. The aim of this problem is to describe the automorphism group of an annulus, and in the process also answer the following question: when are two annuli conformally equivalent? The modulus of an annulus {z : a < |z − z0| < b} with inner radius a and outer radius b is defined to be 1 2π log b a . (a) Show that any conformal map from one annulus centred at the origin to another such annulus extends to a confor

step-by-step explanation:

hans did not square the 40-unit side; he merely multiplied it by 2.   incorrect.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.