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Mathematics: Post your doubts here!

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PhyZac

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applepie1996 said:
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w06_qp_3.pdf
question 7 part 4 :)
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w05_qp_3.pdf
question 7 part 3 :)
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w04_qp_3.pdf
question 9 part 3 :)
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w04_qp_3.pdf
question 10 :) please please solve it somebody !
PhyZac Rutzaba or anyone else
Click to expand...
trgirl, you said these are your doubts too, check the following link, the all except first are solved, and below I am solving the first. https://www.xtremepapers.com/commun...st-your-doubts-here.9599/page-351#post-503295

First draw what you understand from a question, just a simple sketch, I did one, and hope it good enuf to help you.

So, first the black plane is plane p, the purple line is the normal of plane p, the red line is line l, and blue plane is second plane, and green line is normal of second plane,

now from the diagram we ca see that normal of second plane is perpendicular to both line l as well as the normal of plane p, so take the cross product of the normal of plane p (1 , 2, 3) and of the direction vector of line l (1, -2, 1)

I got value (-8, -2, 4)
Now it is nice to have the x value as positve simplify the numbers,
so do this divide with -2 and u get (4, 1, -2)

Now this is the normal and you have ax+by+cz = d as 4x + y - 2z =d
to find but the value of the point they said it lie on plane, that is 2i + j + 4k

you get 4(2) + (1) - 2(4) = 1
therefore d = 1
and equation is

4x + y - 2z = 1
 

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PhyZac said:
trgirl, you said these are your doubts too, check the following link, the all except first are solved, and below I am solving the first. https://www.xtremepapers.com/commun...st-your-doubts-here.9599/page-351#post-503295

First draw what you understand from a question, just a simple sketch, I did one, and hope it good enuf to help you.

So, first the black plane is plane p, the purple line is the normal of plane p, the red line is line l, and blue plane is second plane, and green line is normal of second plane,

now from the diagram we ca see that normal of second plane is perpendicular to both line l as well as the normal of plane p, so take the cross product of the normal of plane p (1 , 2, 3) and of the direction vector of line l (1, -2, 1)

I got value (-8, -2, 4)
Now it is nice to have the x value as positve simplify the numbers,
so do this divide with -2 and u get (4, 1, -2)

Now this is the normal and you have ax+by+cz = d as 4x + y - 2z =d
to find but the value of the point they said it lie on plane, that is 2i + j + 4k

you get 4(2) + (1) - 2(4) = 1
therefore d = 1
and equation is

4x + y - 2z = 1
Click to expand...
Jazak Allah :D
 
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PANDA- said:
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w07_qp_1.pdf
q4 ii and iii
Click to expand...
From part i you get

a+4d and a + 14d

so they 1, 5 and 15 are first three in geometric progression

a, a+4d, a + 14d

so since ratio is same
a+4d/a = a+14d/a+4d
the the denominator up
(a+4d)(a+4d) = a(a+14d)
a^2 +8da+16d^2 = a^2+14da [the a^2 cancel out and 8da is subtracted from 14da]
16d^2 = 6da
8d^2 = 3da
8d = 3a

(iii) ratio is equal to a+4d / a

now fro the equation 8d = 3a, d = 3/8a

now sub this in a+4d / a, making

a+4(3/8)a/a
you get
5/2a/a
a cancel out and you get
5/2 = 2.5
 
PANDA-

PANDA-

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But wait.. how do you equate the two... I mean
a+4d/a=a+14d/a+4d..
Just that part.
 
syed1995

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PANDA- said:
But wait.. how do you equate the two... I mean
a+4d/a=a+14d/a+4d..
Just that part.
Click to expand...


eliminate the denominator by multiplying both sides with a.

a^2 + 4d = a^2 + 14d + 4da
a^2-a^2 + 14d - 4d + 4da = 0

10d - 4da = 0
4da = 10d
a = 10d/4d
a = 2.5
 
PANDA-

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syed1995 said:
eliminate the denominator by multiplying both sides with a.

a^2 + 4d = a^2 + 14d + 4da
a^2-a^2 + 14d - 4d + 4da = 0

10d - 4da = 0
4da = 10d
a = 10d/4d
a = 2.5
Click to expand...

No I meant how did you get
a+4d/a=a+14d/a+4d
 
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PANDA- said:
No I meant how did you get
a+4d/a=a+14d/a+4d
Click to expand...
Okay i will give you an example.
1,2,4,8,
now this is a geometric progression, of ratio 2.
and you see,
2/1 = 4/2 = 8/4
2 = 2 = 2

Always in geometric progression when you divide a number with the one before is equal when you divde a different number with the number before ( hope u get my point. )

Therefore
a, a+4d, a + 14d

a+4d/a=a+14d/a+4d
 
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PANDA-

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PhyZac said:
Okay i will give you an example.
1,2,4,8,
now this is a geometric progression, of ratio 2.
and you see,
2/1 = 4/2 = 8/4
2 = 2 = 2

Always in geometric progression when you divide a number with the one before is equal when you divde a different number with the number before ( hope u get my point. )

Therefore
a, a+4d, a + 14d

a+4d/a=a+14d/a+4d
Click to expand...
Yup, got it, thanks a lot.
 
H

~`Heba`~ :)

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shezi1995 said:
ii) First you have to realise that boxes do not have to slide. We know the mass of A which is 200 kg and can calculate the vertical contact force which is equal to weight i.e 2000 N. Multiply the C. of friction i.e 2000*0.2 to get 400 N. It means that this is maximum force which the box B applies on box A to keep it going without sliding. So using F=ma , we get max a i.e. a=400/200=2 ms^-2.
iii)because you have the max a then you can use again F=ma to calculate the maximum resultant force on A as acceleration will be same for the boxes. resultant force=(200+250)*2=900. resultant=P-3150 .So P=3150 + 900 to get 4050.
I hope you have understood it. :)
Click to expand...
thanks a lot!! :)
 
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can anyone do these two questions on permutaion combination with working (and reasoning)

pleease!
 

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megamind said:
can anyone do these two questions on permutaion combination with working (and reasoning)

pleease!
Click to expand...

1.) 6P4 (Simple 4 choosing from 6)

2.) 4!/2! (Repetition)

3.) 6P4 (There are 2 of everything .. if it has to be unique.. then there can be only 1 of each to choose from .. 12/2 = 6 .. 4 to choose from 6)

4.) This is a difficult one...

R B G O Y Bck

3 different..

If you remove 2R.. remaining will be 10 .. of which there are two of each.. so in total 5 colors to choose from.

5C2 for each..

2R _ _ *4!/2!

2B _ _ *4!/2!

2G _ _ *4!/2!

2O _ _ *4!/2!

2Y _ _ *4!/2!

2Bck _ _ *4!/2!

6*(5C2*4!/2!) (Cuz all of their combinations become 5C2*4!/2!)

6*(10*12) = 720 Ways

5) I don't understand this question .. ? What on earth are we finding here?

12P4 /2!*2!*2!*2!*2!

11880/10

1188.. lol which I think is more than what's possible..

I will do the other question later...
 
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