• We need your support!

    We are currently struggling to cover the operational costs of Xtremepapers, as a result we might have to shut this website down. Please donate if we have helped you and help make a difference in other students' lives!
    Click here to Donate Now (View Announcement)

Mathematics: Post your doubts here!

A

abbey789

Messages
66
Reaction score
12
Points
18
freezingfires said:
Here it says the rate of increase of the surface area of the sphere is proportional to its volume.
so dA/dt=kV
dA/dt=4pi r^2 differentiating this gives us 8pir dr/dt
now equate
8pirdr/dt=k(4/3pi r^3)
put values of dr/dt and r given in the question to get k=12/25
Now put this value of k back in 8pirdr/dt=k(4/3pi r^3) to get dr/dt=0.08r^2
Now apply differential equation solve it and you will get
-1/r=0.08t+k
put t=o and r=5 to get k=-1/5
Now solve it further to get in terms of r and t
your final equation will be r=5/(1-0.4t)
for the last part equate the denominator to 0 you will get t=2.5 which means that if denominator is 0 equation is not valid so values of t must be grater than 0 but less than 2.5.HOPE YOU GOT IT!! PLEASE PRAY FOR ME!! :)
Click to expand...
THANK YOU SO MUCH! Yes I will! :)
I didn't get this part dA/dt=4pi r^2 differentiating this gives us 8pir dr/dt
 
VinnCh

VinnCh

Messages
12
Reaction score
6
Points
3
LMGD33 said:
Hello guys, I'm solving http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_qp_33.pdf and I had this beautifully posted solutions to all the paper, i', just wondering in Question 5 (ii) How did they get that formula? Why did they divide by 70 and multiply by 100? Thank you so much!!
View attachment 26637

Credit to Anika Raisa
Click to expand...

After I went through the question. The initial mass (t=0) of substance B, which is also y is 70. The question asks for percentage mass remaining. Since the mass remaining as t increase to infinite is 70/e, the percentage mass remaining should be (remaining/initial) x 100 , which is also [(70/e)/70]x100.
I hope you understand it. =)
 
VinnCh

VinnCh

Messages
12
Reaction score
6
Points
3
LindaKim123 said:
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w12_qp_31.pdf

question 9 ii) please!!
Click to expand...
Since 1+√2i and 1-√2i are the two imaginary roots, which means x=1+√2i and x=1-√2i . Equate them, ( x - [1+√2i] ) ( x - [1-√2i] ) and expand them. Use the resulting equation ( x^2 -2x + 3 ) to do long division with P(x). You'll get a quadratic equation in return, then just use the usual way to find the roots. =)
 
littlecloud11

littlecloud11

Messages
844
Reaction score
2,495
Points
253
LindaKim123 said:
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w12_qp_31.pdf

question 9 ii) please!!
Click to expand...

This is how I do it.
The two complex roots are 1+√2i and 1-√2i
If you kept it in the form of factors it would be [x-(1+√2i)] and [x-(1-√2i)]. These are the two factors of p(x)
If you multiply these two factors you get a quadratic equation.
(x-1-√2i) * (x-1+√2i)
= x^2 -x +√2xi -x +1 -√2i -√2ix +√2i -(√2i)^2
=x^2 -2x +1 +2
=x^2 -2x +3

Now use long division to divide p(x) by this quadratic factor to get the other two factors.
Hope this helps!
 
Gordious

Gordious

Messages
21
Reaction score
6
Points
13
LMGD33

LMGD33

Messages
44
Reaction score
32
Points
18
VinnCh said:
After I went through the question. The initial mass (t=0) of substance B, which is also y is 70. The question asks for percentage mass remaining. Since the mass remaining as t increase to infinite is 70/e, the percentage mass remaining should be (remaining/initial) x 100 , which is also [(70/e)/70]x100.
I hope you understand it. =)
Click to expand...
Is it something like this? Then i tend to infinity and obtain P = 100/e

IMG019.jpg
THANK YOU SO MUCH!! Remembered in my prayers!
 
You must log in or register to reply here.
Top