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Original post by GreenLantern1
I only posted this for my friend not myself (so it has just been copied from what he has written to me).


That's a bad excuse.

Original post by usycool1
Sorry, it was a typo, I meant the gradient of x = 5 is undefined and the y=3 has gradient 0. My mistake :facepalm:


Cool typo.


Take two lines, y1y_1 and y2y_2, and draw them in a similar way as in the picture below.

perpendicular-lines.png

Notice that tanθ\tan\theta is the gradient of y1y_1, and tanφ-\tan\varphi is the gradient of y2y_2. So, the two lines can be expressed in terms of these angles.

y1=tan(θ)x,  y2=tan(φ)xy_1 = \tan(\theta)x, \ \ y_2 = -\tan(\varphi)x

These will be perpendicular if θ+φ=π2\displaystyle \theta + \varphi = \frac{\pi}{2}, so you'd use φ=π2θ\displaystyle \varphi = \frac{\pi}{2} - \theta.

Spoiler

Original post by jack.hadamard
That's a bad excuse.



Cool typo.


Take two lines, y1y_1 and y2y_2, and draw them in a similar way as in the picture below.

perpendicular-lines.png

Notice that tanθ\tan\theta is the gradient of y1y_1, and tanφ-\tan\varphi is the gradient of y2y_2. So, the two lines can be expressed in terms of these angles.

y1=tan(θ)x,  y2=tan(φ)xy_1 = \tan(\theta)x, \ \ y_2 = -\tan(\varphi)x

These will be perpendicular if θ+φ=π2\displaystyle \theta + \varphi = \frac{\pi}{2}, so you'd use φ=π2θ\displaystyle \varphi = \frac{\pi}{2} - \theta.

Spoiler




Well done, but it still doesn't answer thw question of those lines in specific that were asked with. So unless youa re related to the french mathematician Jacques Hadamard why are you not answering the qesation.

P.S It isn't a bad excuse I copy and pasted his question on to here. If you don't believe me go have a look on the Current Year 11 thread. You are an odd one aren't ypou.
Original post by GreenLantern1
Well done, but it still doesn't answer thw question of those lines in specific that were asked with. You are an odd one aren't ypou.


All you had to see is that you can change coordinates to y1y_1 and y2y_2, where the expression for the product of gradients of xx and yy axes makes sense.
Anyway, I now see that you are not looking for an answer, but for an argument, and I am not interested in this particular one. Sorry!

I have always been an odd one, does that make a difference?
Reply 3703
Original post by jack.hadamard


I have always been an odd one, does that make a difference?


I think "odd one" was a euphemism for "****".
Original post by nohomo
I think "odd one" was a euphemism for "****".


Then I guess it makes a difference. :smile:
Original post by GreenLantern1
Posted for Usycool:

When perpendicular lines meet, the product of their gradient is -1, right?

However, say if we have the lines y = 3 and x = 5.

The gradient of the y=3 in undefined, and the gradient of the x = 5 is 1.

So is this not an exception for the rule that perpendicular lines's gradients have a product of -1? Or is their another explanation for this?


The rule is probably only true for finite gradients.

I once made a thread about it, http://www.thestudentroom.co.uk/showthread.php?t=1937908
(edited 11 years ago)
What was Lebesgue's favourite play?

Spoiler

Original post by ben-smith
What was Lebesgue's favourite play?


Good one. :biggrin: Have you come across this before?

"If you've got a hairy line integral around a simple curve, magic things happen." APM

Spoiler

Reply 3709
Original post by GreenLantern1
Posted for Usycool:

When perpendicular lines meet, the product of their gradient is -1, right?

However, say if we have the lines y = 3 and x = 5.

The gradient of the y=3 in undefined, and the gradient of the x = 5 is 1.

So is this not an exception for the rule that perpendicular lines's gradients have a product of -1? Or is their another explanation for this?


Bit late to the party but, why do you think this poses a problem for the rule?

Gradient of x = 5 is 0.

Let's assume for a second we don't know the gradient of y = 3, but we do know our lines are perpendicular:

m1×m2=1.m_1 \times m_2 = -1.

0×m2=1.0 \times m_2 = -1.

So 0 times what gives -1? There's no value that satisfies so m2 is undefined, as we already know it is.
(edited 11 years ago)
Original post by mimx
Bit late to the party but, why do you think this poses a problem for the rule?

Gradient of x = 5 is 0.

Let's assume for a second we don't know the gradient of y = 3, but we do know our lines are perpendicular:

m1×m2=1.m_1 \times m_2 = -1.

0×m2=1.0 \times m_2 = -1.

So 0 times what gives -1? There's no value that satisfies so m2 is undefined, as we already know it is.


Very interestiing! If you can ask your maths teacher. I am on study leave so won;t see them till next year
quick question

by using the substitution t=tanx evaluate the definite integral 1/(9cos^2x - sin^2x) dx with the limits being pi/4 and 0

will pos rep whoever gives me the answer. thanks
Original post by Entrepreneur123
quick question

by using the substitution t=tanx evaluate the definite integral 1/(9cos^2x - sin^2x) dx with the limits being pi/4 and 0

will pos rep whoever gives me the answer. thanks


Before making the substitution, divide through by cos2xcos2x\dfrac{cos^2x}{cos^2x}. Then the substitution and the rest is very easy.
Reply 3713
i don't know if this is the right place to ask this

anyway, on my calculator, how to i convert decimals to pi?? i need this for an upcoming maths exam

i have a casio fx-115ms calculator, i've searched online and found no answers to this. my friend's calculator is able to toggle between decimals and pi using the same button to convert decimals to fractions (which on her calculator is the s<=>d button), yet the equivalent button on my calculator does not do this??

my brother's calculator (casio fx-83es) is able to toggle between decimals and pi/fractions using this button while on the mathio mode, i'm don't see this mode in my calculator (unless it's under a different name and i'm missing it)

thanks, sorry again if this isn't the right place to ask
guys you all possibly know this. but i have a problem on game theory. the thing is that it assumes none of the people involved in the game will work collaboratively with the other people involved. what if they do. are we sure that they will get the highest profit ( none goes to prison)?
Original post by poyyo
i don't know if this is the right place to ask this

anyway, on my calculator, how to i convert decimals to pi?? i need this for an upcoming maths exam

i have a casio fx-115ms calculator, i've searched online and found no answers to this. my friend's calculator is able to toggle between decimals and pi using the same button to convert decimals to fractions (which on her calculator is the s<=>d button), yet the equivalent button on my calculator does not do this??

my brother's calculator (casio fx-83es) is able to toggle between decimals and pi/fractions using this button while on the mathio mode, i'm don't see this mode in my calculator (unless it's under a different name and i'm missing it)

thanks, sorry again if this isn't the right place to ask

not all the calculators have that ability. but out of the interest remember to use 3.1416 as pi. it helps accuracy.
Reply 3716
Original post by mashmammad
guys you all possibly know this. but i have a problem on game theory. the thing is that it assumes none of the people involved in the game will work collaboratively with the other people involved. what if they do. are we sure that they will get the highest profit ( none goes to prison)?


What's the game?
Reply 3717
Original post by mashmammad
not all the calculators have that ability. but out of the interest remember to use 3.1416 as pi. it helps accuracy.


thanks, it's just that i need to give some of my answers in terms of pi (eg 3[pi]/2)

so do you think i will have to use another calculator for the exam? (not something i really want to do since i am more used to the way my calculator works)
Original post by poyyo
thanks, it's just that i need to give some of my answers in terms of pi (eg 3[pi]/2)

so do you think i will have to use another calculator for the exam? (not something i really want to do since i am more used to the way my calculator works)


ok. if you want my opinion dont go for a new calculator. find your answer in radians and divide them by 3.1416( eg if you get 1.5708 radians divide it by 3.1416 and what youll get is 1/2) then times it by pi (e.g. 1(pi)/2) but if you want the method of working with a fancy calculator ill get one of my friends to post it tonight on this thread. hope it helps:smile:
by the way tell me what exam you have. itll be better.
(edited 11 years ago)
Original post by sputum
What's the game?


ok this is the game theory:
two people have stolen something, police can not arrest any of them if they dont confess.if one of them confesses the other one is arrested and jailed for one year, and the one that has confessed is freed. its the same argument for the other person. but if they both confess each will be prisoned for 6 moths. what do you think they will do?

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