse
sin45= x/100
100sin45=x
x=70.711km
But remember, I said not to forget about that 30km from the very beginning? So we add up all of our vertical heights:
30km + 20km+ 70.711km = 120.711km
Answer:
2,-2,1,-1. those r ur x values.
Using an exponential function, it is found that the Tequesta settlement is 1845 years old.
<h3>What is an exponential function?</h3>
The exponential equation for a decaying amount of a substance is given by:

In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
Researching on the internet, the half-life of carbon 14 is of 5,730 years, hence A(5730) = 0.5A(0), which we use to find r.







Hence, the equation is:

The wood chips were found to contain 80% of the atmospheric carbon-14, hence we have to find t for which A(t) = 0.8A(0).







The Tequesta settlement is 1845 years old.
You can learn more about exponential functions at brainly.com/question/25537936