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Likurg_2 [28]
2 years ago
5

Find the length of the side of an equilateral triangle that has an altitude length of 24 feet.

Mathematics
1 answer:
telo118 [61]2 years ago
7 0
\bf \textit{height of an equilateral triangle}\\\\
h=\cfrac{\sqrt{3}\ s}{2}\qquad 
\begin{cases}
h=height\\
s=\textit{one side's length}
\end{cases}
\\\\\\
\cfrac{2h}{\sqrt{3}}=s
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Ksivusya [100]

Answer:

m ≥ 0

Step-by-step explanation:

Since the cost is represented by c = 0.12m, the domain should be a positive number, this is because number of minutes can't be written in negative. Therefore, the most reasonable number for the domain would be the set of positive whole numbers which means, m≥0.

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What is the sum of the first 70 consecutive odd numbers? Explain.
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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

\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1

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

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The second sum is simply the sum of N ones:

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\displaystyle \sum_{i=1}^N 2i-1 = 2\sum_{i=1}^N i - \sum_{i=1}^N 1 = N(N+1)-N = N^2+N-N = N^2

which ends the proof.

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2 years ago
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KengaRu [80]

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Step-by-step explanation:

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