Hydrostatic paradox

What is hydrostatic paradox? 

You might be wondering what this fancy word means, but I am pretty sure you have seen the illustration before. Hydrostatic paradox is a term commonly used to describe a phenomena where the pressure of liquids is independent of the object's size and area. In fact, the pressure only depends on the depth.

Illustration of hydrostatic paradox

Integration with trigonometric functions

Integrals involving trig functions can be tricky. But here are some of the basic rules:
1. If the power of sine or cosine is odd, separate one of the factor, and convert the remaining with the trig identity.
2. If the power of sine and cosine is even, use the half angle identity rule.

For more information on trigonometric integrals, visit here.

Newton's Method of Iteration

Iteration is a repeating process in which the goal is to get a number that is closer to a true value.

There are numerous iteration methods, but we will be focusing on the Newton's Method today.

Newton's Method utilize the Taylor's polynomials to find the root. If the number is getting closer and closer to the true value, we call it converging; and, that's what we want!!


The formula used is

To obtain approximation
1. make an initial guess
2. find the first approximation using the formula
3. repeat the iteration as needed until the values differ in the slightest amount.

Water Hardness

Image credit: google.com

What is Water Hardness?
Water hardness is a measurement of dissolved minerals in the water, typically calcium and magnesium. The higher the concentration of these minerals, the harder the water is. It is commonly measured in mg/L and ppm.

Hard water is safe to drink. However, hard water may increase difficult in cleaning tasks because it creates the white deposits on to the surface. It may also create a scale inside the pipe, which can eventually clog it.

Can I remove the water hardness?
Yes, you totally can. Softening system can be installed to remove the hardness. There are two common approach that can be utilized: (1) ion exchange, (2) reverse osmosis system. Both systems are readily available in the market, make sure to check the pros and cons for both system to meet your need. 

Jelly Roll Pan vs. Cookie Sheet

What is the difference between a jelly-roll pan and a cookie sheet?

Well, I am not a great expert when it comes to cooking. I happen to stumble upon jelly roll pan, which I have no idea what it is when I was looking at a recipe.

Anyway, without further due; cookie sheet has only one or two sides of the metal sheet bent up. The design ensures that air would be circulated freely around the cookie dough. On the other hand, jelly-roll pan has all sides bent up. It is usually used to roast veggies and more.

Business: Why is it important?

Businesses play role in the society, no matter how large or small it is. These businesses provides economic stability for the country by providing jobs for some people and services for the rest of the people.  We can not live by ourselves.

To get some ideas about business lessons, I suggest you guys to watch SharkTank show. I am not affiliated whatsoever with this show. It is just such a great show, you can obtain some business pitch ideas for the project that you are working on,  observe how creative the innovations are, and etc. Today's lesson is to watch SharkTank and hopefully learn something out of it. The show lasts approximately 1 hour per episode.

Happy watching!