Veritas Ratio

Hello, students. I am Dr. Ratio of the Intelligensia Guild. It has come to my attention that there is an untapped opportunity to share even the most mundane of logic and knowledge on the internet. I am quite ashamed to share that there are two reasons I have not thought about this earlier. (1) I am too busy to make an account on Tumblr. I had not even heard of such a site prior to setting up this blog. (2) Some students of mine, to which I will name, the Trailblazer of the Astral Express and Sushang of the Xianzhou Luofu, are terribly dull in knowledge. I have surmised that providing basic information through a more stimulating method (via posts on social media) could possibly help the two and likeminded individuals learn easier. This will also prove as a personal experiment of mine to see if that hypothesis is correct. I feel that it is beneath me to be sharing knowledge on matters as simple as something one would learn in the average high school, but it would mean that I can put minimal effort into this rudimentary thought experiment, and the aforementioned students are close to being lost causes.

I have no doubt someone will know who I am and about the courses I teach, so to those who do know: this is not a substitute for my classes. The classes I teach are miles more advanced, and I am more thorough with the subjects I share my knowledge about in those classes. If any of my students see this blog, the content here should be none of your concern if you are already taking my courses. If you believe otherwise, do not be surprised if I kick you out of my class.

The topics I will provide posts on will vary each week. I will make one post every Saturday, as it is usually the day I can make time for frivolous things while I take my third bath of the day.

i hope life is treating you well. or if not, i hope it gets better soon. your blog has been a huge help and comfort to me; thank you for sharing it with us! <3

Thank you! Prior to making this blog, I watched videos that showcased all of his voicelines and videos about his lore just to make sure I didn’t mischaracterize him. I’m glad to know that the few math lessons I did were especially liked.

When I’m writing in-character for this blog, I get focused on what specific words I’m using, when to put a conjunction, if and when to use slang words or phrases, etc. Besides that, writing in-character for Dr. Ratio is just how I usually write but with a few tweaks and fancy words.

Please take your time and feel better soon <3

Out of character for this response.

I should have made a post detailing why I hadn’t posted for a while. Either way, nothing serious happened, and I am fine. I was not feeling well when I made that post, but it was just a simple illness and went away.

The reason why I stopped posting was because I was dealing with a lot of stress in my personal life, and on top of that, ADHD made it practically impossible to get anything done on my own time. It got especially bad that it felt like I was pretty much immobilized and couldn’t do anything but sit there and get anxious that I wasn’t doing anything. When that period of stress passed, I got occupied on other things and simply ignored this blog. I felt guilty for not posting anything or answering any asks, and I still do. To those who really enjoy this blog, I’m sorry.

I do find it kind of funny that the reason I made this blog also made it difficult to manage it. I have written in my introduction post in a very Dr. Ratio way as to why this blog was made. I actually made it because I found that maybe converging my current fixation (HSR) with education could help others in the same boat as me (neurodivergent with an interest in HSR) soak up information and knowledge about various topics easier. I just came up with an explanation for it that was more in-character for Dr. Ratio.

I never even realized that so many people were so interested in this blog. Sure, I’ve had plenty of asks while I was posting lessons, but there have been quite a handful of folks sending in asks about where I’ve been and if I’ll return while I was away. To those who have enjoyed this blog at all, thank you.

As for if I will return to keep posting lessons, I’m disappointed to say that I’m not really sure. I don’t want to abandon this blog, so if I ever decide to make a new lesson, you will all know.

I will be going over how to write point-slope formula equations and slope intercept formula equations.

Welcome back, my students. I will be continuing our math lessons together, expanding on the previous topic of arithmetic and geometric sequences. However, this time, they will be more commonly referred to as linear and exponential functions respectively. The two formulas I will be teaching you all are ways to find the basics of a sequence. In the last lesson, we covered finding the initial value and common difference/common ratio from a singular sequence. Because we are dealing with functions now, we need two sequences, one of them allowing us to find the initial value itself, or in this case, the y-intercept. You’ll find out more about that when we start the lesson.

Let us begin.

I mentioned the slope intercept formula in the previous lesson when talking about explicit geometric equations. Today, we’ll be revisiting that and expanding upon it. I must specify these formulas are for linear functions. Exponential functions are written under a different formula and will be explained in another lesson. 

Slope intercept is quite easy to understand. The formula goes as such: y = mx + b. You should already know that the y of the equation is the output. The m is the slope, and the b is the y-intercept, or where the line on the graph crosses over the y-axis. This much should not be new to any of you reading. When analyzing a graph displaying a linear function, finding the y-intercept is not difficult. Where the real work lies is in calculating the slope.

I have provided an example of a graph we can use to find the slope for. We have a linear function with its y-intercept being at 2 on the y-axis. To figure out what the slope is, we can use the rise-over-run method. This means we must find two points on the line where they perfectly cross over the grid for simplicity’s sake. We’ll be able to count how many units the points run across the grid and how many units the points rise up the grid until they intersect. 

After counting, the points rise up by 6 and run across by 5. Now we can put the rise over the run in a fraction, 6/5. In some cases, you would need to simplify the fraction, but since 6/5 is in its simplest form, there is no need for that. You can account for the fact that it is an improper fraction and convert it into a mixed fraction or a decimal, but it is also fine to leave it as it is. Now that we have the slope and the y-intercept, we can write the slope intercept equation.

y = 6/5x + 2

Before we move onto point slope form, there is another way to find the slope when you are only given two points instead of a table or a graph. The equation goes as such:

y2 - y1 ——— x2 - x1

I apologize for the lack of better formatting. Tumblr truly is difficult. Anyways, let’s use an example of (4, 2) and (7, 3). The second point given is what is used first in the equation. The first point given is what is used second in the equation.

