Mathematics: Post your doubts here!

[tanmaydube]

Thanks a lot Alice123 and littlecloud11 ! You guys are awesome!!

 

[tanmaydube]

Help Again please Summer 2011 paper 32
Question 6 i)

Question 6 ii) (if possible)
Thank You

 

[Alice123]

Help Again please Summer 2011 paper 32
Question 6 i)

Question 6 ii) (if possible)
Thank You

https://www.xtremepapers.com/community/attachments/maths-solve-q6-001-jpg.2196/

 

[Ammirul Shafiq]

How to solve these questions. 33/M/J/12

Q3) x= sin 2θ - θ, y= cos 2θ + 2 sinθ

show that dy/dx = 2 cosθ/1+2 sinθ

Q6)

It is given tan 3x = k tan x, where k is constant and tan x not equal to 0

i) By first expanding tan(2x+x), show that

(3k-1) tan^2x = k-3


tq

 

[tanmaydube]

Thanks again for the help Alice123 !

 

[Tabi Sheikh]

help plzzzzz!!!!!!!!!!!!!!!!!!
papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20(9709)/9709_s03_qp_1.pdf
Question #1

 

[Ammirul Shafiq]

help plzzzzz!!!!!!!!!!!!!!!!!!
papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20(9709)/9709_s03_qp_1.pdf
Question #1

= Factorise it to get 2x ( 1- 1/2x^2)
= (2x)^5 (1+ 5C1 (-1/2x^2) + 5C2 (-1/2x^2)^2 + 5C3 (-1/2x^2)^3+............)
(32x^5) x (-10/8x^6) = -40/x

* x^5/x^6 = 1/x.

So, coefficient of 1/x is -40.

 

[Ahmedraza73]

Sand is poured on to a horizontal floor at a rate of 4 cm^3/s and from a pile in the shape of a circular cone,of which the height is three-quarters of the radius .calculate the rate of change of the radius when the radius is 4cm.
Please can anyone solve this question for me its urgent?

 

[littlecloud11]

Guys can someone please help me out in this complex number question. Question 8, part ii : http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s07_qp_3.pdf

 

[Ahmedraza73]

View attachment 22208

Please reply to my question

 

[Dug]

Sand is poured on to a horizontal floor at a rate of 4 cm^3/s and from a pile in the shape of a circular cone,of which the height is three-quarters of the radius .calculate the rate of change of the radius when the radius is 4cm.
Please can anyone solve this question for me its urgent?

dV/dt = 4

dr/dt = dr/dV x dV/dt

To find dr/dV, we need an equation connecting V and r.

Volume of a cone = (1/3)πr^2 h

In the question, we are told height is three-quarters of the radius, therefore replacing 'h' by (3/4)r :

V= (1/3)πr^2 (3r/4)
V =1/4 πr^3

dV/dr = (3/4)πr^2
dr/dV = 4/3(πr^2)

dr/dt = dr/dV x dV/dt
dr/dt = [4/3(πr^2)] x 4
dr/dt = 16/3πr^2

When r = 4,
dr/dt = 16/3π(4)^2
dr/dt = (1/3)π cms-1

 

[littlecloud11]

Sand is poured on to a horizontal floor at a rate of 4 cm^3/s and from a pile in the shape of a circular cone,of which the height is three-quarters of the radius .calculate the rate of change of the radius when the radius is 4cm.
Please can anyone solve this question for me its urgent?

Formula for volume of a cone is (1/3)(pi)(r^2)(h)
You're given that h = 3r/4 so the formula becomes (1/4)(pi)(r^3)
V = (1/4) πr^3
dV/dr = (3/4) πr^2
dV/dt = dV/dr * dr/dt
4 = (3/4) πr^2 * dr/dt
4 = (3/4) π (4)^2 * dr/dt
cross-multiply and you get-
dr/dt = 1/3π cm/s

 

[Nab900]

salam

can someone explain me question 4(ii) from may june 2012
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_31.pdf

The complex number u is defined by u =((1+2i)^2)/(2+i)

(i) Without using a calculator and showing your working, express u in the form x + iy, where x and y are real.
(ii) Sketch an Argand diagram showing the locus of the complex number Z such that |Z− u| = |u|.

 

[Shreeram]

Assalamoalaikum!!
Guys please help me out with equilibrium of a rigid body for mechanics paper 5. i need it as soon as possible as im wiriting this year may... thanks a lot in advance

 

[minie23]

Please help me with the following questions;
June 2006 P3 no. 6 (i) and no. 7 (i) & (iii)

Ty

 

[Ammirul Shafiq]

salam

can someone explain me question 4(ii) from may june 2012
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_31.pdf

The complex number u is defined by u =((1+2i)^2)/(2+i)

(i) Without using a calculator and showing your working, express u in the form x + iy, where x and y are real.
(ii) Sketch an Argand diagram showing the locus of the complex number Z such that |Z− u| = |u|.

i) expand u and you'll get -3+4i and then multiply the numerator and denominator by 2 – i (conjugate of 2+i).
So,the answer is -2/5 + 11/5 i
ii) |Z− u| = |u| where u is -2/5 + 11/5 i and |u| is the radius for the locus

Correct me if my answer is wrong.

 

[Rutzaba]

Please help me with the following questions;
June 2006 P3 no. 6 (i) and no. 7 (i) & (iii)

Ty

3x^2 -4xy +y^2 -45=0

lets break this into three parts. the first one is easy lets cum to the second one. -4xy this we are going to solve by the product rule.
take u=-4x and differential wud be -4
take v = y and differential wud be dy/dx
apply product rule
-4y-4x dy/dx

then lets look at part three

Y^2 wud be differentiated as
2y dy/dx
and 45 will becum 0
and that will altogether give you 6x-4y-4x dy/dx +2y dy/dx =0
now make dy/ dx the subject of formula

dy/dx( -4x+2y)= 4y-6x

dy/dx = 4y-6x / 2y-4x

now put the values of x and y
where x =2 and y=-3

 

[minie23]

3x^2 -4xy +y^2 -45=0

lets break this into three parts. the first one is easy lets cum to the second one. -4xy this we are going to solve by the product rule.
take u=-4x and differential wud be -4
take v = y and differential wud be dy/dx
apply product rule
-4y-4x dy/dx

then lets look at part three

Y^2 wud be differentiated as
2y dy/dx
and 45 will becum 0
and that will altogether give you 6x-4y-4x dy/dx +2y dy/dx =0
now make dy/ dx the subject of formula

dy/dx( -4x+2y)= 4y-6x

dy/dx = 4y-6x / 2y-4x

now put the values of x and y
where x =2 and y=-3

Thanks. But I think you missed the question. Its June 2006 P3 no. 7(iii)

 

[Rutzaba]

Please help me with the following questions;
June 2006 P3 no. 6 (i) and no. 7 (i) & (iii)

Ty

was this of any help? il cum to the other Q later perhaps

 

[Rutzaba]

salam

can someone explain me question 4(ii) from may june 2012
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_31.pdf

The complex number u is defined by u =((1+2i)^2)/(2+i)

(i) Without using a calculator and showing your working, express u in the form x + iy, where x and y are real.
(ii) Sketch an Argand diagram showing the locus of the complex number Z such that |Z− u| = |u|.

http://i1275.photobucket.com/albums/y444/Rutzaba/xpc_zpsd8fbcce5.png