The value of -25+50-20+(-12) is -7.
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.
-18 and +2
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Answer:
See below.
Step-by-step explanation:
a. See pic below.
b. Yes because it passes the vertical line test. Any vertical line moving horizontally across the graph intersects only one point on the graph at a time.
c.
Domain: all real numbers
Range: all real numbers greater than or equal to 4
d.
Domain: all real numbers greater than or equal to 4
Range: all real numbers
e.
See pic below.
f. No because it does not pass the vertical line test.
