Absolute value equations Video transcript So we're asked to solve for x, and we have this equation with absolute values in it. So it's 4 times the absolute value of x plus 10 plus 4 is equal to 6 times the absolute value of x plus 10 plus And at first, this looks really daunting, but the key is to just solve for this absolute value expression and then go from there. Let me just rewrite it so that the absolute value expression really jumps out.
Quantum equation predicts universe has no beginning February 9, by Lisa Zyga, Phys. Note on the left the dramatic expansion not to scale occurring in the inflationary epoch, and at the center the expansion acceleration.
The scheme is decorated with WMAP images on the left and with the representation of stars at the appropriate level of development. The model may also account for dark matter and dark energy, resolving multiple problems at once.
The widely accepted age of the universeas estimated by general relativityis In the beginning, everything in existence is thought to have occupied a single infinitely dense point, or singularity.
Only after this point began to expand in a "Big Bang" did the universe officially begin. Although the Big Bang singularity arises directly and unavoidably from the mathematics of general relativity, some scientists see it as problematic because the math can explain only what happened immediately after—not at or before—the singularity.
Ali and coauthor Saurya Das at the University of Lethbridge in Alberta, Canada, have shown in a paper published in Physics Letters B that the Big Bang singularity can be resolved by their new model in which the universe has no beginning and no end.
Old ideas revisited The physicists emphasize that their quantum correction terms are not applied ad hoc in an attempt to specifically eliminate the Big Bang singularity. Their work is based on ideas by the theoretical physicist David Bohm, who is also known for his contributions to the philosophy of physics.
Starting in the s, Bohm explored replacing classical geodesics the shortest path between two points on a curved surface with quantum trajectories.
Raychaudhuri was also Das's teacher when he was an undergraduate student of that institution in the '90s. Using the quantum-corrected Raychaudhuri equation, Ali and Das derived quantum-corrected Friedmann equations, which describe the expansion and evolution of universe including the Big Bang within the context of general relativity.
Although it's not a true theory of quantum gravitythe model does contain elements from both quantum theory and general relativity. Ali and Das also expect their results to hold even if and when a full theory of quantum gravity is formulated.
No singularities nor dark stuff In addition to not predicting a Big Bang singularity, the new model does not predict a "big crunch" singularity, either. In general relativity, one possible fate of the universe is that it starts to shrink until it collapses in on itself in a big crunch and becomes an infinitely dense point once again.
Ali and Das explain in their paper that their model avoids singularities because of a key difference between classical geodesics and Bohmian trajectories. Classical geodesics eventually cross each other, and the points at which they converge are singularities.
In contrast, Bohmian trajectories never cross each other, so singularities do not appear in the equations. In cosmological terms, the scientists explain that the quantum corrections can be thought of as a cosmological constant term without the need for dark energy and a radiation term.
These terms keep the universe at a finite size, and therefore give it an infinite age.
The terms also make predictions that agree closely with current observations of the cosmological constant and density of the universe.Specific Impulse. The specific impulse of a rocket, I sp, is the ratio of the thrust to the flow rate of the weight ejected, that is where F is thrust, q is the rate of mass flow, and g o is standard gravity ( m/s 2)..
Specific impulse is expressed in seconds. When the thrust and the flow rate remain constant throughout the burning of the propellant, the specific impulse is the time for.
Problem: Solution: Two students are bouncing-passing a ball between them. The first student bounces the ball from 6 feet high and it bounces 5 feet away from her. The second student is 4 feet away from where the ball bounced.. Create an absolute value equation to represent the situation. Problem: Solution: Two students are bouncing-passing a ball between them.
The first student bounces the ball from 6 feet high and it bounces 5 feet away from her. The second student is 4 feet away from where the ball bounced.. Create an absolute value equation to represent the situation. We're asked to use the drop-downs to form a linear equation with no solutions.
So a linear equation with no solutions is going to be one where I don't care how you manipulate it, the thing on the left can never be equal to the thing on the right. And so let's see what options they give us. One, they. Nernst Equation. The Nernst equation is an important relation which is used to determine reaction equilibrium constants and concentration potentials as well as to calculate the minimum energy required in electrodialysis as will be shown later.
For example, the area of a rectangle is length times width. Well, not every rectangle is going to have the same length and width, so we can use an algebraic expression with variables to represent the area and then plug in the appropriate numbers to evaluate it.