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inverse sine is the same as arc sine

So use     asin

Do this : / 

E.g. 

1/2

@@ End of Day Wrap    Mon 20/4/15 Sydney,   Australia Time   11:05pm   ♪ ♫

Hello,   

Today our wonderful answerers were Alan, Zegroes, Brodudedoodebrodude, (your name shall hence forth be Brodude), Gibson338, Zacismyname, Geno3141, Zectico, MathsGod1, TitaniumRome, Badinage and Heureka. 

When people repost in the manner requested (giving the address of the original post) could answerers please answer on the original thread. You could also make a note on the new thread that you have done so.

This way the question and all the posts relating to it will be together. :)   Thank you  

Oh, today I stated using the '?' icon in the left margin to indicate which questions I wanted to go back to, some of which were unanswered.  I have a couple of these symbols available to me.  Would anybody like to suggest how they might best be used?

Alan, you seem to be best at finding your way around.  Can you (or someone else) work out a way to bring up questions with these symbols using the search feature?  If you could that would be great :))

The icons are called: 1-question, 2-exclaim, 3-mrgreen, 4-alert

Interest posts:

Tues 21/4/15

FTJ means "For the Juniors"

These are both really good answers.  :))

Heureka, your presentation never fails to astound, but Brodude's answer is really good too :))

Are these simultaneous equations ?

-9x+y=9   (*2)

-18x+2y+18    (1)

-18x-3y=18     (2)

subtract

5y=0

y=0,     x=-1

(-1,0)   is the solution :)

20:15 - 12:00 = 8:15

8 hours and 15 minutes = 8*60+15 minutes

Thanks Heureka,

I just want to look at this a little differently.

y=4x-3

$$gradient= \frac{rise}{run}= \frac{change \;in\; y}{change\;in\;x}=\frac{4}{1}$$

so if x changes by 1 unit y changes by 4.    That is just another way to look at the gradient :)

The gradient IS the change in y if x increases by 1 unit.

$$\\sin^2 0+sin^2 1+sin^2 2....sin^2 90\\\\
=[sin^2 0+sin^2 1+...sin^244]\;\;\;+\;\;\;sin^245\;\;[+sin^246+....sin^2 90]\\\\
=(sin^2 0+sin^2 90)+....(sin^244+sin^246)+sin^245 \\\\
=(sin^2 0+cos^20)+....(sin^244+cos^244)\;\;+sin^245 \\\\
=(1)+....(1)\;\;+sin^245 \\\\
=45+sin^245\\\\
=45+(\frac{1}{\sqrt2})^2\\\\
=45\frac{1}{2}\\\\$$

Alan, could i please suggest that you answer these 'repost' questions on the original thread and then just make an note on the new thread that you have done so please.  

That way the question and answers all stay together :)

Given the equation y=4x-3 , If x increases by 1 unit, what is the corresponding change in y

$$y_1=4x-3\\
y_2=4(x+1)-3\\
y_2=4x+4-3\\
y_2=\underbrace{4x-3}_{=y_1}+4 \\
y_2=y_1+4\\
y_2-y_1=\Delta y = 4$$

 the corresponding change in y is 4

Is Mellie allowed to do that ????

I have never seen a binomial used the way Mellie has used it - are  you allowed to do that ??

I've only  ever used it where p+q=1     

 If you can that would be a really good thing to know.  ://

I am not convinced that you are allowed to do what you did either Alan.

You have multiplied them like as if the 2 probabilities are independant of each other but they are not independent of each other. ://

I was just trying to work it out on my own and I had the same problem as you Alan.

The meaning is not at all clear.

Mmm

its the outside of a shape

Thanks Zac  

Mmm,

I was thinking about this and I think one of the triangles has to be the biggest and they are all equally likely do the probability of ABP being the biggest is 1/3

I also decided to follow Chris and try a visual approach.

You want the probability of triangle 1 being the biggest.

If P is in 1b or 2a then   triangle 3 is the biggest

If P is in  2b or 3a then triangle 1 is the biggest

If P is in 3b or 1a then triangle 2 is the biggest.

So

The probability that triangle 1 is the biggest is 1/3

That is what I think anyway :)

Could another mathematician please comment on this :)

Good point, Melody.

We would need to involve the quadrant diagram for a complete answer.

Hmmmm I think this can also be factorised. . .

$$a^2+ab^2+ab+b^3$$

$$a(a+b^2)b(a+b^2)$$

$$(a+b)(a+b^2)$$

:)

4/22100 = 1/5525

Thanks :)

Yeah I considered that but it basically means the same thing anyway so I left it how it was. 

-2.8=-1(c-0.65)     mult bot sides by =1

2.8=c-0.65

now just add 0.65 to both sides 

$$\\a^2+b(b+1)a+b^3\\
a^2+ab(b+1)+b^3\\
a^2+ab^2+ab+b^3\\$$

Thanks Alan,

Wouldn't you have to say as    $$x\rightarrow 0$$     since h is the denominator and so it cannot equal 0 ?

You have presented this beautifully Zac :))

There is a little thing I would like you to consider. 

If you multiply both sides by 3 right at the very beginning then the fraction disappears immediately.

With some equations this makes the problem much simpler :)