Find the center radius of the circle x^2 + y^2 + 3/4x + 5/3y - 1/2 = 0

(-3/8, -5/6) ; √(769)/24  Choice B

Step-by-step explanation:

Convert this to  standard form   ( (x - a)^2 + (y - b)^2 = r^2  where a,b is the centre and r = radius) :-

x^2 + y^2 + 3/4 x + 5/3 y - 1/2 = 0

x^2 + 3/4 x + y^2 + 5/3 y  = 1/2

(x + 3/8)^2 - (3/8)^2 + ( y + 5/6)^2 - (5/6)^2 = 1/2

( x + 3/8)^2 + ( y + 5/6)^2 = 1/2 + 9/64 +  25/36

( x + 3/8)^2 + ( y + 5/6)^2 =  769/576

So comparing this with the above standard from :-

center = (-3/8, -5/6) and radius is sqrt (769/576)  = sqrt 769 / 24

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

b

step-by-step explanation: