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Maths homework question that I'm a bit stuck on..

"Prove that y=4(1-x) is a tangent to the hyperbola xy=1, and find the point of contact."

So far I've done this..

y=4(1-x)

=4-4x

xy=1

x(4-4x)=1

4x-4x(sqaured)-1=0

4x=4x(squared)+1

4x-1=4x(sqaured)

-4x(sqaured)+4x-1=0

0=4x(sqaured)-4x+1

b(squared)-4ac

16-(16)

=0 therefore it is a tangent.

Is that right? Also to find the point of contact would I factorise?

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Maths homework question that I'm a bit stuck on..

"Prove that y=4(1-x) is a tangent to the hyperbola xy=1, and find the point of contact."

So far I've done this..

y=4(1-x)

=4-4x

xy=1

x(4-4x)=1

4x-4x(sqaured)-1=0

4x=4x(squared)+1

4x-1=4x(sqaured)

-4x(sqaured)+4x-1=0

0=4x(sqaured)-4x+1

b(squared)-4ac

16-(16)

=0 therefore it is a tangent.

Is that right? Also to find the point of contact would I factorise?

What you have done is correct. By proving that b^2-4ac is zero you have shown that the equation only has one solution. You need to solve the full quadratic equation using (-b plus or minus sqrt (b^2-4ac))/2a. Solving will give x, then put that into an equation to get y. To check your answer put it into both your initial equations to see that they give the same answer.

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Guest The Phoenix

I posted this in the junior forum as well but might get a quicker response here. Does anyone know if linlithgow rose are at home on saturday?

Home to Spartans.

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i have a question. i have just been watching Dog the Bounty Hunter and they were on there walkie talkies and i presume 10 4 means i got it or something along them lines

Where did 10 4 come from?

Glad to see you're not wasting time on your holidays.

10 4 is CB rhyming slang for "Say no more" as in understood, like you have said.

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If one was to buy a device, from elsewhere in Europe, that you can't really buy here, would customs let it through?

Are flares illegal in Britain, or to import them?

:lol:

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I am currently reading this pdf on the net. However it does not give the function to copy parts of it so I can paste into a word document.

Is there any way around this?

Not that I know off anyway. Which is one hell of a pain while doing a dissertation :(

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i have a question. i have just been watching Dog the Bounty Hunter and they were on there walkie talkies and i presume 10 4 means i got it or something along them lines

Where did 10 4 come from?

Glad to see you're not wasting time on your holidays.

10 4 is CB rhyming slang for "Say no more" as in understood, like you have said.

CB?

And why say 10 4? Why not 9 10? or anything else?

10-4 isn't rhyming slang!

G-Man, some people communicate via radio as a hobby using what are called "Citizen's Band" radios - CB Radios (a frequency of radio wave available for private citizens as opposed to commercial / public broadcasters).

There is a system of standard codes that go along with these. Ten-four is code for "affirmative".

Just checked, and by simply Googling "ten four" you could have had your question answered in about ten seconds. Do people actually forget about Google before posting on here!?

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10-4 isn't rhyming slang!

G-Man, some people communicate via radio as a hobby using what are called "Citizen's Band" radios - CB Radios (a frequency of radio wave available for private citizens as opposed to commercial / public broadcasters).

There is a system of standard codes that go along with these. Ten-four is code for "affirmative".

Just checked, and by simply Googling "ten four" you could have had your question answered in about ten seconds. Do people actually forget about Google before posting on here!?

Yes it is. Don't listen to him G-Man. I'll keep you right, good buddy. All his talk of fancy standard codes. He ain't never been out on rig, hootin n hollerin frontin' of a convoy in his natural.

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