What is the distance across the lake?
1 answer:
Given:
Height of right triangle = 9 mi
Hypotenuse = 17.5 mi
Base of right triangle = Distance across lake
To find:
The distance across the lake.
Solution:
Using Pythagoras theorem:
In right triangle, square of the hypotenuse is equal to the sum of the squares of the other two sides.
Subtract 81 from both sides.
Taking square root on both sides.
⇒ base = 15
The distance across the lake 15 mi.
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The sum of the first n odd numbers is n squared! So, the short answer is that the sum of the first 70 odd numbers is 70 squared, i.e. 4900.
Allow me to prove the result: odd numbers come in the form 2n-1, because 2n is always even, and the number immediately before an even number is always odd.
So, if we sum the first N odd numbers, we have
The first sum is the sum of all integers from 1 to N, which is N(N+1)/2. We want twice this sum, so we have
The second sum is simply the sum of N ones:
So, the final result is
which ends the proof.