A train track is 5280ft. long. After adding another foot of track, an arc is created. What is the height of the arc and how would i measure it?
FIND THE LEAST COMMON MULTIPLE OF 6,9
The maximum height is given by
[2640(5280) + h^2 = [2640(5280) + 0.50]^2^2 making h = 1.94 ft.
This assumes each half of the track buckles up as two triangles.
The true arc height change is not possible tocalulate on the normal scientific calculator, I believe.
The arc height from the associated chord is given by h = R(1 - cos(µ/2) where R = the central radius and µ = the central angle subtended by the ars.
2+2=
The lcm of 6 and 9 is 18. It's 18 'cause 6times 3= 18 and 9 times 2=18.
To measure the height of the arc created by adding one foot of track to a train track length of 5280ft, you would need to make some assumptions and calculations.
First, let's assume that when the track is extended by one foot, it creates a symmetrical arc with the original track as its chord. In this case, you can consider each half of the track as two triangles.
To calculate the height of the arc, you can use the formula for the maximum height of an arc, which is given by:
h = √[(2R + c) * c]
where h is the height of the arc, R is the radius of the circle (which is half the length of the chord), and c is the length of the chord (5280ft).
Plugging in the given values, we have:
h = √[(2 * (5280/2) + 1) * 1]
= √[(5280 + 1) * 1]
= √[5281]
≈ 72.70ft
So, the height of the arc is approximately 72.70ft.
However, if you're trying to find the exact arc height from the associated chord, you would need to use a more advanced mathematical method involving trigonometry. The arc height can be calculated using the formula:
h = R * (1 - cos(θ/2))
where R is the central radius (again, half the length of the chord) and θ is the central angle subtended by the arc.
Now, switching to the second question...
To find the least common multiple (LCM) of 6 and 9, you can list out the multiples of each number and find the smallest common multiple.
Multiples of 6: 6, 12, 18, 24, 30, ...
Multiples of 9: 9, 18, 27, 36, 45, ...
The smallest number that appears in both lists is 18. Therefore, the LCM of 6 and 9 is 18.