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| Lorryman100 Member Since: 01 Oct 2010 Location: Here Posts: 2686  |
Is the answer 12ft. By using inscribed circle law and squaring both sides then using the Quadratic formula that's what I get?
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5th Jan 2012 11:49pm |
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| 110SEB Member Since: 29 Jan 2009 Location: Essex, England Posts: 1444  
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Isn't this a trick question as the dimension at Y is an unknown amount more than 3ft (Grrr, Imperial) it just so happens a 3ft circle fits in the void. We therefore only know one measurement and can't work out the vertical or horizontal.
Sine, cosine, tangent? Forgotten which is which. B at GCSE maths 16 years go (in Worcester as it happens, Pom). |
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6th Jan 2012 6:56am |
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| kingofthesparks Member Since: 06 Jan 2011 Location: Very close to Watford gap services , northants Posts: 987 
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11.8877777777
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6th Jan 2012 7:52am |
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| JWL Member Since: 26 Oct 2011 Location: Hereford Posts: 3443  
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I get 12' doing a quick scale drawing, that would be close eniough for me, well within any tolerence levels I work with
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6th Jan 2012 7:52am |
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| GREENI Member Since: 22 Aug 2010 Location: staffs Posts: 10383
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Isn't it a kiss?
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6th Jan 2012 7:56am |
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| JWL Member Since: 26 Oct 2011 Location: Hereford Posts: 3443
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 Damn smart phone, double post |
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6th Jan 2012 8:18am |
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| ZeDefender Member Since: 15 Sep 2011 Location: Munich Posts: 4731  
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Pom - you tell me your answer and I'll tell you if it's right
 Tell someone you love them today because life is short.
But shout it at them in German because life is also terrifying and confusing... |
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6th Jan 2012 8:46am |
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| XS Pete Member Since: 13 Jan 2011 Location: Suffolk Posts: 632 
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I get 12' too. As Lorry says, as the three sides of the triangle form three tangents with the circle, you can treat it as an inscribed circle (or incircle).
Pete |
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6th Jan 2012 8:50am |
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| T1G UP Member Since: 08 Dec 2009 Location: Bath Posts: 3101 
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turn the circle into a box, you know its 3 ft.
then you end up with 2 x right angled triangles and a box easy from there on in.....think this was a starter question when i did my HNC some time ago. heads full of mantec storage and shower cubicals at the mo! |
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6th Jan 2012 9:07am |
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| blackwolf Member Since: 03 Nov 2009 Location: South West England Posts: 17568 
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There are two possible answers mathematically, x=12 or x=3.5
If we consider y to be the length of the short side, we know that: (x - 1.5) + (y - 1.5) = 12.5 (since chords are of equal length) => x + y = 15.5 which we will call eq1 We also know that x^2 + y^2 = 12.5^2 (Pythagoras) which we will call eq2 Squaring eq1 and subtracting eq2 gives us eq3) 2xy = 15.5^2 - 12.5^2 => 2xy = 84 considering eq1 again: x + y = 15.5 => y = 15.5 - x Subsitute for y in eq3: 2x(15.5 - x) = 84 multiply out: 31.1x - 2x^2 = 84 therefore 2x^2 -31x +84 = 0 Solve the resulting simple quadratic equation: x = (31 +- sqrt[961 - 672])/4 = (31 +- sqrt[289])/4 = (31 +- 17)/4 So two solutions, either x = 12 and y = 3.5 or x = 3.5 and y = 12 There may be a simpler way, but I can't see one at the moment! |
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6th Jan 2012 10:37am |
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| Lorryman100 Member Since: 01 Oct 2010 Location: Here Posts: 2686 |
The easiest way to find x is to program the diagram into AutoCad and it works everything out for you.
Or you can go down the maths route:  Click image to enlarge |
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6th Jan 2012 11:16am |
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| shaun.mobile Member Since: 12 Dec 2011 Location: England Posts: 156 
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my partner and i were feeding our twins last night. they both take 150ml.
my partner commented that this volume does not seem to have increased over the past few weeks even though they are growing. i asked her to consider this volume as a sphere and compare it to the size of their abdomen's. what size is the sphere? 
no internet or reference books allowed!!! |
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6th Jan 2012 11:17am |
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| Lorryman100 Member Since: 01 Oct 2010 Location: Here Posts: 2686 |
Come on then Pom, what is the answer?
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6th Jan 2012 11:34am |
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| Martin Site Admin Member Since: 02 Apr 2007 Location: Hook Norton Posts: 6635 
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Which size: radius, diameter, volume?  1988 90 Td5 NAS soft top
2015 D90 XS SW |
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6th Jan 2012 11:54am |
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