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blagie [28]
3 years ago
14

Given z1 = -3

Mathematics
1 answer:
trasher [3.6K]3 years ago
8 0

Answer:

See explanation

Step-by-step explanation:

The given complex number are:

z_1=-3\sqrt{3}+3i

and

z_2=6\cos 150\degree+6i\sin 150\degree

When we rewrite z_1=-3\sqrt{3}+3i in complex form, we obtain;

z_1=r(\cos \theta+i\sin \theta)

where

r=\sqrt{(-3\sqrt{3})^2+3^2 }=\sqrt{36}=6

and

\theta=tan^{-1}(\frac{y}{x})

\implies \theta=tan^{-1}(\frac{-3\sqrt{3}}{3})=150\degree

Hence,

z_1=6(\cos 150\degree+i\sin 150\degree)

z_1=6\cos 150\degree+6i\sin 150\degree

Hence

z_1=z_2

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A lab technician is dividing a cell that has a diameter of 4.32×10^-4 millimeters. Each of the new cells has a diameter measurin
RideAnS [48]

Answer:

2.16 \times  {10}^{ - 4}

Step-by-step explanation:

The lab technician is dividing a cell that has a diameter of

4 .32 \times  {10}^{ - 4}

The new cells has a diameter that is half of the diameter of the original cell.

The diameter of the new cell is given as:

\frac{4.32 \times  {10}^{ - 4} }{2}

Rewrite the numerator in standard notation:

\frac{0.000432}{2}

= 0.00216

We rewrite in scientific notation to obtain:

2.16 \times  {10}^{ - 4}

3 0
3 years ago
Which table represents the graph of a logarithmic function in the form y=log3x when b>1?
alex41 [277]

Answer:

<u><em>The satisfied table of the given function</em></u>y = log_{b} (x)<u><em></em></u>

<em>x                    1/8            1/4             1/2              1             2</em>

<em>y                    -3                 -2            -1               0               1</em>

<em></em>

Step-by-step explanation:

<u><em>Explanation</em></u> :-

Given logarithmic function y = log_{b} (x)   if b >1

Given first table

i)

put x = \frac{1}{8}     given b > 1 so we can choose b = 2

y = log_{2} (\frac{1}{8} )

y = log_{2} (2^{-3}  )

we will apply logarithmic formula

log x ⁿ = n log (x)

y = log_{2} (2^{-3}  ) = -3 log_{2} (2) = -3 (1) = -3

<em>y = -3</em>

<em>ii)</em>

<em>put x = </em>\frac{1}{4}<em>     given b > 1 so we can choose b = 2</em>

<em></em>y = log_{2} (\frac{1}{4} )<em></em>

<em></em>y = log_{2} (2^{-2}  )<em></em>

we will apply logarithmic formula

log x ⁿ = n log (x)

y = log_{2} (2^{-2}  ) = -2 log_{2} (2) = -2 (1) = -2

<em>y = -2</em>

<em>iii) </em>

<em>put x = </em>\frac{1}{2}<em>     given b > 1 so we can choose b = 2</em>

<em></em>y = log_{2} (\frac{1}{2} )<em></em>

y = log_{2} (2^{-1}  )

<em>we will apply logarithmic formula </em>

<em>log x ⁿ = n log (x)</em>

y = log_{2} (2^{-1}  ) = -1 log_{2} (2) = - (1) = -1

<em>y = -1</em>

<em>iv) </em>

<em>put x = 1     given b > 1 so we can choose b = 2</em>

<em></em>y = log_{2} (1 )<em> = 0</em>

<em>y = 0</em>

<em>v) </em>

<em>put x = </em>2<em>     given b > 1 so we can choose b = 2</em>

y = log_{2} (2 )

<em>y = 1</em>

<em></em>

<u><em>Final answer:-</em></u>

<u><em>The satisfied table of the given function</em></u>

<em>x                    1/8            1/4             1/2              1             2</em>

<em>y                    -3                 -2            -1               0               1</em>

<em></em>

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TiliK225 [7]

Answer:

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Step-by-step explanation:

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3 years ago
Reuben bought a desktop computer and a laptop computer. Before finance charges, the laptop cost $150 more than the desktop. He p
cupoosta [38]
Same case as Pablo's, more or less.

a = price for the desktop

b = price for the laptop

we know the laptop is 150 bucks more than the desktop,  b = a + 150.

how much is 7% of a?  (7/100) * a, 0.07a.

how much is 9.5% of b?  (9.5/100) * b, 0.095b.

total interests for the financing add up to 303, 0.07a + 0.095b = 303.

\bf \begin{cases}&#10;\boxed{b}=a+150\\&#10;0.07a+0.095b=303\\&#10;----------\\&#10;0.07a+0.095\left(\boxed{a+150}  \right)=303&#10;\end{cases}&#10;\\\\\\&#10;0.07a+0.095a+14.25=303\implies 0.165a=288.75&#10;\\\\\\&#10;a=\cfrac{288.75}{0.165}\implies a=1750

how much was it for the laptop?  well b = a + 150.
8 0
3 years ago
How many sides do 4 hexagons, 1 octagon, and 5 dodecagons have in all?
Vladimir79 [104]
Hexagon = 6 sides = 6 x 4 = 24 

Octagon = 8 sides = 8

Dodecagons = 12 x 5 = 60

24 + 8 + 60 =  92 IN TOTAL 
5 0
3 years ago
Read 2 more answers
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