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3 years ago

Each of 16 students will give a 1 1/5 minute speech in English class.

Mathematics

1 answer:

Mice21 [21]3 years ago

8 0

Answer:

19 1/5

Step-by-step explanation:

1 1/5 * 16

6/5 * 16

96/5

19 1/5

You might be interested in

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

a rectangle has an area of 34 sqaure feet. A larger rectangle has an area of 124 sqaure feet. what is the percent increase of th

amid [387]

Answer:

<u>The difference in areas:</u>

124 - 34 = 90 square feet

<u>Percent increase:</u>

90/34*100% = 264.71%

5 0

2 years ago

an equation for loudness L, in decibels, is L= 10 log R, where R is the relative intensity of the sound. solve 120= 10 log R to

andrew-mc [135]

sorry this question is to hard for me

3 0

2 years ago

Is that the correct order?

wlad13 [49]

Answer:

Yes that a good answer...

8 0

2 years ago

can someone please help me with number 12? there’s only two options and you can see them in the picture.

nataly862011 [7]

Answer:

Step-by-step explanation:

Because it can't be a because if you wanna get P it is 20/16 not 1 /12

7 0

2 years ago