Explain the multiplication rule for independent events

Mathematics

1 answer:

guapka [62]3 years ago

5 0

Probabilities for two events to the probability that they both occur

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Find [5(cos 330 degrees + I sin 330 degrees)]^3

earnstyle [38]

Given a complex number in the form:
$z= \rho [\cos \theta + i \sin \theta]$
The nth-power of this number, $z^n$ , can be calculated as follows:

- the modulus of $z^n$ is equal to the nth-power of the modulus of z, while the angle of $z^n$ is equal to n multiplied the angle of z, so:
$z^n = \rho^n [\cos n\theta + i \sin n\theta ]$
In our case, n=3, so $z^3$ is equal to
$z^3 = \rho^3 [\cos 3 \theta + i \sin 3 \theta ] = (5^3) [\cos (3 \cdot 330^{\circ}) + i \sin (3 \cdot 330^{\circ}) ]$ (1)
And since
$3 \cdot 330^{\circ} = 990^{\circ} = 2\pi +270^{\circ}$
and both sine and cosine are periodic in $2 \pi$ , (1) becomes
$z^3 = 125 [\cos 270^{\circ} + i \sin 270^{\circ} ]$

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4 years ago

Bunyan Farm sells 3 pound and 5 pound bags of onions. The Tuesday morning delivery consists of 34 bags weighing 122 pounds. How

Sergio [31]

<span>24 3-pound bags(72 pounds) and 10 5-pound bags(50 pounds). 72+50 = 122 pounds, 24+10 bags = 34 bags</span>

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3 years ago

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What is the y-intercept of these two functions and how do you calculate it? Thank you!!!! (15 points)

Illusion [34]

5 is the y intercept my good sir

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