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4 years ago

Help me solve for 1,2,3,and 4 PLEASE

Mathematics

1 answer:

Brums [2.3K]4 years ago

3 0

1. $(-7,-3)$

2. $[5,\alpha )$

3. $(-4,-\alpha )$

4. $(-1,0)$

Explanation

a shaded circle in number line indicates that the number in the shaded point is also included in the interval. In the interval notation this limit is expressed using a square bracket.

A circle that is not shaded in a number line indicates that the number is not included in the interval. In interval notation a bracket is used to represent that point on the number line.

An arrow shows the extension to negative or positive infinity. The symbol $\alpha$ is used to represent infinity and is always included in bracket.

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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

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GaryK [48]

Answer:

Step-by-step explanation:

To solve, I converted the fraction to decimals

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4 years ago

Simplify. 3{[9(x-2)+7]-2[4(x+5)-36]}

Tcecarenko [31]

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((There has been a malfunction or this users account may have been deleted))).....))

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3 years ago

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I'll give brainlyiest to whoever answers right first.

alekssr [168]

Answer:

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Step-by-step explanation:

When finding the slope intercept form using 2 points, we do the following.

y=mx+b (Slope intercept from)

y=7x+b (7 is slope)

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7=7(1)+b

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3 years ago

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