Answer:
about 17 meters
Step-by-step explanation:
We can use the Pythagorean theorem to put an upper bound on the height of the bump in the rail. This assumes half the expanded rail length (d+e) is the hypotenuse of a right triangle whose legs are the bump height (b) and the 2500 meter distance (d) from the center of the rail to its end.
The Pythagorean theorem relates these distances this way:
b^2 + d^2 = (d+e)^2
Expanding the square on the right, we can simplify the expression to find b.
b^2 = (d^2 +2de +e^2) -d^2
b^2 = e(2d +e)
b = √(e(2d +e))
Using lengths in meters, we can fill this in to calculate b.
b = √(.06(2·2500 +.06)) = √300.0036
b ≈ 17.32 . . . . meters
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<em>Comment on this solution</em>
We don't expect rails to tear loose from the rail bed and rise up to a height matching that of a 3-story building. That is why there are typically expansion joints and shorter rail lengths used in the construction of railways.
The height is a little lower if we take physics into account and distribute the stress in the rail along its length. No doubt the final curve is somewhat more complicated than the triangle we have assumed.
If it were an ellipse, the height might only be 9.4 meters, with the steepest rise occurring near the ends of the rail. The math for this model is beyond the scope of this answer.
Let x be a time in hours and y be an amount of remaining entries. You have that:
- At start Ariel wants to write 8 entries for her blog. This means that x=0 and y=8 (0 entries were written). The point with coordinates (0,8) belongs to needed graph.
- After 2 hours, she has 5 entries left. This gives you that at x=2, y=5 and graph passes through the point (2,5).
- After 4 hours, she has 2 entries left. This gives you that at x=4, y=2 and graph passes through the point (4,2).
Find the slope of the line that is passing through the points and by formula
Thus, the slope is
Answer: graph of line going through (0, 8) with a slope of -1.5
Answer:
15 children can divide them with eachother, each get 2 sweaters and 3 trousers
Step-by-step explanation:
15×2=30
15×3=45
a.
is a proper joint density function if, over its support, is non-negative and the integral of is 1. The first condition is easily met as long as . To meet the second condition, we require
b. Find the marginal joint density of and by integrating the joint density with respect to :
Then
c. This probability can be found by simply integrating the joint density: