Question

Write the equation -2x + 6y = 7 in polar form.

How do I do this? Please help!

Answer 1

oh no that is wrong sorry
that would be a line through the origin, and this one is not

Answer 2

let me see if i can do it with pencil and paper, might take a few

Answer 3

does \(P=r\cos(\theta -\phi)\) look familiar?

Answer 4

Yes, polar form.

Answer 5

so what i think you need is \(\phi\) and \(P\)

Answer 6

\[-2x + 6y = 7 \\
-2x+6y-7=0\]

Answer 7

correct me if i am wrong but i think you need \(\sqrt{2^2+6^2}=\sqrt{40}=2\sqrt{10}\) and then divide all by that

Answer 8

that gives
\[-\frac{x}{\sqrt{10}}+\frac{3}{\sqrt{10}}-\frac{7}{\sqrt{10}}=0\]

Answer 9

i might be off by a minus sign there, not sure

Answer 10

no, i think that might be right

Answer 11

That's what I did, but the answer I got wasn't one of my options.

My options are:

\[7\sqrt10=r \cos(\theta-108°)\]
\[\sqrt10/20=r \cos(\theta-108°)\]
\[7\sqrt10/20=r \sin(\theta-108°)\]
\[7\sqrt10/20=r \cos(\theta-108°)\]

Answer 12

ok good

Answer 13

evidently the angle is \(108\) because that is all your choices
here we have \(\tan(\phi)=3\) so \(\phi =\tan^{-1}(3)\) lets check that

Answer 14

ah damn in the wrong quadrant
\(180-71.57=108\) i guess if you round to the nearest degree

Answer 15

you sure it is not \(\frac{7}{\sqrt{10}}\) out front?

Answer 16

Yes, I got that too, but it's the value of P that I don't understand.

Answer 17

Yeah, I'm sure

Answer 18

oooooh i made a mistake i see it now

Answer 19

you divide by \(\sqrt{40}=2\sqrt{10}\) i cancelled the 2 for the x and y term, but also cancelled one for \(-7\) which was a mistake
it should be \(p=\frac{7}{2\sqrt{10}}\)

Answer 20

That's still not one of my options though :(

Answer 21

rationalize the denominator and get
\[\frac{7}{2\sqrt{10}}=\frac{7\sqrt{10}}{20}\]

Answer 22

now it is one of your options right?

Answer 23

Ohh I was plugging it into wolfram alpha wrong ahaha yes thank you so much!!

Answer 24

last option i believe is the right one