Solve the system of x^(log y) + (y^(log x))^(1/2) = 10 and x.y =1000?

1). Solve the system of x^(log y) + (y^(log x))^(1/2) = 10 and x.y =1000
2). Prove that if a + (b/a) – (1/b) is integer, then it is a perfect square, where a, b element of N

1) x^(log y) + (y^(log x))^(1/2) = 10,
xy = 1000

Let’s use identity 10^(log a) = a, here logarithm is with a base 10, in the first equation:

10^[log(x^(logy))] + {10^[log(y^(log x))]}^(1/2) = 10

10^(logy * logx) + {10^(logx * logy)}^(1/2) = 10

10^(logy * logx) + 10^(logx * logy/2) – 10 = 0

Substitution t = 10^(logx * logy/2) (t > 0) , equation becomes

t² + t – 10 = 0
D = 1 + 40 = 41

t1 = ( – 1 + √41)/2
t2 = ( – 1 – √41)/2 < 0 rejected

So 10^(logx * logy/2) = (√41 – 1)/2 or to look shorter set (√41 – 1)/2 = T

10^(logx * logy/2) = T

take logarithm of both sides
log(10^(logx * logy/2)) = logT

logx *logy /2 = logT
logx * logy = 2logT

Now we have system of equations
logx * logy = 2logT
xy = 1000

logx * logy = 2logT
y = 1000/x

logx * log(1000/x) = 2logT

logx * (3 – logx) = 2logT

3logx – log²x – 2logT = 0

log²x – 3logx + 2logT = 0

Set logx = X

X² – 3X + 2logT = 0

D = 9 – 8logT

X1 = (3 – √(9 – 8logT))/2 ===> x1 = 10^X1 = 10^[(3 - √(9 - 8logT))/2]

X2 = (3 + √(9 – 8logT))/2 ===> x2 = 10^X2 = 10^[(3 + √(9 - 8logT))/2]

Ultimately
y1 = 1000/x1 = 10^[(3 + √(9 - 8logT))/2]

y2 = 1000/x2 = 10^[(3 - √(9 - 8logT))/2].

So, the solutions are
x1 = 10^[(3 - √(9 - 8logT))/2] ; y1 = 10^[(3 + √(9 - 8logT))/2] and

x2 = 10^[(3 + √(9 - 8logT))/2] ; y2 = 10^[(3 - √(9 - 8logT))/2],

where T = (√41 – 1)/2.

The values approximately
(476; 2.1) and (2.1; 476).

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Looking for a picture of the solar system without the planets in perfect circular orbits, in real orbits?

I’ve seen all the typical circular orbit pictures online, I want to see the real orbits of all the planets in our solar system. I know the planets are not in perfect alignment as the typical pictures suggest. Some planets may be farther down in the X, Y, or Z axis and I want to see them like that.

The problem with diagrams of the solar system is scale. You can’t scale the planets and the orbits the same because you then either can’t get the orbits on a single page or else the planets are too small to be seen. If you scale the orbits, the separations between the outer planet orbits are such that the inner planets are all crammed into a very small space in the middle. The pictures you have seen are accurate as far as the limitations I just described allow.

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Do the death penalty system needs to be altered in this country?

I think far less people in America are executed as they should. Blacks don’t make up 50% of the population yet make up half of death row inmates. Females make up somewhere close to 10% of first degree convictiosn but make up less than 2% of death row inmates. In a perfect system more white males and females should be put to death. I suggest requiring only 9 or 10 juors to sentence someone to death as opposed to 12 jurors.

Actually the key factor is the race of the victim. About the same number of whites and blacks are murdered each year. Yet just under 80% of all executions are for murders of whites.

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Second Conjugation Perfect System? Latin help!?

I’m having trouble understanding exactly WHAT the question is asking me for here- it’s giving me a headache!
The question is:

Conjugate in the perfect, past perfect and future perfect, Latin and English. Use this format:
singular plural
1st _____ _____
2nd _____ _____
3rd _____ _____

moneo, monere, monui, monitus – warn

I tried answering a question like this in a previous quiz and I got it wrong wrong wrong! Can anybody help me? Even if you just give me a partial answer, so I can understand the question, I can probably figure the rest out :) Thanks a ton!

I would get a headache too.. your teacher does know how to make a question complicated. I have no idea what they mean with 1st, 2nd, 3rd.. person??
Well, do the english first:
perf: I have warned, past perf: I had warned, future perf: I will have warned.
Then the plural: we have warned etc.
then look up moneo: http://www.allverbs.com/cache/verbtables/9/m/moneo.shtml

Hope this helps!

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Survey:If your system supports Indic scripts, please select the script you think more perfect?

1.तुम्हारा नाम क्या है? 2.உங்கள் பேயர் என்ன உள்ளது? 3.നിങ്ങളുടെ പേരെന്താണ്? 4.ನಿಮ್ಮ ಹೆಸರು ಎನ್ನು?

preference for 2

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Why do Cons think all Liberals are against Capitalism, and what would you do to perfect our capitalist system?

I am a capitalist — but I think we need a fairer social contract and the means to enforce it ~

By having a gov”t that is beholden to the middle class.

Capitalism works best when the most people can participate.

Trickle-down economics destroys the middle class by pushing wealth upwards into a concentration of a very few super-wealthy individuals. They didn’t use their tax breaks to raise salaries or create more jobs. They outsourced the jobs, cut workers pay and bought themselves more foreign vacation house, bigger yachts and more Ferraris.

Senator Bernie Sanders just pointed out this month that 400 richest families have as much wealth as 150,000,000 Americans combines. Republican Steve Forbes, arguing for a flat tax points out that 14,583 wealthiest Americans have alMOst three times the wealth of the the bottom 50% (everybody under $50,000)

For capitalism to work we need to fight the extreme gluttony and excessive greed of a few super billionaires at the very tip top, so more of us can participate in the American dream

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why is nature evolving when we have a perfect food chain system?

so the whole food chian system gets out of whack because of a species evolving. that would leade to extinction of many animals.

Perfect? Had your portion of listeria of E. coli today?

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What are the Perfect World International system requirements?

And no, don’t give me a link to the PWI website or any website. Just give me the requirements

Operation system: Windows® XP, Windows 2000, Windows Vista, or Windows 7

CPU: Intel® Pentium® 4 1.5Ghz or AMD Athlon 1500+ or newer and faster CPU

RAM: 512MB or more of RAM (Vista and Windows 7 require 1GB or more, 2GB+ preferred)

Hard disk: 5GB of Hard Drive Space or more (14GB or more preferred)

Graphics Display: 3D video chipset with pixel and vertex shader model 1.3 supported. GeForce 4 Ti4200 64MB or ATI™ Radeon™ 8500 64MB or newer for Windows XP. For Windows Vista and 7, a GeForce FX 5200 128MB or ATI Radeon 9500 128MB or newer is needed.

Sound Drivers:DirectX compatible sound chip or onboard audio capability with the latest sound
drivers

Network: Broadband Internet connection required

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How to create an perfect home audio system for an ipod?

Moving into flats next year and want to put together a decent sound system. I already have a Bose speaker dock but want to move into a more surrounding experience. I don’t know much about audio systems but realise the importance of speaker placement and the variety of speakers present. The rooms is 3 x 7 (meters) and any advice will be useful! i have a budget of around £750 and just want a good quality system!
Thanks

First, recognize that an iPod is far from a high quality sound source. The point being that MP3s are (generally) fairly poor quality recordings. Second, MP3 is not a surround format, so unless you use some type of matrix format to simulate surround sound from MP3 you are not going to get surround.

That said there are some speaker systems that don’t do a bad job of making an iPod the heart of a basic stereo music system.

See the link for some suggestions.

Personally, I’d suggest considering a CD based system (DVD/CD player, receiver, speakers) or if you want surround (and are willing to pay a premium price for surround recordings … SACD, DVD-A, etc) look at a SACD or DVD-A capable home music system. Your budget of £750 will certainly allow you to get into a low end DVD/receiver/speaker system setup … although it won’t give you anything wonderful it will almost undoubtably beat an iPod based system.

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What movie is this? Guy who designs a perfect security system…?

A father designs the perfect security system for his home. His daughter’s boyfriend along with other people break into the house because the father’s daughter gave her boyfriend the code.

I’m pretty sure that it is the movie "Fear" with Reese Witherspoon, Mark Wahlberg, William Petersen, Amy Brenneman and Alyssa Milano.

"Nicole Walker (Reese Witherspoon) is a fairly innocent teenager, living with her overbearing father, Steven (William Petersen) (whom she has a rebellious relationship with), her stepmother, Laura (Amy Brenneman), and her stepbrother, Toby (Christopher Gray). At a rave, she meets David McCall (Mark Wahlberg) and is swept off her feet by his sweet, polite nature. Steven does not trust David from the moment he meets him."

http://en.wikipedia.org/wiki/Fear_%281996_film%29

Hope this helps!

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