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Mathematics: Post your doubts here!

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PLZ someone help me with these questions !!
 

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PLZ someone help me with these questions !!
5)i) mgh = 1/2mv^2
10(0.45) = (0.5)(v^2)
v = 3 m/s
ii) 0.39 + PE = (.5)(.3)(3^3)
PE = 0.96 J
(0.3)(10)(h) = 0.96J
h = 0.32m

4)i) motion of A:
3.6sin60 - T = (0.36)(0.25)
T = 3.03N
ii) motion of B:
3.03 - (Friction + 2.4sin60) = (0.24)(0.25)
Friction = 0.892N
Friction = uR
0.892 = u* 2.4cos60
u = 0.74
 
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n of q = (1,b,c)
Angle between 2 planes is 60
(1,b,c) . (1,1,0)/ sqrt(1 + b^2 + c^2) * sqrt2 = cos60
(1 + b)^2 = 1/4 * 2 * (1 + b^2 + c^2)
1 + 2b + b^2 = 0.5 + 0.5b^2 + 0.5c^2
0.5b^2 + 2b + 0.5 - 0.5c^2 = 0 --- eq 1

AB lies in q so its direction vector is normal to n
(1,b,c) . (3,1-1) = 0
c = 3 + b
substitute this in equation 1 and you'll get b = -4, c = -1
x -4y - z = (1, -4, -1).(2, -3, 2)
x -4y -z = 12

When is equation
b² - 4ac
used?
It's used to check how many real roots a quadratic equation has.
 
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For questions 5:

First differentiate the equation in terms of x
replace dy/dx as 0
You will get the equation: 3x^2+y^2-6ax=0
From original equation make y the subject
Replace in the equation above.
You will get the value of x= (3a)^1/2
Sorry to Interrupt :).. How do we elminate y2 in the equation??
 
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HELP NEEDED
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s12_ms_32.pdf
QUESTION 5
MY ANSWER IS Y=X-0.5LN3
is it the same thing as the answer in the marking scheme??
No, the answer in the scheme doesn't work if x > .54

1/r(r+1)(r-1) ≡ A/r + B/(r+1) + C/(r-1)
1 = A(r+1)(r-1) + B(r)(r-1) + C(r)(r+1)
at r = 1, C = 0.5
at r = -1, B = 0.5
at r = 0, A = -1

cosAOP = cosBOP
(1,2,2).(1+2s, 2+2s, 2-2s)/3 = (3,4,0).(1+2s, 2+2s, 2-2s)/5
solve for s and you should get s = 3/8
 
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Greetings,
Yes, I'm stuck with question 8 in Exercise 16B in Pure Mathematics 2 & 3.
I'd be very thankful if somebody helped me out with it.
 

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