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Mathematics: Post your doubts here!

Esme

Esme

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WayneRooney10 said:
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w09_qp_31.pdf
Why is the answer to Q1 only one value? Why isn't it -1/2<x<5/4? And do question Q2 as well please! :) Thanks.
Click to expand...

Q1 It's because you don't have a modulus on both sides of the inequality. When such is the case, you need to check your answer and see if it satisfies the inequality. So, here take any value of x which is greater than 5/4 eg x=2. Even though this value is outside the range, it satisfies the inequality. Hence you ans is only x> -1/2

Q2 3^(x+2) = 3^x + 3^2
(3^x)(3^2) = 3^x + 3^2
Take u=3^x
You get:
(3^2)u = u + 9
9u = u+9
u= 9/8

Now 3^x=9/8
x=0.107
 
kiara15

kiara15

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are we suppose to attempt all varient papers or only regional that is p42 and p32?
 
WayneRooney10

WayneRooney10

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Esme said:
Q1 It's because you don't have a modulus on both sides of the inequality. When such is the case, you need to check your answer and see if it satisfies the inequality. So, here take any value of x which is greater than 5/4 eg x=2. Even though this value is outside the range, it satisfies the inequality. Hence you ans is only x> -1/2

Q2 3^(x+2) = 3^x + 3^2
(3^x)(3^2) = 3^x + 3^2
Take u=3^x
You get:
(3^2)u = u + 9
9u = u+9
u= 9/8

Now 3^x=9/8
x=0.107
Click to expand...
Esssmeeee! Thank you soooo much! I swear had you not solved so many of my problems I would've been doomed! You deserve a distinction in maths! :)
 
MustafaMotani

MustafaMotani

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F

freezingfires

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abbey789 said:
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w09_qp_31.pdf

Question 10
Click to expand...

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!! :)
 
MustafaMotani

MustafaMotani

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I m retiring to ecOnomics ... only subject which gives me tough time ... and Also its just next day after P3... :(
 
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