Mr. williams physical education class lasts 7/8 hour. Instructions are 1/5 of that time, how many minutes are NOT spent on instr
1 answer:
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Answer: The answer is 314.28 cm² (approx.).
Step-by-step explanation: Given that an engineer is going to install a new water pipe. The diameter of this circular pipe is, d = 20 cm.
We need to find the area 'A' of the circular cross-section of the pipe.
Given, diameter of the circular section is
So, the radius of the circular cross-section will be
Therefore, cross-sectional area of the pipe is
Thus, the answer is 314.28 cm² (approx.).
Let's start from what we know.
Note that:
(sign of last term will be + when n is even and - when n is odd).
Sum is finite so we can split it into two sums, first
with only positive trems (squares of even numbers) and second 
with negative (squares of odd numbers). So:
And now the proof.
1) n is even.
In this case, both and 
have 
terms. For example if n=8 then:
Generally, there will be:
Now, calculate our sum:
So in this case we prove, that:
2) n is odd.
Here, has more terms than . For example if n=7 then:
So there is
terms in , 
terms in and:
Now, we can calculate our sum:
We consider all possible n so we prove that:
Note that:
(sign of last term will be + when n is even and - when n is odd).
Sum is finite so we can split it into two sums, first
And now the proof.
1) n is even.
In this case, both
Generally, there will be:
Now, calculate our sum:
So in this case we prove, that:
2) n is odd.
Here,
So there is
Now, we can calculate our sum:
We consider all possible n so we prove that: