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3 years ago

N ÷ 10 exponent 2 = 0.123(Help please)

Mathematics

2 answers:

slamgirl [31]3 years ago

7 0

Answer:

n = 12.3

Step-by-step explanation:

Ilia_Sergeevich [38]3 years ago

4 0

Answer:

n = 12.3

Step-by-step explanation:

I'm assuming we're looking for n, to find it, we need to isolate it.

Our equation will be solved through PEMDAS :

Parenthesis

Exponent

Multiply/Divide

Add/Subtract

n / 10^2 = 0.123

Get rid of the exponent by applying it to 10,

10^2 = 100

n/100 = 0.123

Now to get rid of the division, multiply the denominator (100) to both sides.

n/100 * 100 = 0.123 * 100

n = 12.3

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Integration by Parts Evaluate e-2x cos(2x) dx.

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Let

$I = \displaystyle \int e^{-2x} \cos(2x) \, dx[/]texIntegrate by parts:[tex]\displaystyle \int u \, dv = uv - \int v \, du$

with

$u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \cos(2x) \, dx \implies v = \dfrac12 \sin(2x)$

Then

$\displaystyle I = \frac12 e^{-2x} \sin(2x) + \int e^{-2x} \sin(2x) \, dx + C$

Integrate by parts again, this time with

$u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \sin(2x) \, dx \implies v = -\dfrac12 \cos(2x)$

so that

$\displaystyle I = \frac12 e^{-2x} \sin(2x) - \frac12 e^{-2x} \cos(2x) - \int e^{-2x} \cos(2x) \, dx + C\\\\ \implies I = \frac{\sin(2x)-\cos(2x)}{2e^{2x}} - I + C \\\\ \implies 2I = \frac{\sin(2x) - \cos(2x)}{2e^{2x}} + C \\\\ \implies I = \boxed{\frac{\sin(2x) - \cos(2x)}{4e^{2x}} + C}$