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ANEK [815]
3 years ago
7

Can you solve for y plz

Mathematics
1 answer:
vredina [299]3 years ago
8 0
Solve the top equation for x and then substitute that into the bottom equation and solve for y:
Top equation: subtract 4 from both sides to get x = y - 4
Substitution and simplify:
y = 4(y - 4) - 10
y = 4y - 16 - 10
y = 4y - 26
-3y = -26
y = 26/3 or 8 1/3 or 8.333 (those are all the same but in different forms)
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Convert the complex number z = 4 - 10i from rectangular form to polar form.​
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ANSWER

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

EXPLANATION

The polar form of a complex number ,

z = x + yi

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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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