Qualification > Math
[CIE] All Pure Mathematics (P1, P2 and P3) doubts here !
doubtigetastar:
Help! :
A quantity u varies with respect to t so that du/dt = a+bt where a & b are constants.
Given that it has a maximum value of 5.5 when t=1 and that its rate of change when t=2 is -3 , find u in terms of t.
Vin:
--- Quote from: iluvme on May 06, 2011, 07:30:08 pm ---CIE November 2010 Variant 2
Q7 iii)
I got the answer using a very very long method, does anyone have a shorter method since its 1 mark only?
--- End quote ---
Don't you complete the square for f(x) and substitute in hg? I think that's the smallest way. :/
--- Quote from: physichemaths on May 06, 2011, 09:12:46 pm ---
THANK YOU! :D
--- End quote ---
Sorry there was a typo. (corrected- bold) please check again?
--- Quote from: doubtigetastar on May 06, 2011, 09:13:34 pm ---Help! :
A quantity u varies with respect to t so that du/dt = a+bt where a & b are constants.
Given that it has a maximum value of 5.5 when t=1 and that its rate of change when t=2 is -3 , find u in terms of t.
--- End quote ---
Do you have the answer? Cant be sure of mine actually :/
SkyPilotage:
--- Quote from: doubtigetastar on May 06, 2011, 09:13:34 pm ---Help! :
A quantity u varies with respect to t so that du/dt = a+bt where a & b are constants.
Given that it has a maximum value of 5.5 when t=1 and that its rate of change when t=2 is -3 , find u in terms of t.
--- End quote ---
-du/dt=-3 when t=2 soo : a+2b=-3
-maximum value of u is 5.5 so du/dt=0 : a+b=0
So solve the eqns you get b=-3 and a=3
Then integrate du/dt to get u= 3t-1.5t^2+c --->subsitute (1,5.5) to get c=4 -----> so u=3t-1.5t^2+4
Hope it helps...
bulono:
M/J 2004 question 8 i....
http://www.xtremepapers.me/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s04_qp_1.pdf
in the answer scheme the perimeter of the semi circle is written as (pie)r...dont understand
SkyPilotage:
--- Quote from: bulono on May 06, 2011, 10:37:06 pm ---M/J 2004 question 8 i....
http://www.xtremepapers.me/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s04_qp_1.pdf
in the answer scheme the perimeter of the semi circle is written as (pie)r...dont understand
--- End quote ---
Circumference of circle is 2pi(r) since its half a circle the perimeter of semicircle is pi(r)..
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