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That was nice!!

1: Cos(30) = 1/r therefore r = 2/sqrt3 and r^2 = 4/3

2:Area of equil Triang = (1/2)*(2)*sqrt((2^2)-(1^2))=sqrt3 therefore Area of rectangle = xy = sqrt3

3 Draw lines to the opposite vertices of the rectangle then add the area of the 4 triangles you just made inside the rectangle = total area:

2*area Tri A= 2*[(1/2)(x)sqrt(4/3 - (x^2)/4)

2*area Tri B= 2*[(1/2)(y)(x/2)]

4, Solve simultaneous equation to get x and y:

xy = sqrt3

(x)sqrt(4/3 - (x^2)/4) + (1/2)xy = sqrt3

--> If doing manually you substitute the first equation into the second then solve for x, followed by y, but since I'm lazy I used Wolfram alpha to do this for me and got

x≈2.16662 and y≈0.799424

3x - y = 7             (1)

2x + y = 8            (2)

Add (1) and (2) term by term to eliminate y

5x = 15

Divide both sides by 5

x = 3

Put this back into (2)

2*3 + y = 8   or   6 + y = 8

Subtract 6 from both sides

y = 8 - 6  or  y = 2

You should check these by putting them back into the original equations to see if the left-hand sides equal the right-hand sides.

.

$$(5 + \frac{1}{6})\times 7\rightarrow5\times 7 + \frac{1}{6}\times 7\rightarrow 35+\frac{7}{6}\rightarrow35+1+\frac{1}{6}\rightarrow 36\frac{1}{6}$$

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40 metres every 2 minutes is only 20 metres in one minute MG, not 1200 metres!

.

Hi Melody,

In LaTeX when you use $ for spaces in my coding it doesn't work..For the first line it does but for the rest it doesn't leave spaces between my words so i had to stick with \; , however I'd prefer to just use the dollar sign as it's easier...

E.g. recent code.

\\\\$Let's hope Steve has high stamina\\\\
\\So 40m every two minutes (2\times30=60 minutes) so\;40m\times30= a\;hour = 1200\;meters\\
\\$1200 meters\times\;24\;for\;a\;day\;=\;28000\;meters$\\
\\$28000\times\;365\;for\;a\;year\;=\;10512000\;meters$\\
\\10512000m\;is\;a\;year,\;a\;century\;is\;100\;years\;\\
\\10512000m\times\;100=1051200000m\\
\\\\Convert\;1051200000m\;into\;centermeters\;=\;105120000000 cm\\\\
Your\;answer\;is\;105120000000 cm

$$\\\\$Let's hope Steve has high stamina\\\\
\\So 40m every two minutes (2\times30=60 seconds) so\;40m\times30= a\;minute = 1200\;meters\\
\\$1200 meters\times\;60\;for\;a\;hour\;=\;72000\;meters$\\
\\$72000\times\;24\;for\;a\;day\;=\;172800\;meters\qquad(here's\;where\;it\; gets\;big)$\\
\\172800\times\;365\;for\;a\;whole\;year\;=\;630720000m\\
\\630720000m\;is\;a\;year,\;a\;century\;is\;100\;years\;\\
\\630720000m\times\;100=63072000000m\\
\\\\Convert\;63072000000m\;into\;centermeters\;=\;6307200000000 cm\\\\
Your\;answer\;is\;6307200000000 cm$$

Just trying to make my LaTeX usefull.

But when you showed me all the harder things like Quadratic Equation, i don't think I'll make use of that with LaTeX since i don't understand it (unless i copy for learning) for now fractions, text, indices are it's us for me.

@@ End of Day Wrap   Tues 12/5/15   Sydney, Australia Time   10:40pm  ♪ ♫

Hello everyone,

Today our answer credits are awarded to Mathcad, Xerxes, Geno3141, Civonamzuk, Alan, DarkBlaze347, Beary, HeatherF, CPhill, Zacismyname, MathsGod1, Headingnorth amd Kes1968.  Thanks guys (I could add 'and girls' but I don't need to because in Australia, if 'guys' is used in this way, it automatically includes the girls   )

Yeah i know?

Isn't what i said right?

HeadingNorth said it simplified so i made the answer more specific ( 400 ) .

Thank's Melody, you always put a   smile   on my face.

Wed 13/5/15

If you would like to comment on other site issues please do so on the Lantern Thread.  Thank you.    

FTJ means 'For the juniors' 

Interest Posts:

2x-4+x=

3x-4

MathsGod1, you have a great deal of enthusiasm and intelligence.

I have a passion for mathematics and I know that you do too.

Helping you to learn is a geat pleasure for me :)

Titanium:

The slogan was Lancelot for Camelot!

It is a great slogan, I expect the chimp will use it again the next time he runs of office.   :D

Yes xerxes that sounds right.  

Of course it would work for any but there would only be a real answer if the denominator was odd.

You might find this interesting Xerxes,

8 batteries costs 5.99

1 battery should cost 1/8 of the price of 8 batteries.

therefore 1 battery cost     $$5,99/8=$$

the median is the value in the middle.

if you got 1,3,4,4,5,6,7,8,9 then 5 is your median because it is in the middle.

What if you got 5,9,3,11,2,8,4,6?

then you sort the values from smallest to largest: 2,3,4,5,6,8,9,11. the value in the middle is the median.

in this scenario we got two numbers in the middle so in this case the median is the average of the two values in the middle (5+6)/2 =13/2=6,5

:)

Thanks Kes,

I think that you mean THE ABSOLUTE VALUE OF -5/8 IS  5/8    

for example x=4

and y=0,05

to solve this you need one more equation otherwise it´s not possible to solve it.

Thanks Alan,

This would be a really nice one for Zac (or somene else) to explain in detail.

Where is Zac when we need him. Any other takers?  LOL

WOW.  That is really fast!     

And the cops book us for speeding!!      

MG

The answer is 400.      NOT 1/6

Thanks. It took me quite a few minutes to get my head around it. 

Yeah I haven't learnt that yet.

I did consider this.

$$\frac{5x+2}{2}=2x-1$$

$$5x+2=2{(2x-1)}$$

$$5x+2=4x-2$$

$$x=-4$$