This bifurcation is called a saddle-node bifurcation. In it, a pair of hyperbolic equilibria, one stable and one unstable, coalesce at the bifurcation point, annihilate each other and disappear.
<h3>What is a bifurcation equilibria?</h3>
- The mathematical study of changes in a family of curves' qualitative or topological structure, such as the integral curves of a family of vector fields or the solutions to a family of differential equations, is known as bifurcation theory.
- A bifurcation happens when a tiny, gradual change in a system's parameter values (the bifurcation parameters) results in an abrupt, "qualitative," or topological change in the system's behavior.
- This term is most frequently used to refer to the mathematical study of dynamical systems.
- Both continuous systems (represented by ordinary, delay, or partial differential equations) and discrete systems can experience bifurcations (described by maps).
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Answer: Virtual, upright and diminished.
Explanation:
A transparent material that focuses or diverges light is known as a lens. There are mainly two types of lens: concave lens and convex lens. Other lens can be made using combination of these two and plane one.
A concave lens is a diverging lens. It means the light from any real object after passing through this lens appears to diverge from the focus. A image formed by a diverging lens is virtual, upright and diminished.
Answer:
Increases
Explanation:
From Newton's second law:
F = ma
If F stays the same and m decreases, then a increases.
Therefore, the magnitude of the train's acceleration increases (the acceleration becomes more negative).
The amount of potential energy the block contains is 2,822.4 Joules
<u>Given the following data:</u>
- Height of platform = 24 meters.
We know that the acceleration due to gravity (g) of an object on planet Earth is equal to 9.8
.
To determine the amount of potential energy the block contains:
Mathematically, potential energy (P.E) is given by the formula;

Where:
- g is the acceleration due to gravity.
- h is the height of an object.
Substituting the parameters into the formula, we have;

Potential energy (P.E) = 2,822.4 Joules
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