check my anwsers please.

How do we detect black holes?
I think you observe their gravitational influence on things around them
Is that correct?

Respectively, Einstein's special theory of relativity and his general theory of relativity replace Newton's theory whenever...?

I think its when the speed is very large and the gravitational force is very large.

Is that correct?

What would happen to your weight if you were to climb to the top of a mountain?
It would decrease, right?

Let's go through each question and check your answers:

1. How do we detect black holes?
You mentioned observing their gravitational influence on things around them, and that is correct. One way to detect black holes is by observing the motion of nearby objects, such as stars or gas, which can be influenced by the strong gravitational pull of the black hole.

2. Respectively, Einstein's special theory of relativity and his general theory of relativity replace Newton's theory whenever...?
You mentioned that it happens when the speed is very large and the gravitational force is very large. While that is partially correct, let me provide a more detailed explanation. Einstein's special theory of relativity replaces Newton's theory when the objects are moving at speeds close to the speed of light or when the gravitational forces are weak. On the other hand, his general theory of relativity replaces Newton's theory in the presence of strong gravitational forces, such as around massive objects like black holes or during extreme cosmic events.

3. What would happen to your weight if you were to climb to the top of a mountain?
You mentioned that your weight would decrease, and that is correct. As you climb to higher altitudes, away from the center of the Earth, your distance from the Earth's center increases. As a result, you would experience a slightly weaker gravitational pull, leading to a decrease in weight.

Overall, your answers are mostly correct. Well done!