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3 years ago

1) How many different three-digit numbers divisible by 25 can be made with the

Mathematics

1 answer:

gladu [14]3 years ago

6 0

Answer:

It's B.

Step-by-step explanation:

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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,

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

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

5 0

2 years ago

What is the percent of decrease from 40 to 24?

dem82 [27]

Answer:

37.5 percent !!

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Can someone help me find the length of b of the unknown side in this triangle? Thanks! :)

creativ13 [48]

Answer: 4

Step-by-step explanation:

Using pythagoras theorem =>

b= $\sqrt{c^2-a^2$

b= $\sqrt{5^2-3^2}$

b= $\sqrt{25-9}$

b= $\sqrt{16}$

b=4

7 0

2 years ago

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Which answers show ways to make 5,036?

DerKrebs [107]

5,035+1=5,036. Idk the question issuing specific enough. There can be millions of ways to get 5,036.

3 0

3 years ago

Greatest common factor of 69 and 46

exis [7]

$Greatest\ common\ factor\ is\ the\ highest\ number\ by\ witch\ 69\ and\ 46\\can\ be\ divided\\\\
69:3\\
23:23\\\\46:2\\23:23
\\\\GCF=23\\\\Greatest\ common\ factor\ of\ 69\ and\ 46 \ is\ equal\ to\ 23.
$

4 0

3 years ago

Read 2 more answers