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4 years ago

If I round 2,420 to the nearest ten thousand

1 answer:

5 0

If I round 2,420 to the nearest ten thousand. Yet this number is lacking a digit or rather is incomplete.
Assuming that we add three zeros to the digit number thus becomes, 2,420,000 and we want to round it off to the nearest ten thousand it will be 2,420,000 the same digit.
But if we add only one zero to complete the digit, 24,200 the number becomes 20,000.

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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

3 years ago

Match Term Definition Diameter A) a segment between two points on a circle that passes through its center Circumference B) a pie

Viefleur [7K]

The correct answer to this question is:

Diameter - B) a segment between two points on a circle that passes through its center radius

Circumference - F) the distance around a circle

Radius - C) Circle A and a line segment connecting points B and C which are on the circle.

secant - E) Circle A and a line segment connecting points B and C which are on the circle.

concentric circles - D) Two circles that share the same center.

arc - A) a piece of the circumference of a circle circumference.

5 0

4 years ago

Read 2 more answers

What is <img src="https://tex.z-dn.net/?f=%20%7B5%7D%5E%7B2%7D%20%20%2B%203%20%5Ctimes%2016" id="TexFormula1" title=" {5}^{2

enyata [817]

The answer 73 because you is supposed to use your order of operations so in other words your supposed to use PEMDAS

6 0

4 years ago

Find the product of what is shown

crimeas [40]

Answer:

3.64232057368

Step-by-step explanation:

To 2 decimal place=

3.64

8 0

3 years ago

10/21 divided by (-15/7)

Whitepunk [10]

Answer:

Find the reciprocal of the divisor

Reciprocal of

15/7 : 7/15

Now, multiply it with the dividend

So, 10/ 21 ÷ 15/7 = 10/21 × 7/15

= 10 × 7/ 21 × 15 = 70/ 315

After reducing the fraction, the answer is

2/9

4 0

3 years ago