What is the value of 2×[34−5×(3+1)] ?
1 answer:
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Answer:
6*8=48 groups with elements of order 7
Step-by-step explanation:
For this case the first step is discompose the number 168 in factors like this:
And for this case we can use the Sylow theorems, given by:
Let G a group of order where p is a prime number, with
and p not divide m then:
1)
2) All sylow p subgroups are conjugate in G
3) Any p subgroup of G is contained in a Sylow p subgroup
4) n(G) =1 mod p
Using these theorems we can see that 7 = 1 (mod7)
By the theorem we can't have on one Sylow 7 subgroup so then we need to have 8 of them.
Every each 2 subgroups intersect in a subgroup with a order that divides 7. And analyzing the intersection we can see that we can have 6 of these subgroups.
So then based on the information we can have 6*8=48 groups with elements of order 7 in G of size 168
The average rate of change on the interval (5, 6) is 9. So the correct option is D.
<h3>How to find the average rate of change on the interval?</h3>
Here we want to find the average rate of change of f(x), the function on the table, on the interval (5, 6).
This is just:
I we look at the table we see that:
This is a system of equations.
If we subtract the second and first functions, we get:
From that we take two relations:
Now we can replace these two in the last equations so we get:
Now that we know the value of a:
The quadratic equation is:
Evaluating this in x = 6 we get:
And from the table we know that f(5) = 17, then the average rate of change is:
The correct option is D.
If you want to learn more about average rates of change:
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