Homework Help Thread

[Universezero]

Okay, I have this math problem that I need help with. I've tried everything to solve it, but somewhere I seem to be screwing up.

At the Olympic Games 40 years ago, the average number of competitors per sport was 5 times the number of sports played.

In 2004 there were 10 more sports than there were 40 years ago. In 2004 the average number of competitors per sport was 3.5 times greater than 40 years ago.
At the 2004 Olympic Games there were 10500 competitors.

Write at least ONE equation to model this situation.
Use the model to find the number of sports played at the Olympic Games 40 years ago. Show all your working.

[ninja143]

I can add a Managers Aspect to things as well as how to have good customer service and such. For any Business Majors i can help some. I also do well on computers and Art, some math and a good one to talk to about stuff in general.

[AlliedEnvy]

Inspired, I think I have an approach to the solution.

The solution seems to depend on two parameters:

1. The length of one of the horizontal lines with an endpoint at D - i.e., AD, BD, or CD.
2. One of the horizontal angles including A, B, or C as their vertex - DCB is one of them.

For these, let us choose CD for 1 and DCB for 2. We can determine the length of AD and BD from those two pieces of information, and from those, determine TD for each of A, B, and C. Only one combination of length of CD and angle of DCB should give the same length of TD for all three, and that is the answer.

At this point I am either too tired or too rusty at Trigonometry to proceed, but it goes something like this:

TD_C = some trigonometric function of TDC and CD
BD = some trigonometric function of BC, CD, and DCB
AD = " of AC, CD, and DCB
TD_B = " of TBD and BD
TD_A = " of TAD and AD

solve for TD_C = TD_B = TD_A = TD, using variables of only DCB and CD

[scythe]

The length TD in the diagram is given implicitly by the variable x in the following system of six equations in six variables, obtained by applying the definition of the tangent function to the diagram six times:

h = l * c
h = (l + 50) * b
h = (l + 110) * a
(x + h)(1 - c * sqrt(3)) = l * (c + sqrt(3)
(x + h)(1 - b) = (l + 50)(1 + b)
(x + h)(3 - a * sqrt(3)) = (l + 110)(3 * a + sqrt(3))

The solution of these equations is left as an exercise to the reader.

EXTRA CREDIT: Find the meanings of the variables h, l, a, b, and c, with respect to the diagram. Hint: None of them are labeled.

[AlliedEnvy]

Ok, I did a little more thinking about this, following the outline I laid out yesterday, and came to an answer:

Click to show/hide spoiler

TD_C = sqrt(3)*CD (because it's a 30-60-90 triangle)

BD = sqrt( BC^2 + CD^2 -2*BC*CD*cos(DCB) ) (Side-Angle-Side)
BD = sqrt( 2500 + CD^2 -100*CD*cos(DCB) )

AD = sqrt( AC^2 + CD^2 -2*AC*CD*cos(DCB) ) (Side-Angle-Side)
AD = sqrt( 12100 + CD^2 -220*CD*cos(DCB) )

TD_B = BD (because it's a 45-45-90 triangle)
TD_B = sqrt( 2500 + CD^2 -100*CD*cos(DCB) )

TD_A = AD/sqrt(3) (because it's a 30-60-90 triangle)
TD_A = sqrt( 12100 + CD^2 -220*CD*cos(DCB) )/sqrt(3)
TD_A = sqrt( (12100 + CD^2 -220*CD*cos(DCB))/3 )

TD_C = TD_B
sqrt(3)*CD = sqrt( 2500 + CD^2 -100*CD*cos(DCB) )
3*CD^2 = 2500 + CD^2 -100*CD*cos(DCB)
2*CD^2 - 2500 = -100*CD*cos(DCB)
(1250 - CD^2)/(50*CD) = cos(DCB)

Substitute in TD_A = TD_C
TD_A = TD_C
sqrt(3)*CD = sqrt( (12100 + CD^2 -220*CD*((1250 - CD^2)/(50*CD))/3 )
9*CD^2 = 12100 + CD^2 -220*CD*(1250 - CD^2)/(50*CD)
9*CD^2 = 12100 + CD^2 -4.4*(1250 - CD^2)
9*CD^2 = 12100 + CD^2 -5500 + 4.4*CD^2
3.6*CD^2 = 6600
CD^2 = 5500/3
CD = sqrt(5500/3)

Substitute in TD_C
TD_C = sqrt(3)*CD
TD_C = sqrt(3)*sqrt(5500/3)
TD_C = sqrt(5500)
TD_C = 10*sqrt(55)

Check work:

Substitute in cos(DCB)
(1250 - CD^2)/(50*CD) = cos(DCB)
(1250 - 5500/3)/(50*sqrt(5500/3)) = cos(DCB)
(3750 - 5500)/(150*sqrt(5500/3)) = cos(DCB)
-1750/(1500*sqrt(55/3)) = cos(DCB)
-7/(6*sqrt(55/3)) = cos(DCB)

Substitute in TD_B
TD_B = sqrt( 2500 + 5500/3 -100*sqrt(5500/3)*-7/(6*sqrt(55/3)) )
TD_B = sqrt( 13000/3 + 700*sqrt(5500/3)/(6*sqrt(55/3)) )
TD_B = sqrt( 13000/3 + 7000/6 )
TD_B = sqrt( 16500/3 )
TD_B = 10*sqrt(55)


Substitute in TD_A
TD_A = sqrt( (12100 + CD^2 -220*CD*cos(DCB))/3 )
TD_A = sqrt( (12100 + 5500/3 -220*sqrt(5500/3)*-7/(6*sqrt(55/3)))/3 )
TD_A = sqrt( (41800/3 + 1540*sqrt(5500/3)/(6*sqrt(55/3)))/3 )
TD_A = sqrt( (41800/3 + 15400/6)/3 )
TD_A = sqrt( 16500/3 )
TD_A = 10*sqrt(55)

So, TD_A = TD_B = TD_C = TD = 10*sqrt(55)

[999_Springs]

Inspired: First, cot 60 isn't 1/3, it's 1/sqrt3. Second,

△ABD, cos∠(ABD) = (AB2 + AD2 - BD2) / (2AB * BD)

You mean, cos∠(ABD) = (AB² + BD² - AD²) / (2AB * BD).

Everything else is correct. The equation you get at the end should be:
(3600 - 2h²) / 120h = - ( 2500 + (2/3)h² ) / 100h,
which solves to the same answer that AlliedEnvy got.

If you're using Windows you might like to note that a "squared" symbol is Alt+0178 on the numpad (with num lock on). Just to make your work clearer.

[kamikaze3000]

I can do uni level maths to an extent. lord_day is much more suited than me and at a better uni though :D

(No giving help right now. Too hungover. Bleuuuuuurgh)

[999_Springs]

Easy peasy. cos 3Θ + i sin 3Θ = (cosΘ + isinΘ)³ by de moivre
cos 3Θ + i sin 3Θ = cos³Θ + 3i cos²ΘsinΘ - 3 cosΘsin²Θ - 3i sin³Θ
equate imaginary parts:
sin 3Θ = 3 cos²ΘsinΘ - 3 sin³Θ
just use sin²Θ + cos²Θ = 1 to finish.

[t̷s͢uk̕a͡t͜ư]

I need about 4 films which I can study extensively. These films need to have an underlying theme of deception, extensive use of film techniques eg. Camera shots, post-production, music etc. and a good plot-line. At the moment I have The Prestige and (possibly) The Shawshank Redemption, if you could recommend any that I should check out I would be very appreciative.

The Informant
The Usual Suspects
Thank You For Smoking
Brick

[SlappyMcGee]

I need about 4 films which I can study extensively. These films need to have an underlying theme of deception, extensive use of film techniques eg. Camera shots, post-production, music etc. and a good plot-line. At the moment I have The Prestige and (possibly) The Shawshank Redemption, if you could recommend any that I should check out I would be very appreciative.

The Informant
The Usual Suspects
Thank You For Smoking
Brick

Interesting choices. Frankly, if you want to analyze film techniques within the use of deception, any of these films would be good (although I am a bit wary of The Usual Suspects). But I like to really know that my filmmaker was actually going for what I'm going to accuse him of doing; so, naturally, I suggest Kubrick. A Clockwork Orange and Eyes Wide Shut are two brilliant movies that highlight deception as principal themes, and do so using fabulous camera work, music, and acting.

[SlappyMcGee]

Thanks! I've looked up all of those titles on imdb and all but 'Eyes Wide Shut' will be appropriate. I'll get them out from the DVD store some time this week.

Interesting; is it because of the content?

[t̷s͢uk̕a͡t͜ư]

Thanks! I've looked up all of those titles on imdb and all but 'Eyes Wide Shut' will be appropriate. I'll get them out from the DVD store some time this week.

Interesting; is it because of the content?

As opposed to...?

[SlappyMcGee]

Thanks! I've looked up all of those titles on imdb and all but 'Eyes Wide Shut' will be appropriate. I'll get them out from the DVD store some time this week.

Interesting; is it because of the content?

As opposed to...?

Well, I meant is the content inappropriate for the class, or does he not think that it suits what he is trying to write?

[capt_weasle]

Haha, I seem to be the main user of this thread.

This time I need a bit of help choosing films to study for Scholarship English. Basically, at the end of the school year I must develop 3 indepth essays on a set question using a widerange of literary sources. In the lead up to the exam I have chosen to continue my study into the topic of Deception (Which has gone well for me so far) but I need about 4 films which I can study extensively. These films need to have an underlying theme of deception, extensive use of film techniques eg. Camera shots, post-production, music etc. and a good plot-line. At the moment I have The Prestige and (possibly) The Shawshank Redemption, if you could recommend any that I should check out I would be very appreciative.

Depending on your teacher, you could probably watch Au Hasard Balthazar and get bonus points just for watching a film that makes most modern film students want to rip their eyes out (at least judging by the looks of my classmates). Though you may not enjoy it 'cause the protagonist is an ass.

[otters~1]

Thanks! I've looked up all of those titles on imdb and all but 'Eyes Wide Shut' will be appropriate. I'll get them out from the DVD store some time this week.

Interesting; is it because of the content?

I doubt it. If A Clockwork Orange is fine, there probably isn't a rating issue.

[t̷s͢uk̕a͡t͜ư]

"In an effort to further protect its citizens from reality, a new law in Australia makes it illegal to state or imply the existence of gender to children younger than 35."

[SlappyMcGee]

Stupid school computers deleted my reply. Well, it is a content issue not because of my school but rather my (over protective) Mum who would never let me watch something with such "strong sexual content, nudity, language and some drug-related material. "

I have 3 months left at home until I am out into the world and until then I have a myriad of examinations and study programmes so I am not going to go against my Mum on this. My stress levels are high enough as it is.

Then let me recommend also not watching A Clockwork Orange.

[SlappyMcGee]

Man, I'm such a boss at this movie thing.

[Kablizzy]

Then let me recommend also not watching A Clockwork Orange.

...Okay, I watched A Clockwork Orange...

Ahahahah.

[mintnut]

Later this week I will be hiring out Pan's Labyrinth to watch as well as 2001: A Space Odyssey and possibly If....

You should definitely watch if..., it's a brilliant film. Mum related warning: there is nudity/scenes of a sexual nature and an undercurrent of homosexuality just so you know.

[Slayr]

I have to write an essay about whether they should or shouldn't build a mosque near ground zero. So I'm just wondering if you guys had any unique views about it. I find it silly that I have to write about something that involves something that happened when I was 6, and I'm Canadian.

[SlappyMcGee]

I have to write an essay about whether they should or shouldn't build a mosque near ground zero. So I'm just wondering if you guys had any unique views about it. I find it silly that I have to write about something that involves something that happened when I was 6, and I'm Canadian.

I think it should obviously be allowed. I think the First Amendment and the fact that most Muslims are not terrorists make this one fairly unarguable.

The first amendment was written at a different time, three hundred years ago, and has no relevance today.

[otters~1]

I have to write an essay about whether they should or shouldn't build a mosque near ground zero. So I'm just wondering if you guys had any unique views about it. I find it silly that I have to write about something that involves something that happened when I was 6, and I'm Canadian.

I think it should obviously be allowed. I think the First Amendment and the fact that most Muslims are not terrorists make this one fairly unarguable.

The first amendment was written at a different time, three hundred years ago, and has no relevance today.

I hate the first amendment (and most of the next fifteen).

[Kablizzy]

If they have the money and the permit, they build. There's no reason to not let 'em.

[t̷s͢uk̕a͡t͜ư]

I have to write an essay about whether they should or shouldn't build a mosque near ground zero. So I'm just wondering if you guys had any unique views about it. I find it silly that I have to write about something that involves something that happened when I was 6, and I'm Canadian.

I think it should obviously be allowed. I think the First Amendment and the fact that most Muslims are not terrorists make this one fairly unarguable.

"Should it be allowed" is not the question. The question is "should it be built".
Obviously it should be allowed to be built. Freedom of speech, etc.; only an idiot would contest that.
But if the question is "should a mosque be built at Ground Zero," I can answer that question just after you say the word "built": no, I don't think any mosque building should happen at all. And neither should any churches, synagogues, buddhist temples, hindu shrines, yeti caves, or leprechaun lairs. Location is unimportant.