If there are x teams in a sports league, and all the teams play each other twice, a total of n(x) games are played, where n
1 answer:
1.
Consider a group of n objects. Assume we want to form groups of r, from these n objects.
There are in total
many ways of doing so.
where, r! is "r factorial", calculated as 1*2*3*...*(r-1)*r
2.
C(x, 2) is the total number of pairs out of x objects, that we can form.
so let the x objects represent the x teams, and 2, represent a group of 2, which means a game.
The total number of games is:
n(x)=2*C(x, 2) =
Remark, we multiplied by 2, since there will be 2 matches for each pair of teams.
Answer:
Consider a group of n objects. Assume we want to form groups of r, from these n objects.
There are in total
where, r! is "r factorial", calculated as 1*2*3*...*(r-1)*r
2.
C(x, 2) is the total number of pairs out of x objects, that we can form.
so let the x objects represent the x teams, and 2, represent a group of 2, which means a game.
The total number of games is:
n(x)=2*C(x, 2) =
Remark, we multiplied by 2, since there will be 2 matches for each pair of teams.
Answer:
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Step-by-step explanation:
The first step is to find the (b − a) / n factor in the limit of the Riemann sum. This is the Δx.
The next step is to identify the function and the argument, f(xᵢ). The argument xᵢ looks like a + i (b − a) / n.
From there, you can write two equations:
Δx = (b − a) / n
xᵢ = a + i (b − a) / n = a + i Δx
Since you know xᵢ and Δx, you can identify a. And when you know a, you can plug that into Δx to find b. So now you have the limits of the definite integral.
Finally, write the integral using the limits and the function.
Here's an example. Suppose you have the limit:
lim(n→∞) ∑ᵢ₌₁ⁿ √(1 + 3i/n) (3/n)
First, we notice that Δx = (b − a)/n = 3/n. So b − a = 3.
Next, we identify that xᵢ = 1 + 3i/n = a + i (3/n), so a = 1. Therefore, b = 4.
Now, we identify the function, f(xᵢ) = √xᵢ.
Finally, we plug it all into a definite integral:
∫₁⁴ √x dx
