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2 years ago

6.6 x 1021 in standard notation

Mathematics

1 answer:

Gre4nikov [31]2 years ago

5 0

Answer:

6,600,000,000,000,000,000,000

Step-by-step explanation:

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Evaluate the expression: 231 - g for g = 17 .

nlexa [21]

Answer:

kuyky

Step-by-step explanation:

kmjkfhjmk

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2 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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2 years ago

It takes 2 workers 6 days to paint a mansion. How many days would it take 4

marishachu [46]

Answer:

2 workers = 6 days

4 workers = 3 days

Step-by-step explanation:

If it takes 2 workers 6 days, if you seep up the process with 4 workers, you would divide the days by 2 because you multilpied the workers by 2. So, it would take 3 days with 4 workers. I hope that makes sence.

4 0

2 years ago

The admission fee at an amusement park is $2.00 for children and $6.80 for adults. On a certain day, 388 people entered the park

san4es73 [151]

Answer: 188 children and 200 adults were admitted

Step-by-step explanation:

Let x represent the number of children that were admitted.

Let y represent the number of adults that were admitted.

On a certain day, 388 people entered the park. It means that

x + y = 388

The admission fee at the amusement park is $2.00 for children and $6.80 for adults. The admission fees collected on that day totaled $1736. It means that

2x + 6.8y = 1736- - - - - - - - - - 1

Substituting x = 388 - y into equation 1, it becomes

2x + 6.8y = 1736

2(388 - y) + 6.8y = 1736

776 - 2y + 6.8y = 1736

- 2y + 6.8y = 1736 - 776

4.8y = 960

y = 960/4.8

y = 200

x = 388 - y = 388 - 200

x = 188

4 0

2 years ago

Estimate the amount of tip to include if you want to leave a 20% tip on a Lyft ride of<br> $8.

tankabanditka [31]

Answer:

1.6$

Step-by-step explanation:

first you multiply 8 with 20 and then divide it with 100

you will get the answer of 1.6$

6 0

2 years ago