EvoN1020v

Because [imath]

\cos(2x) = \cos(x+x) = \cos^2 x - \sin^2 x = (1-\sin^2 x) - \sin^2 x = 1 - 2\sin^2 x

[/imath]

I found out a different method to do this:

[math]

cos(a+a) = cos^2a - sin^2a = cos^2a - (1=cos^2a) = 2cos^2a-1

[/math]

Is the answer same as [math]1-2sin^2a[/math]?

Thanks TD!

Can't you give me some proof? Hope the bleach is not corrosive or it will damage my rather nice shoes.

Bleach? That's for laundry!!!!????

One more question: How is this possible: [math]\cos(x+x) = \cos^2 x - \sin^2 x[/math]?

Recently I bought a rather expensive white leather shoes for daily wearing. After 3 weeks of wearing it, the white is turning to brownish and there are black marks on it. So do you guys have any suggestion of what chemical solution to use to remove all the dirts, marks, etc off my shoes? Perhaps limestone liquid? I want it to look like I just got it.

I found out that [math]cos(2x) = 1 - 2sin^2x[/math]. How is this possible?

What a beautiful day! I just learnt about Additive & Subractive Angle Identities today. Let me recollect what I have learnt:

THIS IS THE FIRST SUBRACTIVE IDENTITY I HAVE LEARNT:

[math]

(cos(\alpha+\beta)-1)^2 + (sin(\alpha-\beta)-0)^2 = (cos\alpha-cos\beta)^2 + (sin\alpha-sin\beta)^2

[/math]

LEFT SIDE EXPAND:

[math]

cos^2(\alpha-\beta) - 2cos(\alpha - \beta) + 1 + sin^2(\alpha-\beta)

[/math]

THUS:

[math]

2 - 2cos(\alpha-\beta)

[/math]

RIGHT SIDE EXPAND:

[math]

cos^2{\alpha} - 2cos{\alpha}cos{\beta} + cos^2{\beta} + sin^2{\alpha} - 2sin{\alpha}sin{\beta} + sin^2{\beta}

[/math]

THUS:

[math]

2 - 2cos{\alpha}cos{\beta} - 2sin{\alpha}sin{\beta}

[/math]

COMPLETION OF BOTH SIDES:

[math]

2 - 2cos(\alpha-\beta) = 2 - 2cos{\alpha}cos{\beta} - 2sin{\alpha}sin{\beta}

[/math]

SIMPLFY:

[math]

cos(\alpha-\beta) = cos{\alpha}cos{\beta} + sin{\alpha}sin{\beta}

[/math]

There are 5 more additive/subractive identites but I'm not going to type all the processes right now. It took me awhile to type all the equations above.

Relate to Bio-Hazard's reply:

There absolutely won't be a colour dissipation because the mission of the chip was to relieve the dead cells. I understand what you mean by repetive electrical stimulation, but that's not going to happen. The electrity jolts would only "jump", intialing the cells start to grow alive again. Also, how is EMP (electromagnetic pulse) gonna to screw me up? I thought EMP is a machine that test electrial current in your body??

Relate to Zero Wing's reply:

Could you try to remember which magazine the article was in?? Also I did heard from someone about a show on TV that showed a patient receiving chip in his eye, and its very cool and reliability. The doctors would cut your pupil off and insert the chip in your back of your eye where the retina is located, and then glue the pupil back on the eye. What you think of that?

Relate to Helix's reply:

They have already tested the device on blind dogs and they could see again. As you know that dogs can only see black/white, so I'm not sure about the colour. But I think it does relieve colours, because there are cells in your eyes that cause you to see "colour".

Please do look for published works on the bionic eyes. Thanks

What is an additive identities? (e.g. sin(a+b))? Then what is a double angle identities?

e.g. sin(2x)

sin(x + x) would be the right answer? But how does double angle identity applies to it?

Light is an electromagnetic wave where the maximum speed is rounded to approximately 3.0 x 10^9 metres per second. Also in real life, amplitudes in light wave don't remain constant over long distance with no objects intruding. The waves would be called "damped harmonic oscillator" where the amplitude decrease over a period of time. You would use sin or cos functions to define the wave of light. Use this equation: A=Aoe^-kt. The e is the natural exponential so the value is 2.7182818...

