I think you have to first separate the integral:1/(1+v^2) + v/(1+v^2),
so the integral of the first term is ArcTan (v) and for the integral of the second term i recommend you to do a change of variable:
y= 1+v^2
so
dy= 2v
and
v= dy/2and then you substitute:v/(1+v^2) = (1/2)(dy/y)
and the integral is
(1/2) (In y)finally you plug in the initial variables:
(1/2)(In [1+v^2])
so the total integral is:
ArcTan (y) + (1/2)(In [1+v^2])
Answer:
117
Step-by-step explanation:
6/8 = ?/156
156/8 = 19.5
19.5 x 6 = 117
6/8 = 117/156
A. 485 is %3 of 500, but the deviation sets it slightly lower than that
9514 1404 393
Answer:
- red division: 6 teams
- blue division: 5 teams
Step-by-step explanation:
We can let r and b represent the numbers of teams in the red and blue divisions, respectively. The total number of goals scored in each division will be the average for that division times the number of teams in that division.
r - b = 1 . . . . . . there is 1 more red team than blue
4.5r +4.2b = 48 . . . . . . total goals scored per week
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Solving by substitution, we have ...
r = b +1
4.5(b +1) +4.2b = 48 . . . . substitute for r
8.7b +4.5 = 48 . . . . . . . . simplify
8.7b = 43.5 . . . . . . . . . . subtract 4.5
b = 43.5/8.7 = 5 . . . . . divide by 8.7
r = b +1 = 6 . . . . . . . . . find r
There are 6 red teams and 5 blue teams.
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<em>Additional comment</em>
The basic idea is that you make an equation for each relation given in the problem statement. For a problem like this, you do need to have an understanding of how the average number of goals would be calculated and how that relates to the total goals.
