Answer:
Arnold descended a distance of 5,250 ft after his parachute opened
Step-by-step explanation:
Here in this question, we want to know the distance Arnold descended after his parachute opened.
Mathematically, we know that distance = speed * time
In this case;
The speed is the rate at which he descended = 70 ft per second
Now the time is 1 minute and 15 seconds; since 1 minute is 60 seconds, then 1 minute and 15 seconds is 60 + 15 = 75 seconds
So what we are saying is he descended at a rate of 70 ft per second for 75 seconds
Thus, his distance of descent will be 70 ft per second * 75 seconds = 5,250 ft
Splitting up the interval [0, 6] into 6 subintervals means we have
![[0,1]\cup[1,2]\cup[2,3]\cup\cdots\cup[5,6]](https://tex.z-dn.net/?f=%5B0%2C1%5D%5Ccup%5B1%2C2%5D%5Ccup%5B2%2C3%5D%5Ccup%5Ccdots%5Ccup%5B5%2C6%5D)
and the respective midpoints are
. We can write these sequentially as
where
.
So the integral is approximately
Recall that
so our sum becomes
This is a geometric sequence, so use the formula for the sum of a geometric sequence:
Sum = (a(r^n - 1))/(r - 1)
where a is the first term, -5
r is the common ratio, 5
and n is the number of terms
Thus,
Sum = ((-5)(5^6 - 1))/(5-1) = -19530
