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Aleksandr [31]
2 years ago
10

Help and Explain please

Mathematics
1 answer:
ANEK [815]2 years ago
4 0
You replace x for 2 and add 2 and 3 first b/c there in the parentheses. After that, you will have 5^{3} so you multiply 5 x 5 x 5 because it is an exponent.and your final answer is C) 125.
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For <img src="https://tex.z-dn.net/?f=e%5E%7B-x%5E2%2F2%7D" id="TexFormula1" title="e^{-x^2/2}" alt="e^{-x^2/2}" align="absmiddl
nevsk [136]
I'm assuming you're talking about the indefinite integral

\displaystyle\int e^{-x^2/2}\,\mathrm dx

and that your question is whether the substitution u=\dfrac x{\sqrt2} would work. Well, let's check it out:

u=\dfrac x{\sqrt2}\implies\mathrm du=\dfrac{\mathrm dx}{\sqrt2}
\implies\displaystyle\int e^{-x^2/2}\,\mathrm dx=\sqrt2\int e^{-(\sqrt2\,u)^2/2}\,\mathrm du
=\displaystyle\sqrt2\int e^{-u^2}\,\mathrm du

which essentially brings us to back to where we started. (The substitution only served to remove the scale factor in the exponent.)

What if we tried u=\sqrt t next? Then \mathrm du=\dfrac{\mathrm dt}{2\sqrt t}, giving

=\displaystyle\frac1{\sqrt2}\int \frac{e^{-(\sqrt t)^2}}{\sqrt t}\,\mathrm dt=\frac1{\sqrt2}\int\frac{e^{-t}}{\sqrt t}\,\mathrm dt

Next you may be tempted to try to integrate this by parts, but that will get you nowhere.

So how to deal with this integral? The answer lies in what's called the "error function" defined as

\mathrm{erf}(x)=\displaystyle\frac2{\sqrt\pi}\int_0^xe^{-t^2}\,\mathrm dt

By the fundamental theorem of calculus, taking the derivative of both sides yields

\dfrac{\mathrm d}{\mathrm dx}\mathrm{erf}(x)=\dfrac2{\sqrt\pi}e^{-x^2}

and so the antiderivative would be

\displaystyle\int e^{-x^2/2}\,\mathrm dx=\sqrt{\frac\pi2}\mathrm{erf}\left(\frac x{\sqrt2}\right)

The takeaway here is that a new function (i.e. not some combination of simpler functions like regular exponential, logarithmic, periodic, or polynomial functions) is needed to capture the antiderivative.
3 0
3 years ago
Bradley had 25 baseball cards in his collection. He receives x number of baseball cards for his birthday.
timofeeve [1]

Answer:

25+x=y

Step-by-step explanation:

First, we start as 25, the number of cards he has in his collection. Then we add x, the cards he receive. The sum is y.

6 0
2 years ago
Simplify the following expression.<br><br> √49^8
hoa [83]

Answer:

First calculate 49^8

Then take the square root of that answer.

Final answer is 5,764,801

7 0
3 years ago
6x−3y=5 y−2x=8 ​ How many solutions does the system have?
zhuklara [117]

No Solutions because there are too many = signs.

3 0
3 years ago
Read 2 more answers
Without a calculator, order the following expressions from least to greatest. 9, pie squared, 3 times pie??
Elden [556K]
We have 9, 9.86, 9.42
So in order from least to greatest it would be: 9, 3 times pi, pi squared
5 0
2 years ago
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