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kramer
4 years ago
5

If I round 2,420 to the nearest ten thousand

Mathematics
1 answer:
nikitadnepr [17]4 years ago
5 0

If I round 2,420 to the nearest ten thousand. Yet this number is lacking a digit or rather is incomplete.
Assuming that we add three zeros to the digit number thus becomes, 2,420,000 and we want to round it off to the nearest ten thousand it will be 2,420,000 the same digit.
But if we add only one zero to complete the digit, 24,200 the number becomes 20,000.



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Answer:

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Step-by-step explanation:

First, we need to recall the definition of \cos z when z is a complex number:

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Then,

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Now, recall the definition of the complex exponential:

e^{z}=e^{x+iy} = e^x(\cos y +i\sin y).

So,

e^{2i-3} = e^{-3}(\cos 2+i\sin 2)

e^{-2i+3} = e^{3}(\cos 2-i\sin 2) (we use that \sin(-y)=-\sin y).

Thus,

e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)

Now we group conveniently in the above expression:

e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2.

Now, substituting this equality in (I) we get

\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2.

Thus,

\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)

\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right].

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