Create an equation with the indicated number of solutions.
1) infinitely many solutions: 2(x-1)+6x=)+2
2) one solution of x=1: 5x-(x-2)=
3) infinitely many solutions: -(x-8)+4x=+x

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camilacarrielh15

08.06.2021

Mathematics

In polar coordinates, we have

$x=r\cos\theta\implies\cos\theta=\dfrac xr$
$y=r\sin\theta\implies\sin\theta=\dfrac yr$

From this we can write

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac yr}{\frac xr}=\dfrac yx$

If $\theta=\dfrac{4\pi}3$ , then $\tan\theta=\sqrt$ , so we get

$\dfrac yx=\sqrt3\implies y=\sqrt3\,x$

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Create an equation with the indicated number of solutions. 1) infinitely many solutions: 2(x-1)+6x=)+2 2) one solution of x=1: 5x-(x-2)= 3) infinitely many solutions: -(x-8)+4x=+x