Expect the ironic

Math enthusiast looking to pass the time.

[thegameofabstraction]

How do you simplify stuff like (2x-1) squared?

You have to foil it like you would for something like (x-1) squared to get x^2 - 2x + 1. You multiply (2x-1) by (2x-1). You get (2x)(2x) + (2x)(-1) + (2x)(-1) + (-1)(-1) = 

4x^2 -2x - 2x + 1 = 4x^2 - 4x +1 

[thegameofabstraction]

I can help with all math. Just tell me what math you are doing prior to asking me a question. 

[thegameofabstraction]

An Aspiring Mathematician's Apology

I would like to formally apologize to anyone whose questions have been unanswered. I began this blog because I wanted to help those around me while also becoming more mature in the field of mathematics. As such, it goes without saying that I, as a recent college student, have been dealing with my own workload as well as the occasionally mathematical excursion. Even so, I am sorry that I have not been around as often to help as I would have liked to have been. I will try to make more time as I can, and I hope that anyone who comes to this blog looking for help can bear with me. Thank you for your time. I hope all is well. That is all.

[thegameofabstraction]

I can help with math. Just tell me what math you are doing prior to asking me a question. 

[thegameofabstraction]

I try so hard to understand calculus, I get derivatives but limits are just bleh to me. I wish i was smarter, y'know?

Well a derivative is just a special kind of limit. Just keep on trying. You will get better at it. 

[thegameofabstraction]

Help!!!

Alright. You are solving these formulas for a variable. 

8. For A = lw, you want to solve for w. This means you need to get w alone which can be done by dividing l from both sides which gives you A/l = w.

9. For V = (1/3)pi*r^2*h, you need to get h alone which means you need to divide out everything that is not h.

V = (1/3)pi*r^2*h

divide 1/3 or multiply 3 (same thing) to both sides.

3V = pi*r^2*h

divide pi by both sides.

3V/pi = r^2*h

divide r^2 by both sides.

3V/(pi*r^2) = h

This all could have been done in one step by dividing out (1/3)pi*r^2.

10. This one is a tad trickier, but just take it step by step. 

p = 4(f-3)/(k+5)

(k+5) is one term that can be multiplied by both sides to cancel it out of the side containing f.

p(k+5) = 4(f-3)

divide out 4 from both sides.

p(k+5)/4 = f-3

now just add 3 to both sides to get f alone.

(p(k+5)/4) + 3 = f

There ya go. Hope this helped. 

[thegameofabstraction]

So let me tell you guys one thing that will branch out into infinitely many other smaller but not less important things: Math is a religion in a way. It is a belief system, a thought process. I believe that anyone with enough motivation and vigor can do anything they set their mind to. Especially math. Because math isn't just about memorizing this rule or that or this formula or that formula. Math is process. A reasoning process. Nothing in math is without its proof (except for axioms of course). And that is what makes math so concrete in that everything in it can be proven beyond a reasonable doubt. Every single mathematical viewpoint that we have now is an amalgamation of year, decades, CENTURIES of intellectual reasoning and vigor. This vigor grew into so many different disciplines that you couldn't learn every single one no matter how many lifetimes you had available. Math, in the purest sense, is analysis and reasoning. This is not a class on history where you must memorize fact after fact after fact. This is a subject about reasoning. As pure reasoning as it gets. I see memorization as more of a shortcut once you understand exactly what it is you have just learned. You wouldn't want to keep proving it, so you memorize it with the reasoning in mind. A lot of people simply memorize with no reasoning which I will not blame them because not everyone has to like math. Just like how I don't really like history. And that is alright. Math is math. History is history. I just wanted to say that if you seek math, then you must seek out reasoning. That is all. 

[thegameofabstraction]

I can help with math ranging from arithmetic to calculus II. Feel free to drop by. 

[thegameofabstraction]

If anyone knows anyone who needs help, then please don't hesitate to send them my way. Things have been slow lately.

[thegameofabstraction]

[thegameofabstraction]

I can help with math ranging from algebra to calc II.

[thegameofabstraction]

If figure QRST is a kite with QS = 192 cm, RS = 120 cm, and RT = 252 cm, what is the length of side ST?

Alright. Seeing as QS and RT intersect within the kite, there intersection forms 90 degree angles. As such they are perpendicular to one another. Knowing this, we can solve this using the pythagorean theorem. Split the kite in four into triangles with point U as the intersection of QS and RT. Since this is a kite, the line segment RT splits QS in half. We have four triangles, but we only care about the ones that contain known side length of RS and the unknown we are looking for of ST which are triangles RUS and UST.

Now for the fun part.

Knowing that RT splits QS in half, the length of US is the length of QS divided by 2 which is 192 divided by 2 which is 96 cm. The hypotenuse, longest side, of RS is 120 cm. Pythagorean theorem states a^2 + b^2  = c^2, where c is the length of the hypotenuse. Therefore, b^2 = c^2 - a^2. Let a = US, b = RU, and c = RT.

 RT^2 - US^2 = RU^2

120^2 - 96^2 = RU^2

14400 - 9216 = 5184

RU^2 = 5184

Therfore Ru = 72. Why did we do that? We need a second side length to the triangle UST, since US is already known. Knowing that RT is 252 cm, the length of UT is some portion of that length. Seeing as RU + UT = RT by line segment addition, we needed the length of RU to find UT.

RU + UT = RT

72 + UT = 252

UT = 252 - 72

UT = 180 cm

Now we have two known side lengths to the triangle UST. We know that US = 96 cm and UT = 180 cm. We just need to find ST now. Seeing as ST is the hypotenuse of UST, we use pythagorean theorem again but solve for c this time. Let c = ST, a = US, and b = UT.

a^2 + b^2 = c^2

US^2 + UT^2 = ST^2

96^2 + 180^2 = ST^2

9216 + 32400 = ST^2

41616 = ST^2 

Therefore ST = 204 cm. The end. I hope this helped, and I apologize that this was not graphical.

[thegameofabstraction]

I can help with Calculus AB and some BC topics as far as calculus help goes. I can also help with first order differential equations. I can help with some AP Chemistry and AP physics as well. Just some. Don’t expect me to be an expert. If not an answer, then I can give helpful tips. 

[thegameofabstraction]

Simplify: 2√ 95 over 3√ 45

[thegameofabstraction]

you said you dont know mad but, maybe you can help me with this. the MAD for attendance at marshall high is 10.4 students. the MAD for marshall middle is 21.6. What conclusions can you draw?

Hmm. Well looking at it. I can tell that the spread of the data for student attendance is more spread for Marshall Middle because the deviation is greater. 

[thegameofabstraction]

Data set 1 has μ=72 and σ=4.929. Data set 2 has μ-55 and σ=5.102. Which data set is more spread out? How do you know?

The standard deviation is what determines the spread of data. Therefore, the data with the larger standard deviation has the larger spread. Therefore, data set 2 is more spread out in this instance. 

[thegameofabstraction]

can you help me? 1.) if there is a large MAD (mean of absolute deviation) what does that mean?

I have yet to learn MAD, but I did look up what it is. From what I can tell, it is essentially what the name says. Therefore, the mean when the deviation is low should approach 0. If the MAD is high, then the average deviation from the mean is high meaning that the spread of the data is large.