Dustlooper's Academic Corner

[Dustlooper]

So, a lot of people have been asking me questions about their homework or just things that interest them. That's entirely cool, but I also wanted to be able to share the information to those who would be interested in reading it. So, I'm gonna use this topic to archive answers in the first post (think table-of-contents) while answering questions I receive on the forum or in the IRC channel.

Just a few things, so you know about what I am. I'm a mathematics and physics major at Western Kentucky University; my mathematics major is calculus education (high school) and physics education. I'm part of the SKyTeach program, so I follow a philosophy of inquiry-based learning. That's to suggest that I don't believe lecture and repetition are the most efficient ways of teaching (although they have their uses). Instead, I believe in guiding a lesson through the use of questioning in order to make students draw conclusions; it's through testing their conclusions via assessment (both informal and formal) that I am able to gauge misconceptions and correct them. This leads to a deeper level of understanding for both the student and myself. In addition, my learning theory is heavily based on the idea that students construct knowledge based on their prior experiences (Piaget and cognitive theorists support this claim). Because of this, either creating experiences (through classroom activities) or referring to their prior experiences (often using interdisciplinary education, or teaching a class using multiple subjects, like art+math) is the most effective way to teach children.

Beyond mathematics and science, I'm pretty well qualified. In the realm of English, I've been a nationally known poet since about 7th grade; I was first noted by NCTE (National Council for the Teachers of English). From there, I've continued to work in the some English education. Since my freshman year of college, I've worked with Japanese exchange students and helped them with English in order to prepare for my student teaching (Which originally was to be in Japan, but a certain earthquake with a certain nuclear disaster rendered that null).

In the realm of teaching social studies, I do have some experiences. Honestly, my experiences are not as applicable here as they were in prior mentions. I've actually gone to the floor of my state legislation a few times; the most significant was when I was a co-speaker for a bill. The instance I was able to do this was my junior year of high school. I composed a bill for requiring a seat belt-interlock-initation device to be required in vehicles. Think of this like what alcoholics have: their interlock device requires them to breathe into a breathalyzer before they can start their car. This would require your seatbelt to be locked before you ever start your engine. Bill was killed on the floor because of the lack of ease of implementing it. But, I still remain politically active to this day (namely with volunteering with the Libertarian party). So, I can help a lot with politics and civics homework; history isn't as strong, but you can google that.

So, that's just a bit of my credentials. If you need homework help or just wanna ask about something academic, go for it.

[Lakhvir14]

Mathematics <3

[BigBadWolf]

here is a math question I struggled with back last semester, I got this question wrong on my exam. here it is


Solve for M: integral (from 1 to M) 1/x^2 = 2. (show your work)


and this is another match problem I struggle with

3 men were on a business trip and had to stay in a hotel overnight. The price of the room was $30, so the men decided to split 1 room, 3 ways. Each one paid $10. Well after they paid, the manager realized that he overcharged them on their room. The room only cost $25, so he gave the bell boy 5 one dollar bills to give to the 3 men. On his way up to the room the bell boy was trying to think of a way to split $5 three ways. After thinking about it awhile, he decided to keep $2 for himself and give each man $1 back. Now, if each man (who paid $10) gets $1 back that means they each paid $9 ($10- $1= $9). $9 multiplied by 3 (because there are 3 men) equals $27 plus the $2 the bell boy kept equals $29! What happened to the missing dollar???

[IlIl00]

3 men were on a business trip and had to stay in a hotel overnight. The price of the room was $30, so the men decided to split 1 room, 3 ways. Each one paid $10. Well after they paid, the manager realized that he overcharged them on their room. The room only cost $25, so he gave the bell boy 5 one dollar bills to give to the 3 men. On his way up to the room the bell boy was trying to think of a way to split $5 three ways. After thinking about it awhile, he decided to keep $2 for himself and give each man $1 back. Now, if each man (who paid $10) gets $1 back that means they each paid $9 ($10- $1= $9). $9 multiplied by 3 (because there are 3 men) equals $27 plus the $2 the bell boy kept equals $29! What happened to the missing dollar???

Damn this took a while. But I figured it out and it has nothing to do with math.
EDIT: well a little bit of math.

[Ninjanuity]

3 men were on a business trip and had to stay in a hotel overnight. The price of the room was $30, so the men decided to split 1 room, 3 ways. Each one paid $10. Well after they paid, the manager realized that he overcharged them on their room. The room only cost $25, so he gave the bell boy 5 one dollar bills to give to the 3 men. On his way up to the room the bell boy was trying to think of a way to split $5 three ways. After thinking about it awhile, he decided to keep $2 for himself and give each man $1 back. Now, if each man (who paid $10) gets $1 back that means they each paid $9 ($10- $1= $9). $9 multiplied by 3 (because there are 3 men) equals $27 plus the $2 the bell boy kept equals $29! What happened to the missing dollar???

There is no missing dollar. The men paid $30 for the room. The hotel gave $5 to the bellboy to return and kept $25. The bellboy kept $2 and gave $3 to the men. 25 + 2 + 3 = 30

The faulty reasoning lies in the addition at the end. 9 x 3 = 27, but since that $27 also includes the $2 the bellboy took (remember, $25 was the cost of the room), it makes no sense to add it again. So essentially, they paid $27. The extra $3 were given back to them.

[IlIl00]

alright bro good job. just hide or edit your answer give other people a chance.

[TheTaiwanNinja]

Geni, find the anti-derivative of the function and solve for m when taking the definite integral

Integral(1/x^2) = -1/x. Don't worry about C since we are taking a definite integral.

So now plug in the values 1 and m like any other definite integral

(-1/m)-(-1)=2
(-1/m) + 1 = 2
(-1/m) = 1
-1=m

If someone else already answered oh well : \

[Oculus-Orbis]

and this is another match problem I struggle with

3 men were on a business trip and had to stay in a hotel overnight. The price of the room was $30, so the men decided to split 1 room, 3 ways. Each one paid $10. Well after they paid, the manager realized that he overcharged them on their room. The room only cost $25, so he gave the bell boy 5 one dollar bills to give to the 3 men. On his way up to the room the bell boy was trying to think of a way to split $5 three ways. After thinking about it awhile, he decided to keep $2 for himself and give each man $1 back. Now, if each man (who paid $10) gets $1 back that means they each paid $9 ($10- $1= $9). $9 multiplied by 3 (because there are 3 men) equals $27 plus the $2 the bell boy kept equals $29! What happened to the missing dollar???

Part of the problem lies in the fact that the $25 lies undivided(the value that each man SHOULD have paid).
($)25 divided by 3(men) equals ($)8.33...(eight, and one third)
So if they each got a dollar back, that becomes 9.33...
Multiply that by 3, and you get 28, which, subtracted by 30, gives the $2 difference that the bellboy took(that jerk).

Edit: realized Ninjaunity solved/explained it in a different way. my bad.

Also, another way to look at it, is that the 25 they should have paid plus the 3 they got back equals 28.
Which again, when divided by 3 means each man paid 9.33... NOT 9.

In all answers, it seems the dollar disappears in the logic errors of the problem itself?
I could be wrong here(I'm admittedly terrible @ math). But at least my answers seem to make sense to me.