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Mathematics: Post your doubts here!

Maz

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I've got another doubt in the same paper...
Q10 (iii)...
I got the critical values= 0 and 64/9
but then what would be the inequality... i reckoned that since "a" in negative in -kx^2 + 3kx -16 i.e. -k, the graph would have an upward parabola, but it turned out to be wrong.
 

Maz

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Wouldn't the graph be something like which starts at 3 and the curve cutting x axis at 2Pi instead of pi?
Actually the curve cannot cut the x- axis at pi, tan is undefined for pi. Nor 2pi since they haven't asked for it.
 

Dug

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Q3)
i) Perimeter of sector = ½(Perimeter of rectangle)
2r + rx = 4a
Sinx = a/r
a = rSinx
2r + rx = 4(rSinx)
2 + x = 4Sinx
Sinx = ¼(2 + x)

ii) x1 = 0.8
x2 = 0.7754
x3 = 0.7668
x4 = 0.7638
x5 = 0.7628
x6 = 0.7625

x = 0.76 (2 dp)

Q4)
i)
q4eGgvM.png


ii) tan²x + (6√3)tanx - 5 = 0
Let y = tanx
y² + (6√3)y - 5 = 0

Now you have to use quadratic formula. I am sure you can do that!
 
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i have problem with question 7(ii).....papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20(9709)/9709_w12_qp_12.pdf
 
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you integrate the equation with limits 1 and 0 to give you the area of the first region(R1), then you do it again with limits 2 and 1 this being the region (R2)
you'll have the same answers (1/4) so you can say R1=R2
you integrate the equation with limits 1 and 0 to give you the area of the first region(R1), then you do it again with limits 2 and 1 this being the region (R2)
you'll have the same answers (1/4) so you can say R1=R2
you integrate the equation with limits 1 and 0 to give you the area of the first region(R1), then you do it again with limits 2 and 1 this being the region (R2)
you'll have the same answers (1/4) so you can say R1=R2
thanks (Y)
 
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umm putting it simply find the angles that the tangent makes with the x-axis, subtract the larger from the smaller and voila you have the acute angle

basically you differentiate the curve equation and first put in the x- coordinate of p then of q
what you'll have is (since the gradient y/x)
tan(theta)=the first gradient(2/3)
tan(alpha)= second(3/4)
larger angle(56.3) - samller angle(36.9)
answer (19.4)

the brackets are the answers..
 
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Differentiate the equation of the curve. you would get dy/dx i.e equation of then gradient of curve.
put the x-co-ordinates of P and Q in the gradient equation. You would get gradient of tangent at P and Q.
let the gradient of tangent at P= m1
let the gradient of tangent at Q=m2
Use formula to find angle
tan(x) = m1 - m2 / (1 + m1m2)
find x in degrees.
 
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