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3 years ago

1 dollar = 1.2 euros

Mathematics

1 answer:

MArishka [77]3 years ago

4 0

85 yen are equivalent to 1 euro ⇒ answer O

Step-by-step explanation:

The given is:

1 dollar = 1.2 euros
1 dollar = 102 yen

We need to find how many yens are equivalent to 1 euro

∵ 1 dollar = 1.2 euros

∵ 1 dollar = 102 yen

- Equate the two right sides of 1 dollar

∴ 1.2 euros = 102 yen

- To find 1 euro equals how many yen divide both sides by 1.2

∵ (1.2 ÷ 1.2) euros = (102 ÷ 1.2) yen

∴ 1 euro = 85 yen

85 yen are equivalent to 1 euro

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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,

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

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

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3 years ago

A piece of pie costs .10 and a cup of coffee costs .5. How much will 40 pieces of pie and 20 cups of coffee cost?

dybincka [34]

One pie costs 0.10
you are buying 40 pies so...
40 x 0.10 = $4

one cup of coffee costs 0.50
you are buying 20 coffee so...
20 x 0.50 = $10

$4 + $10 = $14

It costs $14 to buy 40 pieces of pie and 20 cups of coffee

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3 years ago

Which of these fraction shows how much interest the store charges each year?

Kamila [148]

The annual interest is 18% = 18/100 = ...
B. 9/50

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HELP. WILL GIVE BRAINLIEST, WHEN ANSWERED.

maxonik [38]

Answer:

√89 or 9.43 units is the distance between Sophia's house and library

Step-by-step explanation:

H (1 ,1) ⇒ House

L(6 , 9) ⇒ Library

Leg₁ = OH = 6 - 1 = 5 units

Leg₂ = OL = 9 - 1 = 8 units

<h3> Pythagorean theorem;</h3>

Hypotenuse² = leg₁² + leg₂²

= 5² + 8²

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= 89

hypotenuse = √89 units (radical form)

hypotenuse = 9.43 units

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2 years ago

At a coffee shop, the first 100 customers'

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1/20=0.05 or 5%

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