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dx/dt = 1/x - x/4ANY EASY WAY TO ATTEMPT THIS QUESTION!
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s10_qp_33.pdf
Q4
PLZ HELP!!!!!!!!!!!!!!
cos ( q + 60) = 2sinqAssalamu Alikum
Solve the equation
cos(q+60) = 2 sin q
giving all solutions in the interval 0 =< q >= 360 [5 marks]
Oh thank you so much...!!!! Jazak Allah khairan!!!cos ( q + 60) = 2sinq
cosqcos60 - sinqsin60 = 2sinq
1/2cosq - √3/2 sinq = 2sinq
1/2cosq = 2sinq + √3/2 sinq
tan q = 0.1745
q = 9.9 and 189.9
check if its correct in the mark scheme or something and tell me !
P(T=A) = P(T=B) = P(T=C) = 1/3Thank you for your help
We did it this way, and we THINK we got it correct (since we came second)
Let the 3 doors be A ( leading to safety in 2hrs)
B ( bringing man back in 3hrs) n
C ( " " " 5hrs)
possible pathway - probability - time taken
1. A - (1/3) - 2hrs
2. B,A - (1/3).(1/3)= 1/9 - 5hrs
3. C,A - 1/9 - 7hrs
4. B,C,A or C,B,A - 1/27 - 10hrs
so expected time= one with max probability= 2hrs
What do you think?
Ameen ya rab..Oh thank you so much...!!!! Jazak Allah khairan!!!
Yes correct and i understood the method...May Allah reward you for helping me..
can uh make meh understand da followin questions , i will be grateful to ya buddy...
Q : Find the values of k for which the equation k2X2 + 2kX +1 =0 have no roots.
Q 2 : Solve the following inequality :
X(X-2)<5
it give complex roots...For question no. 2 you multiply inside the brackets first and then take the 5 from the other side, it becomes
X^2-2X-5<O
Now it becomes quadratic equation. Now you can solve that, using a calculator aswell.
w alikom al salam..Assalamu Alikum Wa Rahmatullahi Wa Barakatoho.. iKhaled
5 The parametric equations of a curve are
x = ln(tan t), y = sin2t, (it is sin square t )
where 0 < t <1/2π.
(i) Express
dy/dx
in terms of t. [4]
(ii) Find the equation of the tangent to the curve at the point where x = 0.
Jazak Allah Khairan..thank you so much, May Allah reward you for the help ur providing other students with.w alikom al salam..
here is the solution to the question
(i) you have to know that whenever u have a parametric equation, dy/dx = dy/dt X dt/dx
dy/dt = 2sin t. cos t
dy/dt = 2sintcost
dx/dt = (1/tan t) x sec^2 t
dx/dt = (cos t / sin t ) x 1/cos^2 t
dx/dt = 1/sin t cos t
dy/dx = 2sintcost X sintcost
dy/dx = 2sin^2 t cos^2 t
(ii) here we need to find the equation of the tangent at the point where x is 0 so first lets find y so we have a coordinate and we know that dy/dx is out tangent
x = ln(tan t )
0 = ln (tan t)
e^0 = tan t
t = tan^-1(1)
t= 1/4π
dy/dx = 2sin^2(1/4π)cos^2(1/4π)
m(gradient) = 1/2
y = sin^2(1/4π)
y= 1
y-1 = 1/2(x-0)
2y-x = 2
is this how it is in the mark scheme? if its correct pls tell me and i hope u get it! any questions feel free to ask me
oh sorry i made such a stupid errorJazak Allah Khairan..thank you so much, May Allah reward you for the help ur providing other students with.
I fully understood the first part. Alhamdulilah. And your answer is exactly similar to markscheme
coming to the second part of the question..
t=1/4pi ..................i got it
m=1/2 ....................i got it
but in markscheme the equation seem different..... the "c"
here is a copy:
View attachment 20543
wat bout the first 1. BETWEEN! Thanks . May Allah bless you.For the question x(x-2) < 5:
x^2 - 2x - 5 < 0
x^2 - 2x + 1 - 6 < 0
(x-1)^2 - 6 < 0
(x-1)^2 < 6
|x-1| < sqrt(6)
hence,
1-sqrt(6) < x < sqrt(6)+1
LUMS PsiFi This was a question from Math Gauge.I still think the expected time owuld be the sum of all probabilities like it always is. Your solution would be completely correct only if the maximum probabilty was 1 i.e. A was certain to happen so the expected time would definitely be 2 hours.
P.S. Which contest was this?
I knew it!LUMS PsiFi This was a question from Math Gauge.
In fact, it will not have roots only if k = 0.Q : Find the values of k for which the equation k2X2 + 2kX +1 =0 have no roots.
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