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3 years ago

Find the first four common multiples for 3

Mathematics

1 answer:

Anna007 [38]3 years ago

6 0

The answer is 3 6 and 9

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According to astronomers what is a light year

Sindrei [870]

A unit of astronomical distance equivalent to the distance that light travels in one year, which is 9.4607 times 1012<span> km nearly 6 trillion miles.</span>

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3 years ago

Find e^cos(2+3i) as a complex number expressed in Cartesian form.

ozzi

Answer:

The complex number $e^{\cos(2+31)} = \exp(\cos(2+3i))$ has Cartesian form

$\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2)$ .

Step-by-step explanation:

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

$\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}$ .

Then,

$\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}$ . (I)

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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3 years ago

How do you solve 2y-7y=5

scZoUnD [109]

Answer:

$y=-1$

Step-by-step explanation:

1. Combine like terms

2y-7y = -5y

-5y=5

2. Divide by -5 and the answer is $y=-1$

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3 years ago

Sami asked 50 people which drinks they liked from tea, coffee and milk. All 50 people like at least one of the drinks 19 people

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3 years ago

Consider the function f(x)=−2/3x+5 . What is f(12) ? Enter your answer, as a simplified fraction, in the box.

sladkih [1.3K]

Answer:

Step-by-step explanation:

f(12)=-2/3(12)+5

f(12)=-8+5

f(12)=-3

3 0

3 years ago

Read 2 more answers