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Oh honey, in sports, the independent variable is what you control or manipulate, like the type of training program. The dependent variable is what you're observing or measuring, like the athlete's performance. So, basically, you change the independent variable to see how it affects the dependent variable. It's like playing a game of cause and effect, but with more sweat and less drama.
Algorithms are critical to the field of computer science. They embody the logic used to solve a problem. Written in words, they are (computer) language independent, and they allow peer/team review, so that a good design can result.
The derivative refers to the rate at which a function changes with respect to another measure. The differential refers to the actual change in a function across a parameter. The differential of a function is equal to its derivative multiplied by the differential of the independent variable . The derivative of a function is the the LIMIT of the ratio of the increment of a function to the increment of the independent variable as the latter tends to zero.
· The Famous E=mc2 is the most profound mathematics in the history of the world. It tells us that no matter can travel the speed of light because of the mass that would be needed to generate the speed would slow it down with drag.· The Einstein Field Equations (EFE) is a tensor equation relating a set of symmetric 4 x 4 tensors. Each tensor has 10 independent components. Given the freedom of choice of the four space time coordinates, the independent equations reduce to 6 in number.· The Vacuum Field Equations ,If the energy-momentum tensor Tμν is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations. By setting Tμν = 0 in the full field equations, the vacuum equations can be written asThe solutions to the vacuum field equations are called vacuum solutions. Flat Minkowski space is the simplest example of a vacuum solution. Nontrivial examples include the Schwarzschild solution and the Kerr solution.Manifolds with a vanishing Ricci tensor, Rμν = 0, are referred to as Ricci-flat manifolds and manifolds with a Ricci tensor proportional to the metric as Einstein manifolds.
Your question is extremely broad. Perhaps if you could name the particular field or industry, I could better respond. The area of classical statistics includes making inferences of population parameters such as standard deviation and the mean based on limited samples. This area has very wide use in many industries. The area of descriptive statistics, where the visual display of data to aid is used in the interpretation is used extensively. In more technical and engineering analysis, regression analysis is used to develop relationships between independent and dependent variables. Quality control charts based on statistics are used in manufacturing. Please see the related link. You can find many more links by including a particular field, like medicine, manufacturing, sociology and marketing.