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Mathematics: Post your doubts here!

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No i dont get the ans. 12/30+ 16/30 + 3/30 = 31/30
The ans is 5/6.

Oh sorry there has been formula mistake
it should 12/30 +16/30 - 3/30 since intersection has to be deducted as in formula of set
 

Dug

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By setting both equations equal, we get kx+6=x^2+3x+2k.
By refining the resultant equation, we get x^2 +(3-k)x +2k - 6 = 0
Set b^2-4ac = 0 and simplify.
Consequently, you get a quadratic in k. Solve it and you have the values for k.
 
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salam guys: hey i need help with vectorx for AS pure maths (p1) can any1 provide me a link or sumthing for vectorx???
 
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By setting both equations equal, we get kx+6=x^2+3x+2k.
By refining the resultant equation, we get x^2 +(3-k)x +2k - 6 = 0
Set b^2-4ac = 0 and simplify.
Consequently, you get a quadratic in k. Solve it and you have the values for k.

but why did you set the two equations equal shouldn't there gradients be equal?
 
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hey dug thanks a lot for the last post can u tell me any more basics for the past - paper questions on functions .. involving completed square forms n finding 'A' 1,1 functions , domains ranges of inverses , findhing range when x has a domain of real values n all etc etc... Would appreciate it a LOT :)
 
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Assalamalaikum. These are probably stupid questions so don't laugh :) Can anyone help me?
Qs.1) Find the values of k such that the straight line y=2x+k meets the curve with equation x^2+2xy+y^2=5 exactly once.

Qs.2) An Open cylindrical wastepaper bin, of radius r cm and capacity Vcm^3 is to have a surface area of 5000 cm^3.
(a) Show that V=1/2r(5000πr^2)
(b) Calculate the maximum possible capacity of the bin.
 

Dug

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i)
'a' is the amplitude of the function.
a = 9 - 3 = 6

'b' is the number of cycles if in 2pi
The graph shows 2 cycles in 2pi and therefore b = 2

'c' is the y-intercept. Its the number of units the graph has shifted upwards.
c=3

ii) You got the values of a, b and c.
y = 6sin2x + 3
For y = 0,
6sin2x + 3 = 0
sin2x = -1/2
2x = 7pi/6
x = 7pi/12

We could've got another solution too but the question asks for the 'smallest' value of x and thats why we exclude the value from the 4th quadrant.
 
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i)
'a' is the amplitude of the function.
a = 9 - 3 = 6

'b' is the number of cycles if in 2pi
The graph shows 2 cycles in 2pi and therefore b = 2

'c' is the y-intercept. Its the number of units the graph has shifted upwards.
c=3

ii) You got the values of a, b and c.
y = 6sin2x + 3
For y = 0,
6sin2x + 3 = 0
sin2x = -1/2
2x = 7pi/6
x = 7pi/12

We could've got another solution too but the question asks for the 'smallest' value of x and thats why we exclude the value from the 4th quadrant.
thank you so much..but dude what do u mean by "a - 9 therefore 3=6"..didnt get that
 

Dug

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hey dug thanks a lot for the last post can u tell me any more basics for the past - paper questions on functions .. involving completed square forms n finding 'A' 1,1 functions , domains ranges of inverses , findhing range when x has a domain of real values n all etc etc... Would appreciate it a LOT :)
Its a bit difficult to explain it like that. If you could get a question from past-papers involving those concepts, I will be grateful. :p
 

Dug

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its ok..sorry if i am annoying u but is it 9-3 cuz it didnt start from 0?
Exactly!! If it started from the origin, then 'a' would have been equal to 9. You could tell that just by looking at the graph.
 
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