3 - 2 ——— 7 - 4

The answer will come out as 1/3. We can now move onto point slope form. 

The equation for point slope form goes as follows: y - y1 = m(x - x1). This formula does not include the y-intercept, and is used when one or two points from the graph are given. When one point is given, it is usually with the slope. It is only when two points are given that you would need to find the slope yourself using the method I have just explained. Let’s say that the given point is (3, -2) and the slope is 4. When we plug in the values, the formula would go as: 

y + 2 = 4(x - 3)

If you are confused as to how the -2 became positive, it’s because that side of the equation initially turns out as y - (-2). The subtraction sign and the negative number cancel each other out, which makes the negative number positive and turns the equation from subtraction to addition. We are not done yet, however — we still need the y-intercept, so we’ll have to change the point slope equation to a slope intercept equation. 

As you can see, the goal is to isolate y from the other side of the equation. First, we need to distribute the 4 outside of the parentheses to the values inside the parentheses. Since we still have a 2 being added to y, we need to subtract it from both sides. This leaves us with the slope intercept equation of y = 4x - 14.

The example above can be applied to any point slope equation, just with different values in place of the variables, of course. 

This lesson is rather short in comparison to the previous one. I’d like to keep linear functions and exponential functions in separate lessons, so as a result, there is not much to cover in one lesson. There won’t be any homework for you all like last time; I was just curious about how interactive I could make a lesson be for my students. Have a good day.

Let logic disseminate.

Second! You seem to have very high standards for who you consider smart or intelligent, and don't offer much room for error. I can't do math beyond basic calculations because I have Dyscalculia. No matter how long I spend trying to learn it and get better at it, I never make any progress and the entire situation ends up just being upsetting and I almost always end up feeling like I'm just stupid. Do you think I can still be considered intelligent even though I struggle so bad with math?

Sometimes, you cannot control what can make life harder for you, nor is it your fault. My standards are only subjected to the capabilities you present in which you can control. I would not make judgement of what you are able to do when it comes to something that is hindered by a factor that you have no conscious decision over. To do so is simply stupid and ignorant.

They were not lying about quaquaval and the peacock-like characteristics! They are not visible when it is simply standing, however if you view quaquaval’s animations, it has a fan-like tail that is commonly associated with a peacock. Quaquaval is based on a dancer and often dances in its animations, including with the fanned tail.

I cannot say that Quaquaval was the starter I picked, though, as I personally picked meowscarada. my favorite pokemon is also a blue bird, but it is a cormorant. It is called cramorant. It is my favorite and I am its biggest fan.

It got canned.

I think you would love to know that there are many more duck Pokémon. My personal favorite is Psyduck, but there is also Ducklett, the Porygon evolutionary line, Golduck (Psyduck’s evolution), and the Quaxly evolutionary line. Farfetch’d also has a regional variant with an evolution named Sirfetch’d.

Some consider Lotad and its evolutionary line to be ducks as well, but I personally believe that they are plants with duck-like characteristics.

Quaquaval (the final stage evolution of Quaxly) also has some peacock characteristics. I’m not mentioning this for any particular reason. Just thought you should know.

-Cole

(P.S. I’m the anon with the duck collection. I don’t know how to send pictures either.)

These creatures have me perplexed. I could not possibly pick a favorite among them... I will say that Lotad looks like a odd creation of Ruan Mei's that I would find on Herta's space station.

first of all, thank you for answering my last ask! it's been a topic on my mind recently, so i was pleased to get your insight. second, i was pleasantly surprised to see a math lesson, especially one covering a topic i learned in precalc. that, along with calculus, have always been my weakest subject. but your lesson, again to my pleasant surprise, made a lot of sense to me! your explanations, visual and textual, really helped. finally, i did attempt the challenge in your latest lesson, but i wasn't sure what the given equation was and got 3 different answers. i can't attach an image of my work, so i'll lay it out in text...

assuming the function is f(x) = 7 + 5x - 1, then it is arithmetic. the first four terms are 11, 16, 21, and 26.

but if the function is f(x) = 7+5^x-1, where 5 is to the power of (x-1), then it's geometric. the first four terms are 15,632; 3,132; 632; and 132.

or if the function is f(x) = 7 + 5^x + 1, where 5 is to the power of x, it's also geometric. the first four terms are 11, 31, 131, and 628.

sorry for the long ask!! if you could point out any mistakes in my work, that would be greatly appreciated!

Mathematics tends not to be most individuals' strong suits, so I can assure you that you are not alone in this fault.

As for the work you are showing me... I apologize if the equation was not clear in the lesson conclusion, but I was looking for the answer to an arithmetic sequence. Fortunately, you did solve the formula as if it were an arithmetic sequence. Unfortunately, however, your answers are incorrect. "x - 1" next the common difference shows that the term shown previously in the equation is the first term. You solved for the four terms as if it were the 0th term, or the initial value. You added the common difference of 5 to 7 with this assumption that it was the initial value, thus skewing your results.

The first four terms are 7, 12, 17, and 22. Though, I do appreciate you taking up the challenge, my student. I wish you a pleasant day.