Hope this helps.

My last question was: What would be the normal (non-acidic) concentration of calcium ions in a lake lined by limestone?

My answer was:

CaCO3(s) = (Ca 2+)(aq) + (CO3 2-)(aq)

Ksp = [Ca 2+ (aq)][CO3 2- (aq)] = 9.9 x 10^-9 mol^2/L^2

[Ca 2+] = sqroot(Ksp)

=sqroot(9.9 x 10^-9 mol^2/L^2)

=9.9 x 10^-5 mol/L

That was my last question and I answered it. Now for the question that I requested, I know I have to 1/3 sq root of the magnesium hydroxide solution. But how am I supposed to predict the pH value???

Yes P-man that's the problem. My chemistry teacher warned us that we wouldn't be able to answer the question because we never learned about the concepts that need to be know yet. So any suggestions would be wonderful.

I have this question that I can't answer. It's for homework and I need your help.

Q. The solubility product of a saturated magnesium hydroxide solution is 1.2 x 10^-11 (mol/L)^3 at 18 celsusis degree. Predict the pH of a saturated magnesium hydroxide solution at 18 celsusis degree.

Please answer back as soon as possible. Thanks

Is it good enough to be a documented science proof? I'm sure it is ungoing clinical trials, because its very new. But it seemingly readily doesn't it?

Thanks Cap'n Refsmmat. Do you have any idea where I can find documented science study for the bionic eyes?

I am creating this thread because it applies highly to me. My primary motive is that I'm gradually losing my sight over years. I'm only 17 years of age, and I can only see approximately 40 to 45 percent. I just read this inspiring article, "I spy a Bionic Eye" from the magazine "Discover".

The implemenation of this silicon retinal chip was when a physician in Air Force was forced to retire in 1997 because he was legally blinded with retinitis pigmentosa. (I have that. My syndrome is called Ushers Syndrome which is also called retinitis pigmentosa which results in smaller vision field). Several years later, the chip was implant in his right eye, and within days he was able to see the hands on his bedroom clock. Over the next few years, his vision improved drastically, and he could even see the colors of TV newscasters' ties. He was one of 10 people who recieved a retinal chip developed by physician Alan Chow and his brother Vincent. This past spring, yet another 20 patients got the treatments. "When this chip is put into the eye under the retina, its solar cells and the electrodes come into contact with the poorly functioning lightsensing cells. Light stimulates some of the 5,000 microscopic solar cells on the chip to produce a tiny electric current that wakes up the eye's failing photoreceptor cells. Then it will make the cells healthy again and gradually you can get your vision back.

So my motive is: Should I get this kind of retinal chip treatment? It seemingly to have been successful thus far...If yes, Should I write a letter to this physcian that created the chip. If no, why? Also, as I still have some of my vision left, should I wait until I get fully blind then get the treatments? Or should I get it instantly while I have some of the remaining vision?

I appreciate for your sincere concerns.

I have never heard of the PBS series, "String Theory" for a significant reason: I don't have the PBS network on my TV!! Just lonesome Global. (I'm still satisfy to have 1 channel as it broadcasts plenty of good shows during the evenings). Anyway back to the point. As gib65 wanted to discuss the mystery of the string theory, I'd be more happy to join too, as I have some knowledge of string theory.

If the universe is really 11 dimensional, what is a dimension? How did they come to exist?

First of all, I don't think the string theory applies as 11 dimensional. Instead the subatomic world are thought to vibrate in 10 dimensions. Second of all, It's a "theory". Not everybody actually believe the remarkable claim as it don't have a remarkable proof. "Advocates say vibrating strings underlie every particle and every force in the universe. But will anyone every be able to prove that?"

One of the most remarkable claims made in modern times comes from string theory, which holds that everything in the universe is composed of tiny vibrating strings of energy. In this view, every particle in your body, every speck of light that lets you read these words, and every packet of gravity that pushes you into your chair is just a variant of this one fundamental entity.

So I'm saying that for the past 3 decades, physicists have been hammering away at its equations every day, trying to make the different parts of the theory hang together. To be brutally honest, there is no proof whatsoever that string theory is correct.

Give me some of your thoughts, and if you still want more infomation about string theory, no problem. I can input more information to some extent of what I know.

