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4 years ago

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What is scientific notation

2 answers:

Tatiana [17]4 years ago

8 0

Answer:

Scientific notation is way of writing very small or very large numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

GalinKa [24]4 years ago

5 0

Scientific notation is a way of expression really large or really small numbers.

For instance, 1000000 in scientific notation would be 1 x 10^6

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Use De Moivre's theorem to write the complex number in trigonometric form: (cos(3pi/5) + i sin (3pi/5))^3

docker41 [41]

By De Moivre's theorem,

$\left(\cos\dfrac{3\pi}5+i\sin\dfrac{3\pi}5\right)^3=\boxed{\cos\dfrac{9\pi}5+i\sin\dfrac{9\pi}5}$

We can stop here ...

# # #

... but we can also express these trig ratios in terms of square roots. Let $x=\dfrac\pi5$ and let $c=\cos x$ . Then recall that

$\cos5x=c^5-10c^3\sin^2x+5c\sin^4x$

$\cos5x=c^5-10c^3(1-c^2)+5c(1-2c^2+c^4)$

$\cos5x=16c^5-20c^3+5c$

On the left, $5x=\pi$ so that

$16c^5-20c^3+5c+1=(c+1)(4c^2-2c-1)^2=0$

Since $c=\cos\dfrac\pi5\neq1$ , we're left with

$4c^2-2c-1=0\implies c=\dfrac{1+\sqrt5}4$

because we know to expect $\cos x>0$ . Then from the Pythagorean identity, and knowing to expect $\sin x>0$ , we get

$\sin x=\sqrt{1-c^2}=\sqrt{\dfrac58-\dfrac{\sqrt5}8}$

Both $\cos$ and $\sin$ are $2\pi$ -periodic, so that

$\cos\dfrac{9\pi}5=\cos\left(\dfrac{9\pi}5-2\pi\right)=\cos\left(-\dfrac\pi5\right)=\cos\dfrac\pi5$

and

$\sin\dfrac{9\pi}5=\sin\left(-\dfrac\pi5\right)=-\sin\dfrac\pi5$

so that the answer we left in trigonometric form above is equal to

$\cos\dfrac\pi5-i\sin\dfrac\pi5=\boxed{\dfrac{1+\sqrt5}4+i\sqrt{\dfrac58+\dfrac{\sqrt5}8}}$

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3 years ago

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Arte-miy333 [17]

Answer:

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Step-by-step explanation:

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3 years ago

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zalisa [80]

The slope issssss 2

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3 years ago

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Let's make one thing clear. That thing you see in the mirror is you being garbage.

xenn [34]

Answer:

Nice roast

Step-by-step explanation:

Don’t be mean tho :(

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3 years ago

The endpoints of line segment RS are R(-2,-1), and S (2,3). Find the coordinates of the midpoint of line segment RS.

madam [21]

Midpoint coordinates are ( - 2 + 2) / 2 , (-1+3) / 2

= (0,1) Answer

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4 years ago