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Atomic Boo

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This is from a set of problems we were given by an exchange school. The maths teachers can't do it, so any maths enthusiasts - knock yourselves out!

 

You are given a triangle ABC. The point M is the mid-point of BC. The length of MA is d. Prove that, given d < AB and d < AC, BC is always an even integer.

 

Have fun!

 

They aren't all met - in that case AB and AC would be greater than d.

 

Which is what they are supposed to be.

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Ah, the post got edited... the first time round, it said d > AB &c.

 

That's not possible. If M is on BC and d is greater than AB and AC then ABC can't be a triangle. The furthest point from A has to be one of the corners.

 

Unless I've read it wrong.

 

Oops... sorry. I put the wrong crocodile.

 

Way to go, me...

 

Also, I'm pretty sure it's posible. If I get a proof I'll post it here.

 

You should have read the thread Grunchie. Anyway my post still stands. It's not true.

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It's not true. Draw an equilateral triangle with side 9 and all of those criteria will be met but BC won't be even.

 

Sorry. I'm an idiot.

 

All the sides and d are natural numbers.

 

I must have been drunk or something that night. Getting my inequalities mixed up and forgetting essential information. Oops...

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Sorry. I'm an idiot.

 

All the sides and d are natural numbers.

 

I must have been drunk or something that night. Getting my inequalities mixed up and forgetting essential information. Oops...

 

GRRR.

 

It still isn't true as you could draw and equilateral triangle with sides of 9.323454235345345345 or whatever.

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Another maths one...

 

i, j and k are unit vectors in the x-, y- and z-directions respectively. The 3-dimensional vector r has a magnitude of 5, and makes angles of 1/4 pi radians with each of i and k.

 

Write r as a column vector, leaving any square roots in your answer.

 

whaaaat theee fuuuuuck.

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Well, if it makes angles of pi/4 radians (aka 45 degrees) with both i and k, then it stands to reason that it lies in the i k plane. (draw a diagram if you can't see why this is). So the j component is 0, but what of the other two? Well they'll both be 5cos(pi/4) (or 5sin(pi/4), same thing), which is 5/sqrt(2).

 

So the i component is 5/sqrt(2), the j component is 0 and the k component is 5/sqrt(2), which you can write as a column vector.

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Well, if it makes angles of pi/4 radians (aka 45 degrees) with both i and k, then it stands to reason that it lies in the i k plane. (draw a diagram if you can't see why this is). So the j component is 0, but what of the other two? Well they'll both be 5cos(pi/4) (or 5sin(pi/4), same thing), which is 5/sqrt(2).

 

So the i component is 5/sqrt(2), the j component is 0 and the k component is 5/sqrt(2), which you can write as a column vector.

 

Assuming you mean 5/2 sqrt(2) then awesome. That what the answer apparently is, and now i know how to get to it ^_^.

 

Just check on my calculator, 5cos(pi/4) is 5/2 sqrt(2) :)

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Assuming you mean 5/2 sqrt(2) then awesome. That what the answer apparently is, and now i know how to get to it ^_^.

 

Just check on my calculator, 5cos(pi/4) is 5/2 sqrt(2) :)

Actually, our answers are one and the same, you've just rationalised the denominator by multiplying top and bottom by sqrt(2):

 

5/(sqrt(2)) = (5sqrt(2))/((sqrt(2))(sqrt(2))) = (5sqrt(2))/2 = (5/2)sqrt(2).

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  • 3 weeks later...

Need someone who knows Excel as its been years since I've used it.

 

Basically I want a bar graph that along the side has number of mins, along the bottom is days and along the other side is a different set of numbers (percent of day) which is shown as a line graph.

 

Basically I am doing a project which looks at American tv shown on Britain. The days will remain constant but the number of mins and percent are so different (say 200-odd would make a 8% or whatever) so the two range of numbers have to be different on either side otherwise the line graph just floats around the base.

 

Thanks.

 

Real example (sorry about formatting):

 

W/C 16/02/08 – BBC1

Day No. of Mins % of day

Saturday 225 15.625

Sunday 170 11.805556

Monday 220 15.277778

Tuesday 135 9.375

Wednesday 175 12.152778

Thursday 45 3.125

Friday 100 6.944444

 

As you can see as it stands the left side would read 45-225 and the left should read 3.125-15.625 (or be rounded up)

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  • 3 weeks later...

x= t-1/t y=t+1/t

 

show dy/dx= (t-1)(t+1)/t^2+1

 

 

This is really annoying me, because we've done the problem essentially in a maths exercise before (except y and x other way round) but I can't get the final answer, because I differentiate y to get dy/dt= -t^-2+1

 

which means I have a negative which I don't want. Can someone help me please :) thanks.

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x= t-1/t y=t+1/t

 

show dy/dx= (t-1)(t+1)/t^2+1

 

 

This is really annoying me, because we've done the problem essentially in a maths exercise before (except y and x other way round) but I can't get the final answer, because I differentiate y to get dy/dt= -t^-2+1

 

which means I have a negative which I don't want. Can someone help me please :) thanks.

 

x= t-1/t y=t+1/t

dx/dt = 1+t^-2 dy/dt = 1-t^-2

 

dy/dx = dy/dt X dt/dx

dy/dx = 1-t^-2/1+t^-2

dy/dx = 1+t^2/1-t^2

dy/dx = (t+1)(t-1)/(t+1)(1-t)

dy/dx = (t-1)/(1-t)

 

Multiply by (-1/-1)__________[-1/-1 = 1, so it's correct]

 

(t-1)/(1-t) * (-1/-1) = -1(t-1)/-1(1-t) = (-t+1)/(-1+t) = (1-t)/(1-t)

QED: (t-1)/(1-t) = (1-t)/(t-1), therefore (t-1) = (1-t)

 

dy/dx = (t-1)(t+1)/(t+1)(1-t) = (t-1)(t+1)/(t+1)(t+1)

 

QED: dy/dx = (t-1)(t+1)/t^2+1

 

 

Yes, it's not actually numerically correct, but it is algebraically, oddly...

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I need to condense it into a five minute presentation though...

 

Im going to go at it from the per week angle instead, and have all five channels on one graph.

 

Thanks though :)

 

Here's what I did with the data that you gave:

 

excelscreenshotwl9.png

 

Excel File Download.

 

Hope it helps. You could probably add extra day data quite easily to that graph.

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What core maths is that?

 

C4.

 

Its so annoying, I'm sure I've made a silly mistake. I was hoping to have it figured out for when I take it in tomorrow but I just can't see where I've gone wrong, nor understand the fish.

 

Also fish, when you said (t+1)(t+1) at the bottom = T^2+1, thats wrong. Its t^2+ 2t +1.

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