Seemingly all of us scientists, germuaphobias are using the precautions of eliminating bacterias from our hands when going to washroom. We know all the peril bacterias and what they can cause, while the general population exceeding scientists don't give a darn. Whenever I go to the public washroom in restaurant, school and I would wash my hands with warm water. While I am doing it, I would see a guy escape the washroom without taking the precautions. My face would make a grimance, and think, "Oh, how digusting!!". I've read some sources that people who are extreme germuaphobias can even be more sicker than the general population. Scientists have proved that some of the bacterias are safe and healthy, and we need some of them. So those who use paper towels or kleenex to pull door open or turn facuets, you better put them away. The healthy bacterias won't kill you. Also I have read a newspaper article saying that you can get sick from sharing your saliva. That's why you need to have your own personal hygines such as toothbrush, hair brush, etc. Also if you are a carrier of a bad bacteria such as mengatitis and they are generally locate in your throat. So if you share your lipstick or drinks with someone else, they could catch the mengatitis bacteria and became really sick.

So the point is, I'm just saying to wash your hands regularly, not too much, nor enough. Just do it properly and you'll be fine.

What does the limit indicate for? Like lim x=pi/2. Does it mean only x value less or equal to pi/2?

Also, what does Devrivates mean? Give me examples won't hurt.

Thanks

I did a search for the word, "Threshold". Apparently there's no thread that discuss about this amazing phenomonal TV show. I love all those science and math TV shows, such as "ReGenesis", and "Numb3rs". They made me more interesting into those areas. Oftenly I would think in school, "Why am I learning this crap?". Let me tell you, nothing is crap, because it can come back to you and you wished that you remember it. You'll just never know when you will need the specific information.

A brief overview of Threshold: Broadcasting at 10 PM every friday night on Global. THRESHOLD is a suspenseful drama about a team of experts who are assembled when the U.S. Navy makes a chilling discovery: an extra terrestrial craft has landed in the mid-Atlantic ocean. Dr. Molly Anne Caffrey (Carla Gugino) is a government contingency analyst whose job is to devise response plans for worst-case scenarios. In a single instant, her life changes when one of those plans--THRESHOLD--is activated by Deputy National Security Advisor J.T. Baylock (Charles S. Dutton). Armed only with her hypothetical strategy to address the appearance of aliens on earth, Caffrey now finds herself thrust in the midst of a global crisis. She hand-picks a team of eclectic specialists to prepare for first contact: Dr. Nigel Fenway (Brent Spiner), a disillusioned NASA microbiologist; Lucas Pegg (Rob Benedict), a brilliant but neurotic physicist; Arthur Ramsey (Peter Dinklage), an expert in languages and mathematics; and Cavennaugh (Brian Van Holt), a highly trained covert operative with a mysterious past. Together, they decipher the intention of the craft, the fate of the ship's crew and begin preparations for the possibility of a crisis situation--an alien invasion. Those "aliens" posted a powerful alien signal that influence humans with their static crackling. Their signal appears to have an odd fraternal shape that can overpowers any technology and machines. Molly Caffrey was confronted with an international security indermining infection.

Tell me of any of you watch this show. Tell my your opinions on THRESHOLD.

For example using Aluminum Oxide, Al have 3+ and O is 2- ; hence you need to balance the formula which would come to Al2O3.

Another example: Mercury Oxide. Mercury (Hg) have 2 valence positives so you require to put the roman number after the name in IUPAC name. For example, using Hg 2+ , you will get Hg0 which is Mercury (II) Oxide.

Cute, I like how steps 4 and 8 cancel each other out.

And then how 3,5, and 9 combine to just shift over the first 3 digits.

Did you come up with that one? I love analyzing them, hope you don't mind.

I'm impressed with Cosine's analyzination. I wasn't expecting anyone to really read it hard. I was just providing it for entairment, but thanks anyway.

But to paraphrase Clarke's third law, to any sufficiently math illiterate society, associative, commutative and distributive properties are indistinguishable from magic.

Relate to swansont's reply, I was using the word "magic" metaphorically. Don't you understand that English can have some abrasct imagery. I don't expect any cricitism about English. Plus, English is my second language, so whatever.