A stream begins at an elevation of 200 meters and flows a distance of 400 kilometers to the ocean? what is the average gradient?
2 answers:
Answer:
The average gradient is
Step-by-step explanation:
We have two important data to solve this problem:
1- Stream begins at an elevation (y) of 200 m
2- Stream flows a distance of (x) 400 km.
We need to calculate the average gradient. Gradient definition is the drop in elevation of a stream divided by the distance the water travel.
So, gradient (g) will be elevation (y) divided by distance (x).
Finally, the average gradient is .
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The function is defined as
This means that, taken an input m, the output is the input squared, plus 7.
So, if we take the input -4, we square it to get 16, and we add 7 to get 23.
Consider we need to find f(n).
Given:
Achilles ordered a pizza with 16 slices.
Every hour, he ate half of the remaining slices.
To find:
The function f(n) that is the number of slices Achilles ate in the hour since he got home.
Solution:
Initial number of slices = 16
Every hour, he ate half of the remaining slices. So, the number slices Achilles ate in the hour since he got home are:
8, 4, 2, 1, ...
It is a geometric sequence with first term 8 and common ratio .
The explicit formula for a geometric sequence is:
Where, a is the first term and r is the common ratio.
Substituting , we get
Therefore, the function f(n) that is the number of slices Achilles ate in the hour since he got home is .