Question

Barbie is analyzing a circle, y2 + x2 = 16, and a linear function g(x). Will they intersect?

x g(x)
0 6
1 3
2 0

Answer 1

@mathmate

Answer 2

Yes, at positive x-coordinates or zero

Yes, at negative x-coordinates or zero

Yes, at negative and positive x-coordinates or zero

No, they will not intersect

Answer 3

@mathmate

Answer 4

@mathmale

Answer 5

The circle is centred at the origin, with a radius of 4.
One of the points of the line (2,0) is inside the circle.
So the line must intersect the circle.

Answer 6

at first you have to decide if they intersect or not. trick is to decide the distance of the points (x,g(x)) from the origin. so you know (0,6) is out of the circle but (1,3) is inside the circle. That is enough to decide that those two intersect

Answer 7

ok

Answer 8

Also, the point (0,6) is outside the circle, and (2,0) is inside, so there cannot be any intersection when x<0.

Answer 9

ok

Answer 10

but there is (1,3)

Answer 11

(1,3) has x>0, so that's not a problem.
All you need to know is if there is any intersection for x<0.

Answer 12

ok so there is an intersection at th postive x intercept

Answer 13

There are two intersections, both with positive x-coordinates.

Answer 14

so then it will be A again

Answer 15

@mathmate

Answer 16

yes.

Answer 17

Is it A again

Answer 18

It took me a while to understand the statement, actually it was trying to say
\[x\ge0\]

Answer 19

so is It A again

Answer 20

@mathmate its A again right?

Answer 21

Yes it is A again.

Answer 22

thanks

Answer 23

can you help me with one more