Help me on number four and six please

Mathematics

1 answer:

oee [108]3 years ago

3 0

For number six it's D

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Please solve 108 = 2X-4(2X-9)

Fynjy0 [20]

108=2x-4(2x-9)
108=2x-8x+36
108=-6x+36
-36 -36
72=-6x
72/-6=-6x/-6
-12=x

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2 years ago

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
$z^3 = 125 [\cos 270^{\circ} + i \sin 270^{\circ} ]$

6 0

3 years ago

If you have 20 dollars and you you need to give your friend 5 dollars out of that, how much money will you have left

notsponge [240]

Answer: 15 dollars
20 -5 = 15

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3 years ago

In 2006, the population of a country was 40.2 million people. From 2006 to 2050 comma the country's population is expected to

Hatshy [7]

You can figure the remaining percentage in 2050 and calculate using that, or you can figure the amount of population that will be lost and subtract that from the 2006 value.

<u>First method</u>: The remaining population will be 100% - 5.8% = 94.2% of that in 2006. 0.942×40.2 million ≈ 37.9 million

<u>Second method</u>: 5.8% of 40.2 million is about 2.3 million, so the remaining population will be 40.2 - 2.3 = 37.9 million

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2 years ago

(−9, 9) (i) find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π.

Kisachek [45]

Tan ⊕ 9/-9 = -1 so ⊕ = 3π/4

r = √(9^2+(-9)^2) = 12.73

Answer is (12.73, 3π/4)

8 0

3 years ago