Mathematics: Post your doubts here!

[Ammirul Shafiq]

how to solve this?

two planes have equations 2x-y-3z = 7 and x+2y+2z = 0

b) find vector equation for their line of intersection.

 

[whitecorp]

2x-y-3z = 7 --------(1)
x+2y+2z = 0 -----------(2)

(1)*2 + (2): 5x-4z = 14 =====> x =1/5 ( 14 +4z) ---------(3)

Substitute (3) into (1):

2/5 ( 14 +4z) - y - 3z =7
28/5 +8/5 z - y -3z =7
y= -7/5 - 7/5z

Hence, vector equation of line is given by r = (x, y ,z)

= ( 14/5 + 4/5 z , -7/5 - 7/5z, z)

= (14/5, -7/5 , 0) + z ( 4/5, -7/5, 1)

= (14/5, -7/5 , 0) + z/5 ( 4, -7, 5)

= (14/5, -7/5 , 0) + λ ( 4, -7, 5) where the parameter λ = z/5 (shown)

Hope this helps. Peace.

 

[snowbrood]

whitecorp,
guys i need ur help in this question i dont get the step 3 4 and 5 can anyone please help i dont get how it is derived how pnf is eliminated using mathematics can anyone helppp

 

[snowbrood]

2x-y-3z = 7 --------(1)
x+2y+2z = 0 -----------(2)

(1)*2 + (2): 5x-4z = 14 =====> x =1/5 ( 14 +4z) ---------(3)

Substitute (3) into (1):

2/5 ( 14 +4z) - y - 3z =7
28/5 +8/5 z - y -3z =7
y= -7/5 - 7/5z

Hence, vector equation of line is given by r = (x, y ,z)

= ( 14/5 + 4/5 z , -7/5 - 7/5z, z)

= (14/5, -7/5 , 0) + z ( 4/5, -7/5, 1)

= (14/5, -7/5 , 0) + z/5 ( 4, -7, 5)

= (14/5, -7/5 , 0) + λ ( 4, -7, 5) where the parameter λ = z/5 (shown)

Hope this helps. Peace.

helppp

 

[Nagaanusan]

Assalamoalaikum Wr Wb!

Post your doubts here. Make sure you give the link to the question paper when posting your doubts.


May Allah give us all success in this world as well as the HereAfter...Aameen!!

And oh yeah, let me put up some links for A level Maths Notes here.

Check this out! - Nice website, with video tutorials for everything! MUST CHECK

My P1 Notes! - Only few chapters available at the moment!

Maths Notes by destined007

Some Notes for P1 and P3 - shared by hamidali391

A LEVEL MATHS TOPIC WISE NOTES

MATHS A LEVEL LECTURES

compiled pastpapers p3 and p4 - by haseebriaz

Permutations and Combinations (my explanation)- P6

Permutations and Combinations - P6

Vectors - P3

Complex No. max/min IzI and arg(z) - P3

Sketcing Argand Diagrams - P3 (click to download..shared by ffaadyy)

Range of a function. - P1

pls help me

 

[Nagaanusan]

im a student of a school in srilanka
i need 2012 pastpaper to revise in
math physics chemistry all cie
pls send me

 

[Maz]

i was wondering whether you have to show the working to a quadratic equation's answer or if the values of "x" directly would suffice ?? (since it is a real headache, when you get the answer directly using the calc )

 

[anonymous123]

i was wondering whether you have to show the working to a quadratic equation's answer or if the values of "x" directly would suffice ?? (since it is a real headache, when you get the answer directly using the calc )

ofc u have to show it...you have the option for integration in your calculator too but it doesn't mean u can just write the answer without showing the working..

 

[Kumkum]

can someone please help me with 9(ia)
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_qp_12.pdf

 

[whitecorp]

can someone please help me with 9(ia)
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_qp_12.pdf

Note that for when k=2, cos^2 x will have a range given by [ 0, 1] for the domain [0, pi]
Hence, the range of f would be [ 3-4 =-1, 3-0=3] (shown)

Hope this helps. Peace.

 

[PhyZac]

Asslamu Alikum Wa Rahmatullah Wa Barkatoho...

Can some one explain this question! (Question and markscheme shown below)

 

[soumayya]

http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_31.pdf
someone please help me with no 8
thanks in advance

 

[Kumkum]

Note that for when k=2, cos^2 x will have a range given by [ 0, 1] for the domain [0, pi]
Hence, the range of f would be [ 3-4 =-1, 3-0=3] (shown)

Hope this helps. Peace.

thnx a lot!

 

[anonymous123]

Asslamu Alikum Wa Rahmatullah Wa Barkatoho...

Can some one explain this question! (Question and markscheme shown below)
View attachment 21270View attachment 21271

Walaikum AsSalam Warahmatullahi Wabarakatohu

i am assuming you already know how |z-3i|=<2 is a circle
Centre = 0,3
Radius = 2

In exam you will have a compass and a graph paper so everything will be accurate..the inequality says the circle is less than the radius so you have to shade inside....i forgot to do so

To find the maximum arg..draw a tangent such that u create the largest angle as done in the picture....now u have a triangle in the 2nd quadrant and so u can find arg z easily

 

[whitecorp]

thnx a lot!

No problem. Peace.

 

[SyafiqShazwan94]

i need help
http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_s03_qp_3.pdf
Q.6 part ii
do help thx

 

[PhyZac]

Walaikum AsSalam Warahmatullahi Wabarakatohu

i am assuming you already know how |z-3i|=<2 is a circle
Centre = 0,3
Radius = 2

In exam you will have a compass and a graph paper so everything will be accurate..the inequality says the circle is less than the radius so you have to shade inside....i forgot to do so

To find the maximum arg..draw a tangent such that u create the largest angle as done in the picture....now u have a triangle in the 2nd quadrant and so u can find arg z easily

Jazaka Allah Khairan........Thank you so much !!! Really helpful, thanks for the graph bit !
May Allah reward you for your help Ameen, And In Shaa Allah your exams shall be easy and you score the highest grades in this life and hereafter Ameen!!!!!!!!!!!!!!!!

 

[anonymous123]

Jazaka Allah Khairan........Thank you so much !!! Really helpful, thanks for the graph bit !
May Allah reward you for your help Ameen, And In Shaa Allah your exams shall be easy and you score the highest grades in this life and hereafter Ameen!!!!!!!!!!!!!!!!

wow thanks for the prayer!!!! really needed it May Allah give you success in this world and the Hereafter and make these exams easy for you...Ameen

 

[mimiswift]

ok. so my question is not from any papers or anything. But my teacher gave it to me. And I have no idea how to solve it.
write y=f(x)= modulus of -4x+12 as a piecewise function

how do I do it?

 

[whitecorp]

ok. so my question is not from any papers or anything. But my teacher gave it to me. And I have no idea how to solve it.
write y=f(x)= modulus of -4x+12 as a piecewise function

how do I do it?

The contents of this moduli function is -4x+12. Depending on whether -4x+12 is positive or negative, we will proceed to redefine things sans
the modulus brackets.

Therefore, it simply means |-4x+12| =

(i) -4x+12 for -4x+12 ≥0 ====>x ≤3 (simply remove the modulus sign since the contents are positive)

(ii) -(-4x+12)= 4x-12 for -4x+12 <0 =====>x >3 (append a negative sign to ensure the contents are now positive)

(shown)

Essentially y=|-4x+12| is interpreted as two separate functions, one for x ≤3 and another for x>3.

Hope this helps. Peace.