A chord of P measures 8 inches and the distance from the center to the chord is 3 inches. Find the radius of P.
2 answers:
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Let x represent the speed of of boat.
We have been given that the river current is 3 miles per hour.
The speed of boat upstream will be .
The speed of boat downstream would be .
We have been given that you travel 2 miles downstream to a marina for supplies, and then you travel 3 miles upstream to a dock.
We can represent this information in an equation as:
Since the speed of the boat is 18 miles per hour, so we will substitute in above equation and solve for time.
Since time is in hours, so let us convert our given time in minutes.
1 hour = 60 minutes.
Rounding to nearest tenth of minute.
Therefore, it will take approximately 17.7 minutes for the boat to take the trip.
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