Using the triangle of pascal we have that the expression equivalent to (x + y) ^ 6 is given by:
x ^ 6 + 6x ^ 5y + 15x ^ 4y ^ 2 + 20x ^ 3y ^ 3 + 15x ^ 2y ^ 4 + 6xy ^ 5 + y ^ 6
Therefore, the coefficients of the expansion are given by:
1, 6, 15, 20, 15, 6, 1
Answer:
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y) ^ 6 are 1, 6, 15, 20, 15, 6, 1
41 and 43 I hope this helps
Answer:
232/15 [as an improper fraction] or 15 7/15 [as a mixed fraction]
Explanation:
16 - 8 / 15 =
(16) - (8 / 15) =
((16 × 15) / 15) - ((8) / 15) =
((240) / 15) - ((8) / 15) =
(240 - 8) / 15 =
232 / 15 =
15 7/15
Cramer's rule works as follows:
x+3y=16
3x+y=8
Then
x=Dx/D
y=Dy/D
where Dx,Dy,D are 2x2 matrices formed from of coefficients and right hand side.
D=
1 3
3 1
=1-9=-8
Dx=matrix D with first column replaced by the vector [16,8]=
16,3
8 1
=16-24
=-8
Dy=matrix D with second column replaced by the vector [16,8]=
1 16
3 8
=8-48
=-40
Therefore
x=-8/-8=1
y=--40/-8=5
Check:
x+3y=1+3(5)=16
3x+y=3(1)+5=8 ok.
Thé vertex of the graph of the following function f(x)=x2+8x-2 is (-4,-18).
