Both is the answer to the problem
Answer: y is less than or equal to -1
How?
The graphs highest value it will ever reach, range wise, is -1. Therefore it isnt 0, or all real numbers.
The reason why it is -1 and not -2 is because the curve hits -1. Sure, -2 is included in the range, but y is less than or equal to -1 INCLUDES -2
:)
y-intercept: Let x = 0 and solve for y:
(x-1)^2 + (y-2)^2 = 10 => (-1)^2 + y^2 - 4y + 4) = 10
=> 1 + y^2 - 4y + 4 = 10, or y^2 - 4y -5 = 0
The solutions of this quadratic are y = 5 and y = -1.
Thus, the y-intercepts are (0, 5) and (0, -1).
Now find the x-intercepts: Let y = 0 and solve the resulting equation for x:
(x-1)^2 = 10 - (-2)^2, or (x-1)^2 = 10 - 4 = 6.
Taking the sqrt of both sides, x - 1 = plus or minus sqrt(6), or:
x = 1 +√6 and x = 1 - √6, so that the x-intercepts
are (1+√6, 0) and (1-√6, 0).
There could be problems like there is a light which would flicker in every 7 seconds and there is another one which would flicker in every 8 seconds. So, how many times would they flicker until they would flicker at the same time?
