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3 years ago

3k - 5 = 20k what is k

Mathematics

1 answer:

Usimov [2.4K]3 years ago

5 0

K is whatever you want it to be

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Write each complex number in rectangular form. a. 2(cos(135)+i sin(135)) b. 3(cos(120))+i sin(120)) c. 5(cos(5pi/4)+i sin(5pi/4)

bagirrra123 [75]

$\bf r\left[ cos\left( \theta \right)+i\ sin\left( \theta \right) \right]\quad 
\begin{cases}
x=rcos(\theta )\\
y=rsin(\theta )
\end{cases}\implies 
\begin{array}{llll}
x&,&y\\
a&&b
\end{array}\implies a+bi\\\\
-------------------------------\\\\
2\left[ cos\left( 135^o\right)+i\ sin\left( 135^o\right) \right]\impliedby r=2\qquad \theta =135^o
\\\\\\
2\left( -\frac{\sqrt{2}}{2} \right)+i\ 2\left( \frac{\sqrt{2}}{2}\right)\implies -\sqrt{2}+\sqrt{2}\ i$

$\bf -------------------------------\\\\
3\left[ cos\left( 120^o\right)+i\ sin\left( 120^o\right) \right]\impliedby r=3\qquad \theta =120^o
\\\\\\
3\left( -\frac{1}{2} \right)+i\ 3\left( \frac{\sqrt{3}}{2}\right)\implies -\frac{3}{2}+\frac{3\sqrt{3}}{2}\ i$

$\bf \\\\
-------------------------------\\\\
5\left[ cos\left( \frac{5\pi }{4}\right)+i\ sin\left( \frac{5\pi }{4}\right) \right]\impliedby r=5\qquad \theta =\frac{5\pi }{4}
\\\\\\
5\left( -\frac{\sqrt{2}}{2} \right)+i\ 5\left( -\frac{\sqrt{2}}{2}\right)\implies -\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}\ i$

$\bf -------------------------------\\\\
4\left[ cos\left( \frac{5\pi }{3}\right)+i\ sin\left( \frac{5\pi }{3}\right) \right]\impliedby r=4\qquad \theta =\frac{5\pi }{3}
\\\\\\
4\left( \frac{1}{2} \right)+i\ 4\left( -\frac{\sqrt{3}}{2}\right)\implies \frac{1}{2}-\frac{\sqrt{3}}{2}\ i$

3 0

3 years ago

What is the radius of a circle with a area of 112 square inches

Ugo [173]

Answer:

$\displaystyle 5,9708213214...\:in.$

Step-by-step explanation:

$\displaystyle {\pi}r^2 = A \\ \\ \frac{{\pi}r^2}{\pi} = \frac{112}{\pi} \hookrightarrow \sqrt{35,650707253...} = \sqrt{r^2} \\ \\ \boxed{5,9708213214... = r}$

I am joyous to assist you at any time.

5 0

2 years ago

The standard form of the equation of a circle is (x−5)2+(y−6)2=1.

Crank

Answer:

(A) $x^2+y^2-10x-12y+60=0$

Step-by-step explanation:

The standard form of the equation of a circle is given as:

$(x-5)^2+(y-6)^2=1$

Simplifying the above given equation, we get

$x^2+25-10x+y^2+36-12y=1$

$x^2+y^2-10x-12y+36+25=1$

$x^2+y^2-10x-12y+61=1$

$x^2+y^2-10x-12y+60=0$

which is the required general form of the equation.

Hence, option A is correct.

3 0

3 years ago

Help ASAP will give brainly 9th grade math

KatRina [158]

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8 0

3 years ago

Solve by using the quadratic formula<br> x^2-4x=-2

atroni [7]

Answer:

x=2+ $\sqrt[]{2}$ or x= 2- $\sqrt[]{2}\\$

Step-by-step explanation:

6 0

3 years ago