Just did a specific one of these; let's do the general case.
The point nearest the origin is (a,b).
The line from the origin through the point is
![bx - ay = 0](https://tex.z-dn.net/?f=bx%20-%20ay%20%3D%200)
The line we seek is perpendicular to this one. We swap the coefficients on x and y, negating one, to get the perpendicular family of lines. We set the constant by plugging in the point (a,b):
![ax + by = a^2 + b^2](https://tex.z-dn.net/?f=ax%20%2B%20by%20%3D%20a%5E2%20%2B%20b%5E2)
![ax + by -( a^2 + b^2) = 0](https://tex.z-dn.net/?f=ax%20%2B%20by%20-%28%20a%5E2%20%2B%20b%5E2%29%20%3D%200)
That's standard form; let's plug in the numbers:
![4 x - 4 y - 32 = 0](https://tex.z-dn.net/?f=4%20x%20-%204%20y%20-%2032%20%3D%200%20)
![x - y - 8 = 0](https://tex.z-dn.net/?f=%20x%20-%20y%20-%208%20%3D%200)
Answer:
what are you asking?
Step-by-step explanation:
Event A - roll a 6-number cube
Event B - flip a coin
*Independent events *not mutually exclusive events
Both events are independent and not mutually exclusive.
Independent event means that one can happen without relying on the outcome of the other one.
Not mutually exclusive event means that both can happen at the same time.
Answer: B
The series converges because it has a sum of 4.
Step-by-step explanation: