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.
Homework Help Thread
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The solution seems to depend on two parameters:
- The length of one of the horizontal lines with an endpoint at D - i.e., AD, BD, or CD.
- One of the horizontal angles including A, B, or C as their vertex - DCB is one of them.
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
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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.
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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)
/\ \ _ _ _ _ ______
/ \ \ | | (_) | | ____|
/ /\ \ \| | |_ ___ __| | |__ _ ____ ___ _
/ / /\ \ \ | | |/ _ \/ _` | __| | '_ \ \ / / | | |
/ / /__\_\ \| | | __/ (_| | |____| | | | V /| |_| |
/ / /________\_|_|\___|\__,_|______|_| |_|\_/ \__, |
\/___________/ Any sufficiently advanced kludge __/ |
is indistinguishable from careful design. |___/
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You mean, cos∠(ABD) = (AB² + BD² - AD²) / (2AB * BD).inspired wrote:△ABD, cos∠(ABD) = (AB2 + AD2 - BD2) / (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.
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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.
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The InformantInspired wrote: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.
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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.T̷s͢uk̕a͡t͜ư wrote:The InformantInspired wrote: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.
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Inspired wrote: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?
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As opposed to...?SłappyMcGee wrote:Inspired wrote: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?

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Well, I meant is the content inappropriate for the class, or does he not think that it suits what he is trying to write?T̷s͢uk̕a͡t͜ư wrote:As opposed to...?SłappyMcGee wrote:Inspired wrote: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?
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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.Inspired wrote: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.

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I doubt it. If A Clockwork Orange is fine, there probably isn't a rating issue.SłappyMcGee wrote:Interesting; is it because of the content?Inspired wrote: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.
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Inspired wrote: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.
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SłappyMcGee wrote:Then let me recommend also not watching A Clockwork Orange.
Ahahahah.Inspired wrote:...Okay, I watched A Clockwork Orange...

vankusss wrote:What 'more time' means?
I'm going to buy some ham.
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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.Inspired wrote:Later this week I will be hiring out Pan's Labyrinth to watch as well as 2001: A Space Odyssey and possibly If....
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The first amendment was written at a different time, three hundred years ago, and has no relevance today.DemonzLunchBreak wrote: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.Slayr wrote: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.
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I hate the first amendment (and most of the next fifteen).=w= wrote:The first amendment was written at a different time, three hundred years ago, and has no relevance today.DemonzLunchBreak wrote: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.Slayr wrote: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.
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vankusss wrote:What 'more time' means?
I'm going to buy some ham.
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"Should it be allowed" is not the question. The question is "should it be built".DemonzLunchBreak wrote: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.Slayr wrote: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.
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.

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