The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r,θ) . Select the correct equation in polar coordinates below. x2+y2−4x=0

a.  r=4 sinθ
b. r=4 cosθ
c. r cos2θ=4 sinθ
d. r sin2θ=4 cosθ

Step-by-step explanation:

Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).

x = rcosθ and y = rsinθ.

Substituting the value of x and y in their polar form into the given expression we have;

x²+y²−4x=0

( rcosθ)²+( rsinθ)²-4( rcosθ) = 0

Expand the expressions in parenthesis

r²cos²θ+r²sin²θ-4rcosθ = 0

r²(cos²θ+sin²θ)-4rcosθ = 0

From trigonometry identity, cos²θ+sin²θ =1

The resulting equation becomes;

r²(1)-4rcosθ = 0

r²-4rcosθ = 0

Add 4rcosθ to both sides of the equation

r²-4rcosθ+4rcosθ = 0+4rcosθ

r² = 4rcosθ

Dividing both sides by r

r²/r = 4rcosθ/r

r = 4cosθ

Hence the correct equation in polar coordinates is r = 4cosθ

answer:

payment just for service  

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payment for service including tax

→

$

94.09

explanation:

service only with 20% tip  

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$

72.6

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$

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in the opening of the question the word 'service' is associated only with the pretax value.

the closing part of the question asks: how much did she pay for the  

service

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so technically the answer is  

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$

72.6

(

1

+

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=

$

87.12

however, the intention of the question provider may have been that your answer is to be  

$

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(

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=

$

94.09

to 2 decimal places.

'

payment just for service  

→

$

87.12

payment for service including tax

→

$

94.09

tony b

mar 21, 2017

answer:

trying to explain it another way

explanation:

service charge  

.

→

$

72.60

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20

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14.52

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add

$

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$

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