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Answer:
(b) segment EG and segment OM
Step-by-step explanation:
SAS is short for side-angle-side. It refers to claiming congruence by demonstrating the sides on either side of a given angle are congruent to their counterparts.
You want to identify the sides that need to be congruent on the other side of the congruent angle.
Note that in triangle MON, sides OM and ON are either side of angle O.
In triangle GEF, sides EG and EF are on either side of angle E.
We already know angle O is congruent to angle E, and we know side EF is congruent to ON. The other sides of the angle need to be congruent for the triangles to be congruent by SAS:
EG ≅ OM . . . . . matches the 2nd choice
The first integral has a well-known beta function representation, so the second one should too. The beta function itself is defined as
and satisfies the identity
Later on, we'll also use the so-called reflection formula for the gamma function; for non-integer z,
as well as the identity
Replace in both integrals, so that
Now replace :
So, the original integral (which I condense here to a double integral) is
Answer:
The distance of the run was 27 miles and the distance of the bicycle race was 88 miles.
Step-by-step explanation:
Since I have entered 115-mile biathlon that consists of a run and a bicycle race, and during my run, my average velocity is 9 miles per hour, and during my bicycle race, my average velocity is 22 miles per hour , and I finish the race in 7 hours, to determine what is the distance of the run and what is the distance of the bicycle race, the following calculations must be performed:
7 x 22 + 0 x 9 = 154
5 x 22 + 2 x 9 = 128
4 x 22 + 3 x 9 = 115
Therefore, the distance of the run was 27 miles and the distance of the bicycle race was 88 miles.