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Softa [21]
2 years ago
15

What is the solution to the system of equations -2x + 4y = 1 - 4x + 3y = 12

Mathematics
1 answer:
Aleks [24]2 years ago
7 0

Answer:

sorry kid

Step-by-step explanation:

I just want points

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3 years ago
Please calculate this limit <br>please help me​
Tasya [4]

Answer:

We want to find:

\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n}

Here we can use Stirling's approximation, which says that for large values of n, we get:

n! = \sqrt{2*\pi*n} *(\frac{n}{e} )^n

Because here we are taking the limit when n tends to infinity, we can use this approximation.

Then we get.

\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} =  \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}

Now we can just simplify this, so we get:

\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\

And we can rewrite it as:

\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n}

The important part here is the exponent, as n tends to infinite, the exponent tends to zero.

Thus:

\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n} = \frac{1}{e}*1 = \frac{1}{e}

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3 years ago
Based on the Pythagorean theorem, select all of the following statements that must be true
8_murik_8 [283]

Answer:

The 1st and 4th statements are true.

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3 years ago
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Answer:

A.

While D is partially correct, A is the way to go, because samples are easier to collect than whole populations. The internet quotes, "It is a much quicker process and is more time efficient." This proves the theory why A is the correct answer.

6 0
2 years ago
If a production line produces 50 mouse traps every 30 minutes over the course of a 10 hour work day with a half-hour break for l
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4 0
3 years ago
Read 2 more answers
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