Question in attachment

a₁ = 3

Step-by-step explanation:

The sum to n terms of a geometric sequence is

=

where a₁ is the first term and r the common ratio

Here = 189 and r = 2, thus

= 189, that is

a₁( 64 - 1) = 189

63a₁ = 189 ( divide both sides by 63 )

a₁ = 3

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: