Convert any mixed numbers to fractions.
Then your initial equation becomes:
15
4
×
4
1
Applying the fractions formula for multiplication,
=
15
×
4
4
×
1
=
60
4
Simplifying 60/4, the answer is
15
(27 mi/hr) x (1 hr / 60 min) = (27/60) (mi/min) = 0.45 mile/minute
Using the same kind of calculation, we can see
that the world record times for other distances
correspond to:
200 meters 23.31 mph
400 meters 20.72 mph
800 meters 17.73 mph
1000 meters 16.95 mph
1500 meters 16.29 mph
1 mile (1,609 meters) 16.13 mph
2,000 meters 15.71 mph
10,000 meters 14.18 mph
30,000 meters 12.89 mph
Marathon (42,195 meters) 13.10 mph
Except for that one figure at the end, for the marathon,
which I can't explain yet and I'll need to investigate further,
it's pretty obvious that a human being, whether running for
his life or for a gold medal, can't keep up the pace indefinitely.
Answer:
b. about 91.7 cm and 44.6 cm
Step-by-step explanation:
The lengths of the diagonals can be found using the Law of Cosines.
Consider the triangle(s) formed by a diagonal. The two given sides will form the other two sides of the triangle, and the corner angles of the parallelogram will be the measure of the angle between those sides (opposite the diagonal).
For diagonal "d" and sides "a" and "b" and corner angle D, we have ...
d² = a² +b² -2ab·cos(D)
The measure of angle D will either be the given 132°, or the supplement of that, 48°. We can use the fact that the cosines of an angle and its supplement are opposites. This means the diagonal measures will be ...
d² = 60² +40² -2·60·40·cos(D) ≈ 5200 ±4800(0.66913)
d² ≈ {1988.2, 8411.8}
d ≈ {44.6, 91.7} . . . . centimeters
The diagonals are about 91.7 cm and 44.6 cm.