Answer:
(1/5 h)^2
Step-by-step explanation:
1/25 h^2
To make this a perfect square we need to take the square root and then square it
(sqrt(1/25 h^2))^2
we know that sqrt(ab) = sqrt(a) sqrt(b)
(sqrt(1/25) sqrt(h^2))^2
(1/5 h)^2
He collected 5 more pennies in the first week than he did in the second.
Answer:
The answer is below
Step-by-step explanation:
The coordinate of the midpoint of a line is gotten by adding the values of the two end points and then dividing the result by 2.
Given that M is the midpoint of AB, A = 7y and B = 3x, hence the coordinate of point M is given as:
M = (A + B)/2 = (7y + 3x)/2
Also, C is the midpoint of AM, hence the coordinates of point C is given as:
Hence the coordinates for point C is 
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.
Answer:
<h2>300:1</h2>
Step-by-step explanation:
900:3 = 300:1
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