/sci/ - Science & Math

[Anonymous No.3976643]

Hey /sci/ I need your mathematical help. I have been working on this problem for 30 mins. Can you help me? I want to know how to do it, not just the answer.

Use factoring to solve this quadratic equation.
5x^2=27-42x

In return I give you Hank Hill!

[Anonymous No.3976648]

/sci/ sure is full of little kids today.

[Anonymous No.3976647]

wolf ram <span class="math">\alpha[/spoiler]

[Anonymous No.3976649]

>>3976643
Oh that's simple, you just need to solve the Navier Stokes Equation.

[Anonymous No.3976656]

You'll want to get everything onto one side of the equation so you have (something)=0, and then factor it. Put some effort in, we'll guide you

[Anonymous No.3976659]

(5x-3)(x+9)

Took me 2 seconds to figure out

[sage No.3976664]

>>3976643
If it's not factorable use the quadratic formula.
If it's factorable you can still use the quadratic formula.

tl;dr use the quadratic formula

[Anonymous No.3976717]

Step back guys...I tutor 'special' people like this for a living.

Ok OP first you want to do this:

<span class="math">\displaystyle 5x^2=27-42x[/spoiler]

and add 42x and subtract 27 from both sides.

<span class="math">\displaystyle 5x^2+42x-27=0[/spoiler]

This should look familiar. If it doesn't, kill yourself immediately.

You have a coefficient in front of the quadratic.This means normal 'AC' method will not work. Use factor by grouping.

What multiplies to 135 but adds to 42? Write out the factors of 135 if you're unsure:

1 and 135
3 and 45
5 and 27
9 and 15

It should be obvious at this point which one adds to 42 but multiplies to 135.

If it's not, kill yourself.

Now rewrite the expression. Also keep in mind that the greater integer attached to the variable has to be positive an they'll have opposite signs.

<span class="math">\displaystyle 5x^2+45x-3x-27=0[/spoiler]

Now factor by grouping:

<span class="math">\displaystyle (5x^2+45x)(-3x-27)=0[/spoiler]

Now take out what you can from both sets:

<span class="math">\displaystyle 5x(x+9)-3(x+9)=0[/spoiler]

Protip: both of the quotients should be identical at this point. They are.

Factor out the quotient:

<span class="math">\displaystyle (5x-3)(x+9)=0[/spoiler]

Set both quotients equal to zero:

<span class="math">\displaystyle (5x-3)=0 (x+9)=0[/spoiler]

Solve for x:

<span class="math">\displaystyle x = \frac{3}{5}, -9[/spoiler]

You can go back and check your answers.

[Anonymous No.3976750]

>>3976717
How to make pretty tex words?

[sage No.3976757]

>>3976717
>factor by grouping

don't bother. just use the quadratic formula

[Anonymous No.3976773]

>>3976717
> which one adds to 42 but multiplies to 135.
You're pretty dumb.

[Anonymous No.3976784]

>>3976664
typical dumbass matlab engineer faggot who knows know theory and sucks shit at math.

[Anonymous No.3976787]

>>3976757
>messy formula where OP which OP is likely to screw up
or
>easy to understand modification of 'AC' method

But I honestly think you should just graph it and find the zeroes that way or use a program to do the quadratic for you.

[Anonymous No.3976794]

>>3976773
http://people.richland.edu/james/misc/acmeth.html

Let's do lunch sometime.

[Anonymous No.3976837]

>>3976794
http://www.wolframalpha.com/input/?i=a%2Bb%3D42%3B+a*b%3D135
Look at the very bottom and never say stupid things again.

[Anonymous No.3976869]

Move everything to one side:
5x^2=27-42x -> 5x^2+42x-27=0

Since 5 is a prime number, you know the factoring will look like
(5x +/- )(x +/- )

27 has a couple of factors:
1*27, 3*9, 9*3 and 27*1

Following FOIL, take those factors and figure out which order will give a positive 42 when one is multiplied by 1 (Inside) and the other is multiplied by 5 (Outside) when they are summed.

9*5 gives 45 (closes to 42) and -3*1 gives you -3. When you sum those, you get 42. So the factoring is
(5x - 3)(x + 9)=0

Solve for x.

x=-9 and 3/5

[Anonymous No.3976888]

>>3976837

Are you fucking retarded or just incapable of reading? Or both?

http://people.richland.edu/james/misc/acmeth.html

See how it states there are two cases? No? Want me to screenshot that for you too?

It's easier to ask what has the potential to add or subtract to 42 but add to 135 without involving signs. I can see that clearly went over your head, though. No worries..you're probably one of the college algebra students I get the pleasure of tutoring on a daily basis. One of the kids who requires a formula and can't interpret what the formula is doing for him.

Also, you know...

>>3976717
>Also keep in mind that the greater integer attached to the variable has to be positive an they'll have opposite signs.
>Also keep in mind that the greater integer attached to the variable has to be positive an they'll have opposite signs.
>Also keep in mind that the greater integer attached to the variable has to be positive an they'll have opposite signs.
>http://people.richland.edu/james/misc/acmeth.html

[Anonymous No.3976895]

>>3976837

Are you fucking retarded or just incapable of reading? Or both?

http://people.richland.edu/james/misc/acmeth.html

See how it states there are two cases? No? Want me to screenshot that for you too?

It's easier to ask what has the potential to add or subtract to 42 but multiply to 135 without involving signs. I can see that clearly went over your head, though. No worries..you're probably one of the college algebra students I get the pleasure of tutoring on a daily basis. One of the kids who requires a formula and can't interpret what the formula is doing for him.

Also, you know...

>>3976717
>Also keep in mind that the greater integer attached to the variable has to be positive an they'll have opposite signs.
>Also keep in mind that the greater integer attached to the variable has to be positive an they'll have opposite signs.
>Also keep in mind that the greater integer attached to the variable has to be positive an they'll have opposite signs.
>http://people.richland.edu/james/misc/acmeth.html

[Anonymous No.3976900]

>>3976895
Please name one advantage of factoring a quadratic equation rather than applying the formula.

[Anonymous No.3976919]

>>3976900

To demonstrate you are not a mouth breather and can perform basic algebra without relying on an equation that you have no idea about.

See: projectile motion.

[Anonymous No.3976924]

>>3976919

Re-read that "sentence" and try again.

[Anonymous No.3976938]

>>3976900

Using logic and discovering the "why it works" with your own process.

[Anonymous No.3976949]

>>3976900

To demonstrate you are not a mouth breather and can perform basic algebra without relying on an equation that you have no idea about.

You know...algebra. That one tool you'll need throughout your mathematics career? Think your quadratic equation will help you solve an integral that requires partial fraction decomp.? No? That's because it won't.

How about when you need to perform some algebra to convert between coordinate systems like polar, parametric, spherical, etc? Nope not going to help you there.

Quadratics are only special cases.

[Anonymous No.3976960]

" The disadvantage of solely relying on reference tables is that students may not learn how to derive a formula. Understanding how some formulas came to be leads to a greater understanding overall of math. It leads to finding new formulas and builds those skills necessary to adapt and change a formula that doesn't quite fit the model.

Another disadvantage is the loss of memorization skills. Memorization is an important brain function exercise. Allowing the use of tables discourages the act of memorization.

The disadvantages of using relationship tables (T-Charts) for X and Y in equations is that the table only shows a finite number of coordinate pairs. For values that fall between the given solutions, interpolation must be done. For values that go beyond the table's range, extrapolation must be done. These methods are not always accurate. Knowing how to solve the equation for these values is the better solution when the table fails to produce the answer."

[Anonymous No.3976976]

You're like this poster:

>>3976256

Probably uses equations for everything from physics to mathematics. Probably doesn't understand anything about them at all.

The crap he's asking about in parametrics are so easy to grasp if you can just connect some simple pieces of information together. If you had relied on memorization of equations up till this point, you'll probably end up like him.

Asking /sci/ questions like, "HOW I SOLVE DIS?" where "DIS" is a simple loop integral that just uses basic understanding of algebra to come to the answer that many students miss because they relied too much on memorization.

>>3976924

Now would you like to try again or are you done for now?

[Anonymous No.3977156]

>To demonstrate you are not a mouth breather and can perform basic algebra without relying on an equation that you have no idea about.
Wait, so your defense of using factoring lies in the idea that it "demonstrates understanding" to boost your self esteem so some mathematician doesn't think you're a mouth breather?

Ok. Assume understanding is present, or need not be demonstrated. Is there a practical reason to prefer factoring over applying the quadratic formula?

FYI I understand algebra well enough for my level of mathematical education, and have explained the derivation of the quadratic formula to algebra-calculus students via completing the square (you're not the only one in here who tutors for spare cash). I've just never heard a valid reason to use a less powerful method once you're past babby's first algebra class where problems are presented in trivially factorable form.

>How about when you need to perform some algebra to convert between coordinate systems like polar, parametric, spherical, etc?
Are you saying that I can use AC factoring methods on <span class="math">x^2 + y^2 + z^2 = 1[/spoiler] to obtain <span class="math">\rho = 1[/spoiler] ?

[Anonymous No.3977176]

>>3977156
No, it reads more like he doesn't know how to form a coherent argument or reach a proper conclusion from a set of premises. In other words he's never read/written a real proof in his life and knows nothing about real math, but thinks that because he has practiced a lot of high school level algebraic manipulations he somehow has natural talent.

tldr; he's a mediocre undergrad at best, but spends a lot of time around math-retarded children so thinks he's smart.

[Anonymous No.3977194]

>Quadratics are only special cases.
>implying factorable quadratics aren't even more special cases.

[Anonymous No.3977213]

Clearly you don't tutor English.

That's not what I said. It demonstrates that you know how to do simplistic algebra that you will need later on.

Practical?

Removable/non-removable discontinuities. Practice and expand on your algebraic knowledge which benefits you later on. Derivatives using quotient and chain rule where factoring makes it obvious how something will simplify algebraically.

These little algebraic maneuvers come in handy later on when you're dealing with things like infinite series tests (particularly ratio an root) or trying to explain why <span class="math">\displaystyle \lim_{n\to\infty} \frac{1}{n} = 0[/spoiler]

>FYI I understand algebra well enough for my level of mathematical education, and have explained the derivation of the quadratic formula to algebra-calculus students via completing the square (you're not the only one in here who tutors for spare cash). I've just never heard a valid reason to use a less powerful method once you're past babby's first algebra class where problems are presented in trivially factorable form.

The less powerful method will usually end up being the one that takes the most amount of time to do.

The quadratic is useful for science courses where you are not necessarily given 'nice' numbers to work with.

Even then, calculators have graphing functions with build-in zero systems that basically perform the quadratic for you.

I should be asking you whether you can think of any practical applications where the quadratic is faster to use than factoring that applies strictly to mathematics.

[Anonymous No.3977226]

>>3977176

Yet it's contradictory to say such a thing since most people struggle with the algebraic concepts of higher level math courses than the actual new content introduced in those courses.

But honestly: what would you know? You don't see the problem on a daily basis like I do.

>No, it reads more like he doesn't know how to form a coherent argument or reach a proper conclusion from a set of premises. In other words he's never read/written a real proof in his life and knows nothing about

And holy hell talk about fallacies out the wazoo. Counted 6 alone in that paragraph. Probably should work on your own argumentative style before critiquing another person's.

[Anonymous No.3977230]

>>3977194

>implying factorable quadratics are the subject under discussion and not generalized factorization

[Anonymous No.3977254]

>>3977213
>Please name one advantage of factoring a quadratic equation rather than applying the formula.

>To demonstrate you are not a mouth breather and can perform basic algebra without relying on an equation that you have no idea about.

>Wait, so your defense of using factoring lies in the idea that it "demonstrates understanding" to boost your self esteem so some mathematician doesn't think you're a mouth breather?

>That's not what I said. It demonstrates that you know how to do simplistic algebra that you will need later on.

To repeat the actual question instead of this bizarre "it's for your future learning!" tangent: Please name one advantage of factoring a quadratic equation rather than applying the formula.

>Even then, calculators have graphing functions with build-in zero systems that basically perform the quadratic for you.
Wait, so you're opposed to people "not truly understanding" the fundamentals, then turn around and say it's ok to just have a machine draw pictures for you?

>I should be asking you whether you can think of any practical applications where the quadratic is faster to use than factoring that applies strictly to mathematics.
How about any situation with large and non-prime a and c. The quadratic equation has a relatively strict upper limit on time (idk how long it takes you to apply but I do it quickly) whereas glorified trial-and-error may very well take you longer than that. And that's assuming it's even factorable, if it's not you just wasted time and STILL have to use another method.

[Anonymous No.3977253]

>>3977213
>science courses where you are not necessarily given 'nice' numbers to work with.
90% of the time it's no numbers at all, just variables. How am I supposed to factor <span class="math">x_0+v\cdot t + \frac{a\cdot t^2}2[/spoiler] using your method?

[Anonymous No.3977258]

>>3977156
>>How about when you need to perform some algebra to convert between coordinate systems like polar, parametric, spherical, etc?

Nope try. Algebraic knowledge will help you with that, though.

[Anonymous No.3977264]

>>3977226
Protip: look at the hypotheses, look at the conclusion. Figure out how to get from one to the other without introducing extraneous information. You have failed to accomplish this.

[Anonymous No.3977270]

>>3977230
>implying factorable quadratics are the subject under discussion and not generalized factorization
Ummm... factorable quadratics ARE the subject under discussion. You are the only person in here who seems to think that AC factorizing generalizes into ALL OF ALGEBRA.

The OP is asking about a quadratic equation, people are suggesting to use the quadratic formula... how do you not see your own logical inconsistencies?

[Anonymous No.3977279]

>>3977258
Ok well at least you're willing to admit that.

Now present an argument that a person has sufficient algebraic knowledge if and only if they first attempt to use AC factoring methods on quadratic equations instead of the quadratic formula.

[Anonymous No.3977302]

>this thread
http://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

[Anonymous No.3977307]

>>3977254
>To repeat the actual question instead of this bizarre "it's for your future learning!" tangent: Please name one advantage of factoring a quadratic equation rather than applying the formula.

>Removable/non-removable discontinuities.
>Derivatives using quotient and chain rule where factoring makes it obvious how something will simplify algebraically.

These are just two. Do you realize how many applications of factoring can be applied to applications in all areas: ranging from trigonometry to DEQ?

Factoring trigonometric functions and finding the zeroes for half angle and double angle identities.

Factoring trinomials and higher degree polynomials.

Optimization. Completing the square. etc Too many to list.

[Anonymous No.3977312]

>Wait, so you're opposed to people "not truly understanding" the fundamentals, then turn around and say it's ok to just have a machine draw pictures for you?

There's a difference? You don't run into students who know how the quadratic really functions or how it was derived. They don't know what they're doing. At least with the graphical approach, they can directly see that the zero values correspond to the x intercepts of (let's just make this simple and call it a parabolic shape). Realizing this, they can link how factoring works to the zero approach on the calculator.

Graphing by hand is even more tedious than the quadratic. But it still allows you to see what is going on.

>How about any situation with large and non-prime a and c. The quadratic equation has a relatively strict upper limit on time (idk how long it takes you to apply but I do it quickly) whereas glorified trial-and-error may very well take you longer than that. And that's assuming it's even factorable, if it's not you just wasted time and STILL have to use another method.

The point is that you are consistently breaking down terms into factors. Eventually, you begin to learn the factors by memory. From this, you can make later inferences about the factors and more applicable uses (especially rewriting two bases as the same with different powers.

It allows you to have more agile mental skill. That way you can automatically see which one will take the most amount of time to complete and select the one based on that. The more factors you know of a certain combination of integers, the less likely you will have to rely on the quadratic.

But there are situations where the quadratic is simply easier if you cannot see the obvious factorization. Then again, that is pretty much my point: overuse of the quadratic usually leads to people who cannot do basic multiplication or division in their head.

[Anonymous No.3977317]

Why does this homework thread have 30+ posts?

[Anonymous No.3977325]

>>3977302
>Dunning Kruger Effect
More like the Dicks Kruger Gayfect. No supporting evidence.

[Anonymous No.3977340]

>>3977307
>Removable/non-removable discontinuities.
>Derivatives using quotient and chain rule where factoring makes it obvious how something will simplify algebraically.
>implying that removable discontinuities or the quotient rule apply to polynomials of degree 2.

[Anonymous No.3977346]

>>3977270
>Ummm... factorable quadratics ARE the subject under discussion. You are the only person in here who seems to think that AC factorizing generalizes into ALL OF ALGEBRA.

This is not what was discussed at all. Where do you see that I suggest that factorizing generalizes into all of algebra? It doesn't. It's a small part but it does help in some specific areas.

>The OP is asking about a quadratic equation, people are suggesting to use the quadratic formula... how do you not see your own logical inconsistencies?

The OP is asking about a quadratic equation. He says solve the quadratic equation. He does not list which method he needs to solve by. Moreover, if you look at some simple factors of 135 it becomes easy to see which two are the only viable options.

My solution (without the explanations) probably took 1/4th the time it took you to set up the quadratic equation for this simplistic factorable problem.

>Now present an argument that a person has sufficient algebraic knowledge if and only if they first attempt to use AC factoring methods on quadratic equations instead of the quadratic formula.

They have sufficient algebraic knowledge if they can easily discern which method would be quicker to use. AC method is not always the quickest but it was in the case of the OP's question.

[Anonymous No.3977348]

tldr; factoring fag tries to blow his load over all of algebra, rest of the math world goes "wtf?"

[Anonymous No.3977353]

I reported OP for being underage, I suggest you people do too.

[Anonymous No.3977361]

>>3977346

>Please name one advantage of factoring a quadratic equation rather than applying the formula.

>...(random inane argument)... You know...algebra. That one tool you'll need throughout your mathematics career?

[Anonymous No.3977369]

>>3976787
>quadratic formula
>messy

[Anonymous No.3977387]

>>3977340

Quotient rule is defined by <span class="math">\displaystyle \frac{h(x)g'(x)-g(x)h'(x)}{h(x)^2}[/spoiler]

See that term on the bottom? That's generally a quadratic in lower level calculus.

Another basic calc 1 problem. Discuss the continuity:

<span class="math">\displaystyle f(x) = \frac{x^2-4}{x^3+2x^2+x+2}[/spoiler]

<span class="math">\displaystyle f(x) = \frac{(x-2)(x+2)}{(x^2+1)(x+2)}[/spoiler]

<span class="math">\displaystyle f(x) = \frac{(x-2)}{(x^2+1)}[/spoiler]

Not even quadratic but could easily be written in that form. And factor by grouping happened to work well. Now if you had relied on the quadratic up till this point, you might be asking what the hell is going on. Where as if you had done factor by grouping as in the OP's example, you would know exactly what to do.

Really, there are too many examples to list in calculus I-III and I don't really feel like providing all of them to prove the point that factoring is a valuable tool and the quadratic formula is simply a tool that you should keep at the back of your box to deal with quadratics that are not easily factorable.

[Anonymous No.3977410]

>>3977361
http://www.nizkor.org/features/fallacies/ad-hominem.html
http://www.nizkor.org/features/fallacies/ad-hominem-tu-quoque.html
http://www.nizkor.org/features/fallacies/appeal-to-belief.html
http://www.nizkor.org/features/fallacies/appeal-to-common-practice.html
http://www.nizkor.org/features/fallacies/appeal-to-ridicule.html
http://www.nizkor.org/features/fallacies/burden-of-proof.html
http://www.nizkor.org/features/fallacies/poisoning-the-well.html
http://www.nizkor.org/features/fallacies/straw-man.html

Pick 5. You've pretty much used them all, though.

[Anonymous No.3977438]

>>3977369
Not him, but answers obtained from factoring never get more involved than fractions.

Obviously OP is in a class where he hasn't learned factoring, and factoring is a really important tool.

[Anonymous No.3977472]

My favorite part about this thread:

Not one of the twats in favor of the quadratic has even mentioned the beauty of

<span class="math">\displaystyle \Delta = b^2 - 4ac[/spoiler]

where:

<span class="math">\displaystyle \Delta = n^2 \Rightarrow \mathb{Q}[/spoiler]

as a wonderful work around for the AC method which goes to show you that these kids simply do not understand the quadratic at all and use it because they are too lazy to do some simple arithmetic in their heads.

[Anonymous No.3977474]

My favorite part about this thread:

Not one of the twats in favor of the quadratic has even mentioned the beauty of

<span class="math">\displaystyle \Delta = b^2 - 4ac[/spoiler]

where:

<span class="math">\displaystyle \Delta = n^2 \Rightarrow \mathbb{Q}[/spoiler]

as a wonderful work around for the AC method which goes to show you that these kids simply do not understand the quadratic at all and use it because they are too lazy to do some simple arithmetic in their heads.

[Anonymous No.3977476]

>>3977387
>discussing 2nd degree polynomials
>cites rational functions

>>3977312
>factoring lets you do mental arithmetic faster
>doesn't just suggest people do arithmetic practice and memorize the multiplication table
>implying anyone in real math cares about memorized things

[sage No.3977488]

>>3976784
>butt hurt
>this guy

pick two.

You're all kinds of jelly of my plug 'n chug.

[Anonymous No.3977499]

as best I can figure the argument for ac factoring centers around "it lets you practice more, therefore you will be better at math later".

That may well be true, but the same can be said about using inferior methods in any other discipline. You might as well ask people to prove all derivatives from the definition of derivative and limit, instead of just using shortcuts like the power rule.

Protip: Nobody actually does this because it's retarded.

[Anonymous No.3977592]

>>3977499
>fails to see how 2nd degree polynomials may be formed (quite frequently) through the use of quotient rule
>thinks arithmetic practice with integers is the same as arithmetic practice with variables
>precalc CC/HS student

>>3977499
>nobody actually does proofing

Whatever you say.

The argument is that the method that is fastest should be chosen. This varies based on problem for factoring and quadratic. This never varies with delta-epsilon proofing. Not to mention <span class="math">\displaystyle \delta-\epsilon[/spoiler] proofing provides little practice overall.

[Anonymous No.3977661]

>>3977592
>You might as well ask people to prove all derivatives from...
>interprets as "nobody actually does proofing"
>fails at basic quantifiers


>fails to see how 2nd degree polynomials may be formed (quite frequently) through the use of quotient rule
>I am unable to understand that rational functions are fundamentally different from quadratic (polynomial) functions and therefore the quadratic formula wouldn't be applied in the first place.

Straw men, Straw Men everywhere!

You are just butthurt because you are trying (unsuccesfully) to link a very specific method choice (ac vs quadratic formula) to a more general understanding of mathematics, and nobody is letting you do that because we're smart enough to understand the restraints of the question.

>>3977474
>implying anyone in defense of the quadratic formula for simply quadratic equations is looking for a "work around" to make the ac method work when it's not already trivially obvious.
See above.
Yes we all know that. We also know that taking the -b/2a part of the quadratic formula is an easy way to find the vertex. Nobody has mentioned it because it's IRRELEVANT to the debate at hand. You mention it because you are the only person in here unable to grasp that.

[Anonymous No.3977682]

>The point is that you are consistently breaking down terms into factors. Eventually, you begin to learn the factors by memory. From this, you can make later inferences about the factors and more applicable uses (especially rewriting two bases as the same with different powers.

>It allows you to have more agile mental skill. That way you can automatically see which one will take the most amount of time to complete and select the one based on that. The more factors you know of a certain combination of integers, the less likely you will have to rely on the quadratic.

>thinks arithmetic practice with integers is the same as arithmetic practice with variables

nigga are you just successfully trolling or actually functionally retarded?

[Anonymous No.3977685]

>this thread could have been resolved in a single post, then deleted
>ensuing 49 posts
>ISH you guys didn't write those

[Anonymous No.3979596]

>>3977661
>"straw man!"
>uses straw man 'unsuccessfully (FTFY)

You don't appear to be smart enough to understand shit. Being able to manipulate numbers and expressions is quite valuable in math. By resorting to a generalized formula /every/ time, you're basically telling us that you either cannot see the obvious patterns (such as with the OP's question) or you have a very lazy approach when it comes to math. Similar to the scientists and engineers who only want formula to plug numbers into without realizing what the formulas are actually doing.

When you looked at kinematics (if you have), you probably just took the base equations for position, velocity given time, and velocity given position without realizing how it was derived much less fiddled around with the concept of variable acceleration.

When you got to (if you have) multiplication with vectors in calculus, you probably just memorized what to do without realizing what dot and cross product actually do to the vector and their implications in physical space.

I could continue but the point is that, if you rely on this equation every time, you probably aren't a very good mathematician or physicist.

Now find the zeroes of <span class="math">\displaystyle x^2-2x+1[/spoiler] using your drawn out equation.

Also, the determinant is very relevant to this discussion and I believe you are mad about the fact that I plucked out one of the more valid (and obvious) rebuttals for your rickety argument before you realized it. If we're discussing the positive and negative aspects of one approach over another, it might be intelligent to look at the big picture.

[Anonymous No.3979603]

But that's the funny part. We're currently discussing your lack of being able to see big pictures due to overuse of equations that you apply to everything without first analyzing what is given and thinking of other simpler methods to arrive at a solution.

So it shouldn't come as a surprise that you want to focus on one section of the argument instead of looking at the entire thing and addressing it.

[Anonymous No.3979618]

fuck u faggot OP reported