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mash [69]
3 years ago
12

What is the equation of the line that is parallel to the given line and passes through the given point?

Mathematics
2 answers:
gogolik [260]3 years ago
7 0

Answer:

is there a multiple choice to this

Lynna [10]3 years ago
6 0

Answer:

y= -4

Step-by-step explanation:

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Express the complex number in trigonometric form -6 + 6sqrt3i
marusya05 [52]
\large\begin{array}{l}\\\\ \textsf{This is a complex number in }\mathsf{a+bi}\textsf{ form:}\\\\ \mathsf{z=-6+6\sqrt{3}\,i}\\\\ \textsf{where }\mathsf{a=-6~~and~~b=6\sqrt{3}.} \end{array}


\large\begin{array}{l}\\\\ \bullet~~\textsf{1}\mathsf{^{st}}\textsf{ step: Find the absolute value of z (complex modulus of z):}\\\\ \mathsf{|z|=\sqrt{a^2+b^2}}\\\\ \mathsf{|z|=\sqrt{(-6)^2+(6\sqrt{3})^2}}\\\\ \mathsf{|z|=\sqrt{36+36\cdot 3}}\\\\ \mathsf{|z|=\sqrt{36\cdot 108}}\\\\ \mathsf{|z|=\sqrt{144}}\\\\ \mathsf{|z|=12} \end{array}


\large\begin{array}{l}\bullet~~\textsf{2}\mathsf{^{nd}}\textsf{ step: Find the argument }\mathsf{\theta}\textsf{ of z:}\\\\ \mathsf{arg(z)=\theta}\\\\ \textsf{is an angle that satisfies the following conditions:}\\\\ \begin{cases} \mathsf{cos\,\theta=\dfrac{a}{|z|}=\dfrac{a}{\sqrt{a^2+b^2}}}\\\\ \mathsf{sin\,\theta=\dfrac{b}{|z|}=\dfrac{b}{\sqrt{a^2+b^2}}} \end{cases}\qquad\quad-\pi


\large\begin{array}{l}\textsf{For }\mathsf{z=-6+6\sqrt{3}\,i,}\\\\ \begin{cases} \mathsf{cos\,\theta=\dfrac{-6}{12}=-\,\dfrac{1}{2}}\\\\ \mathsf{sin\,\theta=\dfrac{6\sqrt{3}}{12}=\dfrac{\sqrt{3}}{2}} \end{cases}\\\\\\ \textsf{Since}\\\\ \mathsf{cos\,\theta0,}\\\\ \theta\textsf{ lies in the 2}\mathsf{^{nd}}\textsf{ quadrant.}\\\\\\\textsf{Therefore,}\\\\ \mathsf{\theta=\dfrac{2\pi}{3}~rad~~(120^\circ)} \end{array}


\large\begin{array}{l}\bullet~~\textsf{3}\mathsf{^{rd}}\textsf{ step: Express z in the trigonometric form:}\\\\ \begin{array}{rcl} \mathsf{z}&\!\!=\!\!&\mathsf{|z|\cdot (cos\,\theta+i\,sin\,\theta)}\\\\ \mathsf{-6+6\sqrt{3}\,i}&\!\!=\!\!&\mathsf{12\cdot \left(cos\, \dfrac{2\pi}{3}+i\,sin\,\dfrac{2\pi}{3}\right)\qquad\quad\checkmark} \end{array} \end{array}


If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2154167


\large\textsf{I hope it helps.}


Tags: <em>complex number trigonometric form trig absolute value modulus argument angle</em>

4 0
3 years ago
What steps do I take to solve y+2&gt;1/2-2 and the solution
kakasveta [241]
<span>y+2>1/2-2 looks a little strange.  Is it OK to combine the last 2 terms?

</span><span>y+2> -3/2

Then y > -2 - 3/2, or y > -7/2.  y must be greater than -7/2, greater than -3.5.</span>
7 0
3 years ago
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