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does ne1 have permutations n combinations notes
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thanx wat bout the other 1- 4[ x^2 - 3x + 3/4]
4 [ (x)^2 - 2(x)(3/2) + (3/2)^2 - (3/2)^ + 3/4]
4 [ (x-3/2)^2 - 9/4 + 3/4]
4(x-3/2)^2 -9 + 3
4(x-3/2)^2 -6
CAN U PLZZ POST THE LINKS OF THE PAPERScan anyone help me out for these questions?
nov2011 paper 11 question 10 part ii) how do we get the gradient..
nov 2011 paper 12 question 8 part i)
sry i luked at the ans closely n didnt understand wat u did cud u plz explain?thanx wat bout the other 1
To solve this problem, you should be familiar with the following fact: a plane can be completely determined by 2 intersecting lines.can someone please explain question 10 (ii) in may/june 2005 mathematics paper 3
how in the mark scheme he got the vector parallel to the place. how can i find a vector parallel to a plane?!!
http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_s05_qp_3.pdf
http://papers.xtremepapers.com/CIE/...AS Level/Mathematics (9709)/9709_s05_ms_3.pdf
please help!
(a) If M is a minimum point, then dy/dx = 0 at this point.help please
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_23.pdf
question 5
(a) If M is a minimum point, then dy/dx = 0 at this point.
dy/dx = d(4*e^(x/2) - 6x + 3)/dx = 4* d(e^(x/2))/dx - 6 = 2* e^(x/2) - 6;
dy/dx = 0 when e^(x/2) = 6/2
or, x/2 = ln(3)
x = ln(3) = ln(3*3) = ln(9). hence a = 9;
(b) The area enclosed by the curve is the definite integral of y wrt x:
Area = integral( from 0 to 2) {y dx} = 8*e^(x/2) - 3*x^2 + 3x;
insert limits:
8*e^(2/2) - 3*4 + 3*2 - 8*e^0 = 8e - 12 + 6 - 8 = 8e - 14;
Hence, the answers are a = 9, area = 8e - 14;
You could use the marking scheme for the papers to find out solutions.
SOMEONE PLS HELP!!! [Arithmetic Series]
Question:
A 62 m length of rope is cut into pieces whose lengths are in arithmetic progression with a common difference of d m. Given that the lengths of the shortest and longest pieces are 0.5m and 3.5m respectively, find the number pieces and the value of d.
Thank you very muchh!Beautiful Question.
So, Sum = 62
First Term is going to be the shortest piece, a = 0.5
Last Term is the longest piece, L =3.5
So Sum =62
n ( a + L)/2 = 62
n ( 0.5 + L ) = 124
n ( 0.5 + 3.5 ) = 124
4n =124
n = 31
And we use the information that last term is 3.5 to find the value of d
a + d ( n-1) = 3.5
0.5 + d ( 31-1)= 3.5
30d = 3
d = 3/30
d = 0.1
THE SUM OF THE 1ST 2 TERMS IS EQUAL TO x. ILL USE THE 1ST TERM AS VARIABLE z AND THE COMMON DIFFERENCE AS dI would be very grateful if someone could help!
Another question on Arithmetic Series:
The sum of the first and the second terms of an arithmetic series is x and the sum of the (n-1)th term and nth term is y. Show that the sum of the first n terms is n/4(x+y). Find the common difference in terms of x, y and n.
ok listen up for part b:
"(n-2)d=(n-1)d-d" - I didnt understand this part!THE SUM OF THE 1ST 2 TERMS IS EQUAL TO x. ILL USE THE 1ST TERM AS VARIABLE z AND THE COMMON DIFFERENCE AS d
THEREFORE : z+(z+d)=x
AND :[z+(n-2)d]+[z+(n-1)d]=y
(n-2)d=(n-1)d-d
THEREFORE: z+(n-1)d-d+z+(n-1)d=y
2z+2(n-1)d=y+d
2[z+(n-1)d]=y+d
z+(n-1)d=(y+d)/2
THE SUM OF ARITHMETIC SERIES: S=n/2[2z+(n-1)d]
WE SUBSTITUTE THE VALUE OF z+(n-1)d
THUS WE GET: S=n/2[z+{(y+d)/2}
BY SIMPLIFYING WE GET : S=n/4[2z+y+d] y+d=x
THUS S=n/4(x+y)
AS FOR FINDING COMMON DIFFERENCE IN TERMS OF x, y, n
ITS EQUAL to : d=x-y
hope it helped
if u get confused ask ill explain
ill explain u how (n-2)d=(n-1)d-d"(n-2)d=(n-1)d-d" - I didnt understand this part!
Pls explain it again...
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