Vivax Solutions Blog

  The constellation of satellites of Starlink, owned by SpaceX, is already revolutionizing the broadband internet in terms of speed of data transmission, low latency and of course, the possibility of accessing it from anywhere in the world - even in the remotest parts of the world. Since Arthur C Clark, the science fiction writer, first envisioned the possibility of using satellites in communication, the use of geostationary satellites grew by leaps and bounds.  Since those who deploy them want them to be 'stationary' above a specific position of the Earth, they are compelled to make them revolve around the planet at the same speed of the Earth's rotation around its own axis - 24 hours in rotational time.. Newton's Law of Gravitation and Kepler's Laws of Motion help us calculate the specific altitude of a geostationary satellite as follows: F = GMm/r²,  t he force between the Earth and a satellite of mass m The centripetal force of the satellite = mrω², where w i

The creation of a Chrome extension from scratch, submitting it to the Browser Web Store, getting it reviewed - and then, published - in less than 24 hours is something that any aspiring developer can be proud of. Google Browser Extension - reviewed and approved in within 24 hours I managed to do just that today, on 2 August, 2023 and in this tutorial I am going to explain the whole process. Google broke the good news of the success with an email, saying that the browser extension has been reviewed and published to the Chrome Web Browser Store. Browser extension published - reviewed and approved by Google In order to understand the process, I assume you have the following skills at a reasonable level, but not necessarily at a very advanced level. 1) Good knowledge in HTML 2) Knowledge in CSS 3) Good knowledge of JavaScript 4) Knowledge in the DOM - Document Object Model 5) Some knowledge in JSON In addition, you need the following: A Google developer account - a fee has to be paid The

  Concave functions If f''(x) ≤ 0 in a given interval of x, the function is said to be concave. Convex functions If f''(x) ≥ 0 in a given interval of x, the function is said to be convex. Point of Inflection The point at which a curve changes being concave to convex or vice versa is called a point of inflection. E.g. f(x) = x 3 - 2x² + 5x - 4 f'(x) = 3x² - 4x + 5 f''(x) = 6x - 4 At the point of inflection, f''(x) = 0 6x - 4 = 0 x = 2/3 = 0.67 There is a point of inflection at x = 0.67. If x = 0.6 f''(0.6) = 3.6 - 4 = -0.4 f''(0.6) < 0 - the function is concave. If x = 0.8 f''(0.8) = 4.8 - 4 = 0.8 f''(0.8) > 0 - the function is convex. In the above simulation, there are two points of inflection. The simulation can be practised interactively here; just move the point gently to see the change.   Points of inflection on the Bell Curve - Normal Distribution There are two points of inflection on the bell curve.

 

  Snell's Law When light refracts from one medium to another, the ratio of sine of the angles is equal to the ratio of refractive index of each corresponding medium. Snell's Law implies that light, when refracting from one medium to another, takes the shortest path. We can show by differentiation that when the light takes the shortest path, it obeys Snell's Law, verifying the 400-year-old law discovered  by the Dutch astronomer and mathematician. 

  The above simulation is produced in Python with aid of three functions. They are as follows: Factorial function  A function to generate combinations - nCr A function to produce the Pascal's Triangle You can practise it interactively with the following simulation. Please make sure you keep the number of rows below 10 so that the format of the output stays the way it should. The number of rows is the only parameter that Pascal(n) function needs.

  Created with GeoGebra, this applet lets you generate straight line graphs at random, displaying the corresponding equation for each. In addition, you can find a parallel line - and its equation - for each line. Moreover, for each generated line, a random point is created. Then, the perpendicular line  that goes through the point in question can be created too. It is ideal for teachers at GCSE, IGCE, GCE O Level, GCE A Level and of course, A Level. The interactive simulation of the above is as follows: you can generate unlimited number of lines for practice for you students: just press the button - Draw Line -  to create random lines.