Science & Mathematics - 17 January 2007

I ran into this problem while tutoring one of my kids for the SAT math. Basically There is a large square with a smaller square inscribed into it. The problems provides the length of the sides of the larger square but asks for the area of the smaller square.

I solved the problem intuitively by assuming that the points where the smaller square inscribes the larger sqaure must be the midpoint of the larger side of the sqaure. Therefore the sides of the smaller sqaure can be solved using the 1:1:root 2 ratio and thus its area.

But my problem was finding a rigiourous proof using simple euclidean geometry to prove that infact the corners of the smaller square touch at the midpoint of the larger side of the sqaure as I do not have a geometry book handy and I could not find it on line.

Can you guys prove it? or suggest a proof? I hope my presentation of the question is not too confusing!

2007-01-17 23:57:50 · 3 answers · asked by David H 1 in Mathematics

2007-01-17 23:52:17 · 14 answers · asked by Booyah! 3 in Medicine

in need of a circuit for producing hydrogen from tap water

2007-01-17 23:51:44 · 6 answers · asked by sukumaran_se 2 in Engineering

i wanna (sorry the kids wanna) play out!

2007-01-17 23:51:09 · 10 answers · asked by Anonymous in Weather

2007-01-17 23:50:59 · 12 answers · asked by michreq 1 in Physics

woke up to a wonderful white garden, was still snowing, now it's raining and fastly dissapearing. Perfect. I've seen it, it was very pretty, now it's gone!

2007-01-17 23:49:46 · 11 answers · asked by Anonymous in Weather

Can an exponential function be negative? Or they are always positive?
Give me examples please.

2007-01-17 23:48:45 · 7 answers · asked by Eltromeche E 1 in Mathematics

2007-01-17 23:45:14 · 5 answers · asked by Booyah! 3 in Medicine

Related to science. physics

2007-01-17 23:40:36 · 19 answers · asked by rea 2 in Physics

Researches, case study

2007-01-17 23:40:20 · 2 answers · asked by ahmed a 1 in Engineering

Or does it depend on your frame of reference?

2007-01-17 23:36:57 · 12 answers · asked by Save the Fish 2 in Astronomy & Space

how do you change the ln and ft height into metres?

2007-01-17 23:34:23 · 10 answers · asked by Anonymous in Mathematics

please show complete solution

2007-01-17 23:33:39 · 6 answers · asked by roro 1 in Mathematics

2007-01-17 23:33:04 · 9 answers · asked by zanydumplings 3 in Biology

When do you get yellow and orange from mixing two of these colours:
Blue
Green
Red

2007-01-17 23:32:29 · 4 answers · asked by AnTeM 1 in Physics

Be it natural disaster, enivromental degradation caused by mankind, space invasion?

2007-01-17 23:24:20 · 19 answers · asked by Anonymous in Earth Sciences & Geology

I know that the effect of relativity to become obvious when an object travels approaching light's speed,but if someone travels a lot,i mean most of his life is spent on air plane,doesn't that have affect? Maybe appear a little bit younger than other people of same age. I stressed on 'a little bit'.

2007-01-17 23:24:08 · 5 answers · asked by faizt 2 in Other - Science

i was assigned to detect a existance of living in a closed room. i have to develop a device, which is able to detect the body heat outside that closed room.

We can use Infrared to detect human body heat. but, when a human is standing behind a thick masonry wall, is it possible for that infrared device to detect that human body heat, to show that there's a existance of living behind the wall? Reason why?

2007-01-17 23:23:45 · 2 answers · asked by eyeow 1 in Engineering

2007-01-17 23:21:46 · 12 answers · asked by Jono 1 in Mathematics

Is an inverse function defined for discrete summation (sigma)(finite or infinite), in a way that the differential exists as an inverse for integration?
For example if f(x) = sigma(n from 0 to infinity) ( x^n)
What would be its inverse?

2007-01-17 23:21:22 · 2 answers · asked by Parry 3 in Mathematics

Think Logical and Answer logical

2007-01-17 23:20:10 · 12 answers · asked by abhicoolfire 1 in Astronomy & Space

2007-01-17 23:17:50 · 4 answers · asked by chargewell 1 in Astronomy & Space

2007-01-17 23:15:31 · 19 answers · asked by Anonymous in Physics

2007-01-17 23:13:58 · 10 answers · asked by Anonymous in Engineering

2007-01-17 23:07:44 · 4 answers · asked by shree30 1 in Engineering

2007-01-17 23:02:50 · 9 answers · asked by Anonymous in Physics

I haven't heard anything lately.

2007-01-17 23:02:13 · 2 answers · asked by j_fencsak 1 in Weather

It's now cold!!! I want some warm temps!!!

2007-01-17 23:01:27 · 4 answers · asked by j_fencsak 1 in Weather

2007-01-17 22:59:33 · 1 answers · asked by Luke Z 1 in Engineering

Sceptics say it was filmed out in the desert. Noting the flag was blowing,whereas theres no wind on the moon. There was no blast point where the thrusters fired down while landing. They also reckon the US did this in a race to beat Russia to the moon

I myself dont think we ever have walked on the moon.

Would be interesting to hear your opinions

2007-01-17 22:54:25 · 23 answers · asked by Anonymous in Astronomy & Space