Algebra Questions

Subscripts in algebra
A subscript is a symbol that is written in small type below a variable in regular type. For
example: ?0
is read as “P sub-zero.”
Subscripts are used to distinguish between variables that represent similar quantities.
For example, if you were working with a problem in which there were different prices
over time, you might want to use ? to represent all of those prices, but you also want to
be able to tell the difference between them. So, you could use ?0
for the initial price,
then ?1
(“P sub-one”) for the second price. The subscript is only a label; it is not an
operation.
Information about the context in In-Class Activity 13.B
The grade of a road is important information for drivers of large trucks in mountainous
terrain. If a trucker begins to travel too fast going downhill, then it is possible for brakes
to fail. Of course, as the driver of a car, you might be frustrated with a truck that is
traveling up a hill with a steep grade, especially if you cannot pass. Runners and
bicyclists who compete in hilly terrain also consider the grade of the hill in predicting
their stamina and speed.
The grade of the road quantifies the rate of increase (or decrease) in height over some
horizontal span. The grade is written as a fraction with the numerator as the change in
height (vertically) and the denominator as the change in distance (horizontally).
Typically, the grade is reported as a positive value (even though mathematically, “uphill”
is positive and “downhill” is negative). In practice, if one car is traveling uphill on a road,
then oncoming cars are traveling downhill, so it would be confusing to report the sign as
+ or –.
Notice that the units will divide out, leaving a number that is dimensionless. That
number is then written as a percent.
Example: Determine the grade of a road that decreases 72 feet in height over a
horizontal distance of 600 feet.