Mathematics: Post your doubts here!

[farhan141]

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Angle in a semicircle is 90.
cos(x) = AB / (2r)

Wow thanks

 

[farhan141]

 

[The Sarcastic Retard]

Thanks. Can u explain me how is cos x equal to (1/2 AB)/R

Here you go.

 

[qwertypoiu]

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[qwertypoiu]

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[darks]

'

Help please thanks

 

[farhan141]

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How is y' = 0 for minimum?

Thanks for the other question.

 

[The Sarcastic Retard]

How is y' = 0 for minimum?

Thanks for the other question.

For any staitonary point, dy/dx = o as dy/dx is a gradient, on maximum point or minimum point, change in y is 0 thus dy/dx should be zero

 

[Nazirah Ahmad]

Hello, any kind soul can help me with MJ/13/33/ Question 7 (ii) (the highlighted part) ?

I managed to get the equation before it, but don't know how to show the result from that equation, please help. Thanks !

 

[mohmed ahmed soliman]

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help in (i)

help

 

[Saad the Paki]

help

First write out all the possible selections.
L is lucy; M is monica
(1 L,9 M) OR (3 L, 7M) OR (5 L, 5 M) OR (7 L, 3 M) OR (9 L, 1M)
Now write the individual possible selections and add them.
(10C1*9C9) + (10C3*7C7) + (10C5*5C5) + (10C7*3C3) + (10C9*1C1) = 512

 

[qwertypoiu]

Hello, any kind soul can help me with MJ/13/33/ Question 7 (ii) (the highlighted part) ?

I managed to get the equation before it, but don't know how to show the result from that equation, please help. Thanks !

View attachment 59894

Let's say you want to expand:
|z-a|^2
where a is a real number. Your expansion will be:
|z-a|^2 = (z-a).(z-a)* = (z-a).(z*-a*)
Note that since a is real, a* = a. So:
(z-a).(z*-a*) = (z-a).(z*-a) = zz* - az - az* + a^2.

For example:
|z-5|^2 = zz* - 5z - 5z* + 25

Notice that the coefficients of z term and z* term are both -5, and then the constant term is (-5)^2. (Also coefficient of zz* is 1)

Now let's say you wanted to expand:
|z - si|^2,
where si is an imaginary number. Your expansion will be:
|z-si|^2 = (z-si).(z-si)* = (z-si).(z*-(si)*)
Notice that (si)* = -si, (eg (5i)* = -5i). So:
(z-si).(z*-(si)*) = (z-si).(z*+si) = zz* + si.z - si.z* + s^2

For example:
|z-5i|^2 = zz* + 5iz - 5iz* + 25

Notice that the coefficient of z and z* is +5 and -5 respectively. They alternate in sign. Also, the constant term is +s^2 (where s is coefficient of the imaginary term)

So anyhow with enough practice you can learn the above formats and reverse it as if completing the square. So in summary:
|z-a|^2 = zz* - az - az* + a^2
|z - si|^2 = zz* + si.z - si.z* + s^2

So to your question. You have:
zz* - 2iz* + 2iz - 12 = 0 (Note that they have listed the z* term before z term. In my expansion above I did opposite.)
So this matches with:
|z - si|^2 = zz* + si.z - si.z* (+s^2)

We need to provide the s^2 term by adding 2^2=4 and then subtracting it. (just like when completing square):
zz* - 2iz* + 2iz - 12 = 0
zz* - 2iz* + 2iz +4 - 4 - 12 = 0
|z - 2i|^2 - 16 = 0
|z - 2i|^2 = 16
|z - 2i| = 4

 

[mohmed ahmed soliman]

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help in V

help in part v

 

[mohmed ahmed soliman]

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help in II

help in II

 

[Eugene99]

help in part v

No. of ways of arranging 3 cards without restriction (also found in iii) = 9C3 x 3!
= 504
( Two cards out of 3 are green and pink together) = 7C1 x 1C1 x 1C1 x 2P2 x 2P2
= 28
504-28= 476

 

[mohmed ahmed soliman]

help in II june 2013 p12

 

[mohmed ahmed soliman]

help

 

[mohmed ahmed soliman]

also i always dont get exact answer due to rounding in p1 when to round a side or an angle to get exact answer

 

[qwertypoiu]

also i always dont get exact answer due to rounding in p1 when to round a side or an angle to get exact answer

You can show long decimals as rounded in your working, but you should keep the exact value on your calculator. The only time you should round a number is in your FINAL answer. Or else you'll suffer from premature approximation. Your final answer is in 3 sig figures. If you must round in between, I suggest 5 sig to be safe

 

[mohmed ahmed soliman]

You can show long decimals as rounded in your working, but you should keep the exact value on your calculator. The only time you should round a number is in your FINAL answer. Or else you'll suffer from premature approximation. Your final answer is in 3 sig figures. If you must round in between, I suggest 5 sig to be safe

and angles calculation