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Anarel [89]
3 years ago
13

What the place value of the digit 3 in the number: 252.073

Mathematics
1 answer:
MariettaO [177]3 years ago
6 0
1000 place because the 0 in the tenths place and 7 in the hundredths and the 3 in thousands
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Sin(4x) in the term of just x<br> Please help!!
Nina [5.8K]

I think you mean in terms of \sin(x)?

Recall Euler's identity

e^{ix} = \cos(x) + i \sin(x)

and de Moivre's theorem

\left(e^{ix}\right)^n = \left(\cos(x) + i \sin(x)\right)^n = \cos(nx) + i \sin(nx) = e^{inx}

where i=\sqrt{-1}.

It follows that

\sin(4x) = \mathrm{Im}\left(\cos(x) + i \sin(x)\right)^4

By the binomial theorem, expanding the right side gives

\cos^4(x) + 4i \cos^3(x) \sin(x) - 6\cos^2(x) \sin^2(x) - 4i \cos(x) \sin^3(x) + \sin^4(x)

and so

\sin(4x) = 4\cos^3(x) \sin(x) - 4 \cos(x) \sin^3(x)

We can factorize this as

\sin(4x) = 4 \cos(x) \sin(x) \left(\cos^2(x) - \sin^2(x)\right)

and using the Pythagorean identity

\cos^2(x)+\sin^2(x) = 1 \implies \cos(x) = \pm \sqrt{1-\sin^2(x)}

this reduces to

\sin(4x) = \pm 4 \sqrt{1-\sin^2(x)} \sin(x) (1 - 2 \sin^2(x))

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In a class, 42 students, there are 8 more boys than girls write and solve a system of 3 equations
zhenek [66]

Answer:

x = 17

Step-by-step explanation:

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x = 17            



i hope this helps!  you don't need the 2x = 42 - 8 to be an equation      ;)

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Answer:

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Step-by-step explanation:

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