Final answer:
To solve for x, we apply different methods like subtracting positions for displacement, using scale factors for dimensions, cross-multiplying in proportions, and employing the quadratic formula when necessary. Verification of the solution ensures that the result is reasonable and units are correct.
Step-by-step explanation:
To solve for x, we need to apply the relevant mathematical concepts to each provided scenario. Let's address each example separately:
For the case where xf = 6.70 km and xo = 4.70 km, we calculate the displacement by subtracting the original position from the final position, which would result in x = xf - xo. Thus, x = 6.70km - 4.70km = 2.00 km.
When dealing with a scale model where the scale factor is given, such as "the larger square has dimensions twice the first square", we can conclude that the side length of the larger square is 8 inches because 4 inches multiplied by the scale factor of 2 equals 8 inches.
In a proportion problem like 1.5 inches/10 feet = 42 inches/x feet, we can cross multiply to solve for x, giving us an equation x = (42 inches * 10 feet) / 1.5 inches, which simplifies to the height of the actual building.
For the scale drawing scenario described in example 4.8.4.2, we use the proportion 2":3' to solve for the actual dimension when the scale measurement is 6". In this case, we set up a proportion and solve for the missing length.
If we encounter a situation where the value of x is not less than 5% of a given number and the quadratic formula is required, we would solve using the coefficients provided in the equation to find the value of x.
Each problem requires a different approach, but always involves identifying the known values, setting up an appropriate equation or proportion, solving for x, and then verifying that the solution is reasonable and that the units are correct.