This document appears to be notes from a math lesson covering topics like factorials, permutations, combinations, and logarithms. It provides examples of calculations and explains concepts like:
- 5! = 120, showing the factorial of 5 is equal to 120
- There are 2 ways to toss a coin for heads or tails, and multiplying all the possible outcomes gives the total number of arrangements.
- Combinatorics shows the number of ways arrangements can be made, while modeling demonstrates examples like 3 ways to arrange 3 items.
- A worksheet on logarithms is provided with examples of applying logarithm properties and the change of base law.
2. 2
this called 5 factorial
5 = 120
1 people remaining
2 people remaining
3 people are remaining
we used up one number, so we have 4 people to be seated.
there are 5 people that can be seated in this staright line.
4. The difference between Combinatories
and modeling is that combinatories
shows how many ways that can be done
and arrange items. the following
example show how to use it.
Mr. K gives us this example
there are 3 ways to wear the P1, P2 and P3,
then there are P1 x P2 x P3 ways to do three
things.
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5. = 40320
the basic idea is we have 6 student and 8
possible position they can occupy.
we could solve this equation in the same way as the other equation by using
the spaces and multiply all the numbers, but there is a shorter way. The
factorial function on your calculator will perform this calculation for you!
5
6. then we ask to solve this
ln is like log. This is change of base law.
first I expand the lnx and lny using
lnx2 + lny3÷ ln√z the product law and by quotient
law, I devide √z.
2lnx + 3lny ÷ ½lnz and the rest are self explanatory
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7. ln(x1) + ln(x + 3)3 ÷ ln √(x2 + 2)
We can't expand ln(x1) and ln(x+3) any
further since logs are not distributive!
ln(x1) ≠ lnxln1, ln(x+3) ≠ lnx + ln3
and the rest are for the review.......
this is a useful website to practice logarithms
http://www.bmlc.ca/PreCalculus%20Math%2040s%20%20Logarithms%20%
20Lesson%202.pdf
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