Rewrite the rectangular equation x^2+y^2-8y=0 as a polar equation

Step-by-step explanation:

We'll use the following identities:

r = √(x2 + y2), from which we also have r2 = x2 + y2

y = r*sinθ

First, let's re-write your equation:

r = 8*sin(θ).  Multiply both sides by r:

r2 = 8r sin(θ)

Now, we'll use substitute using the identities:

x2 + y2 = 8y

Re-arrange and complete the square:

x2 + y2 - 8y = 0

x2 + (y-4)2 - 16 = 0

x2 + (y-4)2 = 16

This represents a circle with center (0,4), and radius 4.

Step-by-step explanation:

sorry if it wrong

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: