Answer:
Yes, the aquarium <u>will</u> fit in 15 cubic feet of space.
Step-by-step explanation:
Given:
An aquarium has a base area of 6 square feet and a height of 2 feet.
Now, to find will the aquarium fit in 15 cubic feet of space or not.
<em>So, as given the dimensions:</em>
Base area = 6 square feet.
Height = 2 feet.
Now, to get the volume of aquarium by using formula:
<u><em>As, the volume of aquarium is 12 cubic feet.</em></u>
<u><em>And, the aquarium to be fit in 15 cubic feet space. So, 15 is more than 12.</em></u>
<u><em>Thus, the aquarium will be fit in 15 cubic feet space.</em></u>
Therefore, the aquarium will fit in 15 cubic feet of space.
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.