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The geometric mean only applies to positive numbers.

It has a geometric interpretation.  Image a rectangle with sides 10 and 30.  It has an area of 300.  A square of side √(10*30), i.e. one with side lengths equal to the geometric mean of the two rectangle lengths, has the same area.  

Similarly, for higher order geometric means. e.g. a cuboid with side lengths u, v and w has the same volume as a cube with side lengths ³√(u*v*w), etc.

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I haven't heard of this before, but here's some info........

For interest's sake then, let's suppose the two cars collide elastically, conserving both energy and momentum.

Momentum before:  1300*30 - 900*15 kg.m/s = 

Momentum after: 1300v1 + 900v2   

so 1300v1 + 900v2 = 25500   ...(1)

Kinetic energy before:  1300*30²/2 + 900*15²/2 = 686250 J

Kinetic energy after:  1300*v1²/2 + 900*v2²/2

so 1300*v1²/2 + 900*v2²/2 = 686250   ...(2)

Equations (1) and (2) can now be solved for v1 and v2. (v1 = -75/11 m/s ≈ -6.8 m/s;  v2 = 420/11 m/s ≈ 38.2 m/s).

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Except that P(A∩B) is given as 3!!!  Perhaps this was meant to be 0.3.

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P(A l B) = P(A ∩ B) / P(B) = ( .4 * .5) / (.5) = .20 / .5   = .40 = 40%

Goodnight Rosala :)   You are always a VIP, whether you are in the wrap or not :)))

oh yes i believe it will

but no over confidence......

you know whenever india wins a cricket match so important then you can hear crackers all night!ah its such a pain!

Thank you Alan. I usually understand these intuitively, first, then learn the maths. In this case, it is the other way around. I need to develop a mental picture from the scalar and vector dimensions via the maths. 

_7UP_

@@ End of Day Wrap   Sat 14/2/15 Sydney,    Australia Time 12:50 am    (Really Sun morn)  ♪ ♫

Hi everyone,

Our answerers today were CPhill, Sorasyn, Sobewo, alan, SevenUP and Nauseated.

Thanks all.  

Interest Posts:

Sun 15/2/15  and mMon 16/2/15

Well, tomorrow you will see if the trend continues LOL :))

we dont need luck...i saw an add in which a pakistani man has his box of crackers which he is unable to burn every year as pakistan never wins...and as this goes on,....he gets old too!LOL

$${\left({\mathtt{9}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{5}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{5}}}}\right)} = {\mathtt{6.699\: \!875\: \!826\: \!622\: \!859\: \!3}}$$

2         The minus 3s cancel out.

Hi Rosala,

Course we beat the poms!!

Out goes the chant

Aussie, Aussie, Aussie, Oi,Oi,Oi      

I wish India luck tomorrow :)

a circle has a radius of 6 and centre (-2,1). write down the equation of the circle

$$(x+2)^2+(y-1)^2=36$$

btw Melody...today Australia won by 111 runs.....ooooohhhh!

check  it out!

https://www.google.co.in/search?site=webhp&q=2015+Cricket+World+Cup&oi=ddle&ct=cricket-world-cup-opening-2015-5747017477259264-hp&hl=en&sa=X&ei=hkbfVNSGC5fmuQSuyICgAg&ved=0CAQQNg&biw=1360&bih=667&dpr=1#hl=en&q=2015+Cricket+World+Cup+

look under formulary at the top of the page :)

SO

The geometric mean of 7,6,8 and 2

is it   $$\sqrt[4]{7*6*8*2}$$

$${\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{2}}\right)}^{\left({\mathtt{0.25}}\right)} = {\mathtt{5.091\: \!459\: \!790\: \!043\: \!661}}$$

what happen if there is negative numbers?

I expect that you mean

(3 x 10^-2) / (12 x 10^4)

$$\\3/12 * 10^{-2-4}\\
=0.25*10^{-6}\\
=2.5*10^{-1}*10^{-6}\\
=2.5*10^{-7}$$

$$\\If x=2,\;\; y= -1\;\; and\;\; z=3 \\\\
$find the value of the following: $\\\\
\frac{1}{3}x^2y+\frac{5}{6}y^2z^3-2y\\\\
=\frac{1}{3}*2^2(-1)+\frac{5}{6}(-1)^2*3^3-2(-1)\\\\
=\frac{1}{3}*4*(-1)+\frac{5}{6}*27+2)\\\\
=\frac{-4}{3}+\frac{5}{2}*9+2\\\\
=\frac{-4}{3}+\frac{45}{2}+2\\\\
=\frac{2}{3}+\frac{45}{2}\\\\
=22+\frac{2}{3}+\frac{1}{2}\\\\
=22+\frac{4}{6}+\frac{3}{6}\\\\
=22+\frac{7}{6}\\\\
=23\frac{1}{6}\\$$

I can't see how the 1/5 is relevant  

1/12 were absent and 11/12 were at school

so 

$$\\\frac{11}{12}X=704\\\\
X=704\times\frac{12}{11}$$

$${\mathtt{704}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{12}}}{{\mathtt{11}}}}\right) = {\mathtt{768}}$$

there are 768 students in the school.

NOTE: Alan has interpreted it differently from me.  

I hope you feel better soon Baba,

You don't need to worry about Nauseated. 

Did you know that he is a capybara.  He is just a giant rodent that cannot even digest meat.  He's a would be if he could be kind a critter. He is never going to eat you because he'd get too sick.  Capybaras are slow and stupid, but not THAT stupid.

Look here he is, with a few of his friends.  Do you really think that you need to be wary of him?

Nauseated with his friends

Thanks Alan, the pic should help a lot :))

Here's an approximate geogebra confirmation of Melody's result.

Scale everything so that h = 1.  Look down from above to see the following:

The distances DE and AE are just 3/4 of distance AD (KD is √3).

The radius of the circle centred on K and going through E is approximately 2.04, so the angle of elevation from E to the top of the post is tan^-1(1/2.04)

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{1}}}{{\mathtt{2.04}}}}\right)} = {\mathtt{26.113\: \!912\: \!630\: \!291^{\circ}}}$$

or approximately 26°

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