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max2010maxim [7]
3 years ago
13

Convert the complex number z = 4 - 10i from rectangular form to polar form.​

Mathematics
1 answer:
mrs_skeptik [129]3 years ago
6 0

ANSWER

r = 2 \sqrt{29} ( \cos(292 \degree)  + \sin(292 \degree))

EXPLANATION

The polar form of a complex number ,

z = x + yi

is given by:

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

where

r =  \sqrt{ {x}^{2} +  {y}^{2}  }

The given complex number is:

z = 4 - 10i

r =  \sqrt{ {4}^{2}  +  {( - 10)}^{2} }

r =  \sqrt{16  + 100}

r =  \sqrt{116}  = 2 \sqrt{29}

And

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

\theta=  \tan^{ - 1}(\frac{  - 10}{4} )

\theta=  292 \degree

Hence the polar form is :

r = 2 \sqrt{29} ( \cos(292 \degree)  + \sin(292 \degree))

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Volume of cone: pi * r^2 * h/3
Given volume, height

942in^3 = 3.14 * r^2 * 9/3
942in^2 = r^2 * 9.42
Divide by 9.42
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Cannot be negative so...

Solution: radius is 10 in.
8 0
2 years ago
Read 2 more answers
Help please show step by step
kobusy [5.1K]

Answer:

82.5 sq ft

Step-by-step explanation:

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7 0
3 years ago
Is this a function?<br> (4,12)<br> (4,15)<br> (5,18)<br> (5,21)<br> (6,24)
cluponka [151]

Answer:

No this is not a function.

Step-by-step explanation:

This is not a function because some of the x-values repeat, which is not how a function works. For this to be a function, each x-value would have to be different. In this case, the 4 and 5 repeat in the x-values.

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8 0
3 years ago
Rate and Ratio Sipho paid 605,50 for 70litres of petrol.What did the petrol cost per litre.​
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6 0
2 years ago
Can I Get A Little Help Here?
Musya8 [376]
Hey there :)

We know the formula for simple interest is 
I = prt
{ The picture includes what each stands for }

Lehena:
Initial amount = $100
Interest rate = 2.5% = \frac{2.5}{100} = 0.025
Time = 3 years
I = ( 100 )( 0.025 )( 3 )
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Total = $100 + $7.5 = $107.5

Marty:
Initial amount = $100
Interest rate = 2% = \frac{2}{100} = 0.02
Time = 3 years
I = ( 100 )( 0.02 )( 3 ) 
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Total = $100 + $6 = $106

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= 107.5 - 106
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Your answer will be option B) $1.50

7 0
3 years ago
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