A sound engineer uses a cardioid microphone to record a musical performance. The microphone records sounds according to the equation r = 12 + 12sin(θ), where r is measured in meters. What does the sum of the constant, 12, and the coefficient, 12, in the equation represent?

a) The maximum possible distance between the performer and microphone
b) The minimum possible distance between the performer and microphone
c) One half the maximum possible distance between the performer and microphone
d) One half the minimum possible distance between the performer and microphone

A

Step-by-step explanation:

Trust

step-by-step explanation:

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.