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Alekssandra [29.7K]
3 years ago
10

Solve: 1000 + 69 - 55 =

Mathematics
2 answers:
notka56 [123]3 years ago
8 0
The answer would be 1014


ziro4ka [17]3 years ago
7 0
You have to first add 1000 and 69 which would be 1069 then you subtract 55.
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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
Is y=2x + 1 a function
shepuryov [24]
Yes. It's a linear function.
4 0
3 years ago
What is this answer whoever could solve it is super smart
BigorU [14]

Answer: 3.19 feet.

Step-by-step explanation: 319 divided by 100 is 3.19

3 0
3 years ago
Factorise <br> a) (2+2) a) x2 -11x + 28 <br><br> b) 6x2 -5x – 4
Serga [27]

Answer:

6264

Step-by-step explanation:

(2+2)×2-11×+28 6×2

= 6264

3 0
2 years ago
Read 2 more answers
PLEASE HELP!!!!!!!!!!!! !
FinnZ [79.3K]
Sorry idk reeeeaaaaaallllllyyy wish I could help
4 0
3 years ago
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