Algebra
Lesson 3-8
Vocabulary: dimensional analysis
dimensional analysis is the process of carrying units throughout a computation.
Example 1. For dimensional analysis
The formula s=1\2at2 will represent the distance s that a falling object will fall on the ground given a time t and a for acceleration due to gravity.
Solve the formula for a.
s=1\2at2
2\t2(s)=2\t2 (1\2at2) Multiply each side by 2\t2.
2s\t2= a Your answer should be this.
EXAMPLE 2
Solve 2x - 3y = 6 for y.
2x - 3y = 6
Subtract 2x from both sides.(Remember to keep the minus sign in front of the 3)
2x -3y -2x = 6 -2x
-3y = 6 - 2x
Divide -4 on each side.(You can't divide 5-2x and -2, so you leave it there)
-2y = 5 - 2x
-2 -2
Your answer should be this:
y = 6 - 2x or 2x - 6
-2 2
EXAMPLE 3
Solve 2m - t = sm + 4 for m.
2m - t = sm + 4
Subtract sm on both sides.(You can't subtract t-sm, so leave the sm where it is)
2m - t - sm = sm - sm + 4
Add t on both sides.(You can't add t to 4, so leave the t where it is)
2m - t - sm + t = 4 + t
Then divide each side by 2 - s.(You can't divide 4+t and 2-s, so leave the 2-s where it is)
m(2 - s) = 4 + t
2 - s 2 - s
Your answer should be this.
m = 4 + t
2 - s
Example 4
Solve c = 2~r for r.
There is no pi symbol on the computer, so ~ will represent pi.
c = 2~r
Divide each side by 2~.
c = 2~r
2~ 2~
Your answer should be this.
c = r
2~
Now find the radius if r = 8.5.
First Replace the C with 8.5.
8.5 = r
2~
Solve.
8.5= r
2~
Your answer should this: r = about 0.5
More examples that may be tricky.
Solve Q = 3a + 5ac for a
The trick comes in on the second line where you may be confused. If you look closly you will see that really it's just working backwards from the distributive property so that you can use the "a".
Then you simply divide the whole thing from both sides and you're done!
Here is an easy one and also another one for a formula.
Solve 
for h. This is the formula for the volume of a cylinder.
To solve for h, you will need to divide both sides byand
.
Additional Information:
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_FunctionsRelationsLiteralEquations.xml examples and problems to solve on your own
Pictures:
This page by: DS, ZA, AS