Find the coefficient of the x^9in the expansion of (3x* - 1/x)^6

Calculate the binomial coefficient and appropriate powers of
2
and
3
to find that the required coefficient is:
1088640

Explanation:
(
2
x
+
3
)
10
=
10
∑
k
=
0

(
10
k
)
2
10
−
k
3
k
x
10
−
k

The term in
x
6
is the one for
k
=
4
, so has coefficient:
(
10
4
)
2
6
⋅
3
4

=
10
!
4
!
6
!
⋅
64
⋅
81

=
10
×
9
×
8
×
7
4
×
3
×
2
×
1
⋅
64
⋅
81

=
210
⋅
64
⋅
81
=
1088640

Instead of calculating
(
10
4
)
, you can pick it out from the appropriate row of Pascal's triangle...
enter image source here

Step-by-step explanation:"

The electrician charges an initial fee of $42", AND "The electrician charges $22 for every hour worked" is true.

The equation is y=22x+42. The formula is y=mx+b.m is the slope, or is this case, the number of dollars for every "x", which is the number of hours worked. So you have to pay $22 for every hour the electrician works.b is the y-intercept, or the amount it starts with, in this case, you have to pay a fee of $42 even when the electrician worked 0 hours. This is because $42 is the amount it starts with.On a graph, the line will start at (0,42) because that is when you start paying. And then it will increase by 22 for each hour, so the next coordinate would be (1,64).