MATH!! HELP PLEASE!?

Question

Please solve these problem. I need to pass it on tuesday!

1.In a finite sequence of real numbers, the sum of any three consecutive terms is negative and the sum of any seven consecutive terms is positive. Determine the maximum number of terms in the

sequence.

2. A circle is tangent to the coordinates axes. Its center lies in the fourth quadrant and is 2√ 2 units away from the origin. What is the point of intersection between the circle and the y-axis?

Answer 1

Dude its your homework figure it out.

Answer 2

Sorry bro, never took finite math.  Can't remember how to do 1.

2) 2√ 2 is the hypotnuse to the triangle with the points (0,0), (0, -X) and (X, -X), which is the center of the circle in the fourth quadrant.  If your teacher needs proof of this, draw it.  

***The axes are tangent to the circle, so the distance to the axes has to be equal by definition of a circle.  The axes are perpendicular by definition, and the lines from the center to the axes are perpendicular by definition of a tangent.  These four lines create a square.  The diagnal to any square = side*√ 2.

Therefore, Y intercept = (0,2)

Answer 3

1. The maximum number of terms in the sequence is 8. An example of an 8-term sequence of desired type is

3, 3, -7, 3, 3, -7, 3, 3,

2. ( 0, -2 )

The origin, the center of the circle. and the point of intersection between the circle and the y-axis form an isosceles right triangle with the hypotenuse of length 2√ 2 units.

Answer 4

1. I can't figure out the first one.

2. Answer is 2 units.