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3 years ago

Express these fractions and mixed numbers as a percent.

1 answer:

4 0

Okay so you start with 1/3. Fractions are just a fancy way of saying (in this case) 1 divided by 3. And if you do that you'll get .3333. After that to make it a percent you just move the decimal spot in front of the 3 over two places, getting 33.33%. With mixed numbers it's just one more step. So in this case 2 1/5 you would have to make it a normal fraction first so I got 11/5ths and here's how I got it. 2 1/5. Multiply the denominator (5) with 2. You get 10. Then add the numerator (1) to get 11. Tack on the 5 and you get 11/5. To make this a percent just do the same thing as the normal fractions... 11 divided by 5 to get 2.2. Move the decimal two places to the right to get 220%. Try the rest on your own and if you get confused ask... :)

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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

The Langleys spend 40% of their monthly income on rent. If their monthly income is $4,400, how much money do the Langleys spend

oksian1 [2.3K]

100%=$4400

40% $=?

40 ×4400/100

$1760

3 0

3 years ago

How do I factorise 4 + 6x. Please show working out as well as answer, thanks!

Vaselesa [24]

Answer:

2(2 + 3x).

Step-by-step explanation:

The greatest common factor of 4 and 6x is 2, so we divide by 2 to get the factors:

4 / 2 = 2 and 6x / 2 = 3x so:

4 + 6x

= 2(2 + 3x).

8 0

3 years ago

a triangle has one leg of 32 inches and one leg of 18 inches. For the triangle to be a right triangle, which best represents the

scZoUnD [109]

You take the square roots √18²+32² = 36.7
Hope this helps.

6 0

3 years ago

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?

zlopas [31]

Answer:

a b

Step-by-step explanation:

3 0

3 years ago