Vidyogamasta

50% greater.

100% - 33% = 67%

67% * 150% = 100%.

This isn't quite the same thing, but I worked an online chat support line for a few months. We basically had the same thing as what you're talking about, but they were hotkeys we pressed that spit out some commonly used phrases (intros, outros, a custom simplified explanation I wrote about how one of the plans worked, the "it's taking a while to gather the information you need. Just assuring I'm still here and will be back with your answer shortly" one, etc.)

In a chat, it's just a nicety that isn't too intrusive, doesn't take a long time for the support tech to actually use, and can usually be safely ignored if you wanted. I imagine on a live call it'd be far more annoying.

As for people getting mad, that just happens randomly. No amount of smooth talking is going to be able to calm down a certain group of people. But the place I worked at said we were not obligated to take abuse, and could give the customer one or two warnings before making the decision to end the chat.

I'll take a shot at it-

Hopefully you remember from basic algebra that a slope is the rate of change from point a to point b. So if point a is (0, 0) and point b is (1, 5), you went up 5 units in the time it took to go right one unit. So the slope is (5-0)/(1-0) = 5. This works great for straight lines, because the slope never changes, it keeps moving straight.

Curves lines are trickier. You can have a curve where the slope starts off very small, and then raises to be high at the very end. The slope is constantly changing, and we want to know what the slope is at a particular point. The problem is, the slope function uses two points, and we only have one! So what we do is we say "I'll take my point and a point very very close to it to get a best guess." Then you use some clever algebra to move the second point infinitely close and get the slope of your single point.

Integrals function similarly. The area function for a straight line is very easy, you often just multiply width * height and cut it in half or something simple like that. But for curved lines, finding the area can get really crazy. Again, you can make a "guess" by drawing a straight line from the beginning to the end and finding the area of that, but it's not going to be accurate. For example take a "U" shaped curve. If you start at the beginning and the end, you make a square and and including all of the extra space above the "U". Oops!

So we do something similar. We cut our "best guess" structure in half, adjust the middle point, and now we have two shapes to add together to give us an even better guess. In our "U" example, it would make two triangles that touch at the bottom of the U. We're including a lot less of that extra space now, it's a little more accurate. Here's a picture if you can't visualize it from my description. Now we cut all of those shapes in half and get an even BETTER guess. Again, we use some clever algebra to make all of our pieces small enough to get 100% accuracy.

You say there was a 3x3x2 / 4x4x3 mass... What is the unit of measurement here??