Railroad tracks’ rails must be a precise distance from each other. If the distance between the rails is too narrow or too wide, the train will derail. Come prepared to discuss the following questions: Imagine traveling back to 1865 when railroads were being built all across the American frontier. How do you think they built the tracks to be the right width apart from each other? What could have gone wrong? Could you teach the railroad workers about parallelism (alternate interior and exterior angles, etc.) so they could always build tracks the right width apart?
Do you think it would be practical to use principles of parallelism for building railroads during that time period? Why or why not?
What other methods could be used to ensure parallel rails (any method, not just the geometry kinds)?

add an image

step-by-step explanation:

yes the data was not prsented

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt