In kilometers, the approximate distance to the earth's horizon from a point h meters above the surface can be determined by evaluating the expression 12h−−−√. about how far is the apparent horizon to a person looking out to sea from the top of a cliff 350 meters above sea level?

In kilometers, the approximate distance to the earth's horizon from a point h meters above the surface can be determined by evaluating the expression 



We are given the height h of a person from surface of sea level to be 350 m and we are to find the the distance to horizon d. Using the value in above expression we get:



Therefore, the approximate distance to the horizon for the person will be 64.81 km

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

Ibelieve the answer is b. y=0 would make the line horizontal across the x.