So the last few classes we have been learning about perms and coms.
Permulations- are the # of possible orderings of a set, provided that the order of set elements matters. Examples would be you phone digits..books on a shelf.locker combinations. Perms-BEST EXAMPLE EVER- put five blanks down on a sheet, then you put 26 (cause there is 26 letters in the alphabet)then 25 cause you used one then 24 then 23 then 22, and that equals: 7893 600 then the formula starts here: 26!/21!=n!/(n-r)!
n being the # of items to select from and r selecting items r at a time.
nPr=n!/(n-r)! "n things, permulated 5 at a time.
Coms- BEST EXAMPLE EVER: you have three different toppings for pizzas like turnips sardines and liver--> you have turnips + liver turnips+sardines sardines+liver, no matter what order you put them in its the same pizza ex) like turnips+liver, liver+turnips.
Perms: big #, order matters, nPr=n!/(n-r)!
Coms: small #, order does NOT MATTER, nCr=n!/(n-r)!
Another example: How many 3 digit #'s can be formed from digits 1,2,3,4,5,6,7
Provided they are both even+greater than 300? you then can make a ven diagram first circlwe having 3,5,7 middle circle having 4,6 then second circle having just 2. A=first # possible 3,4,5,6,7 B=even number ends in 2,4,6
Case 1= 5 time 5 times 1 = 25
Case 2= 4 times 5 times 1 =20
Case 3= 4 time 5 times 1 =20
All equal 65 3 digit even numbers greater then 300.

Another Example is Solve: nP2=30 n!/(n-2)! time (n-2)!/(n-2)!= three (and the (n-2) cancels out. n^2-n-30=0
(n+5)(9-6)=0 n=-5 n=6

Well...today was a productive day I tell ya. We had a substitute,and that meant we all got to do some catching up. I worked on my accelerated math, I'm doing a test right now. Whenever I did not know how to do a question, I just asked my handy dandy friend William, or Caity. They are tons of help.

Last class was on tuesday because we got wednesday off, due to Rememberance Day. Well anyway, we learnt "Approximating "e" and the natural logrithm(ln)"
What is e? e is approx. 2.71828... it is an irrational number. Our class learnt the new formula: f(n)=1+1/n;g(n)=(1+1/n)^n. For values n E II
A natural exponential function looks like a line facing upwards on a graph,(concave up)

Last class we learned more about logarithms."The Change of Base Therom" the last log law.
logb^n=loga^n/logab
ex) heres a little rule
log (x + 3) = IS ABSOLUTELY NOT- logx + log3
instead, it becomes:
log(2(3^x)) = log5
log2 + log3^x = log5
log2 + x * log3 = log5
x * log3 = log5 - log2
x = log5 - log2 / log3
x = .8340437671

Yesterdays class we learned logarithmic functions.
y=log6x if x=by(y as the exponent) y is the logarithm, b is the base and x is the argument.
Logarithms are exponents.
We did an example like, find log2(subscript)8=3 in exponential form. 2to the 3=8
2 to the ?= 16 9 to the ?=3
2 to the 4=16 9 to the x=3
log2(being the subscript)16=4 (3 to the 2)=3 therefore 2x=1 x=1/2
then: 2 to the ?=1/4 2x=4 to the exponent -1 2x=(2 to the exponent 2) -1(exponent) therefore x=-2 therefore log2(subscript)(1/4)= -2

Today in class we learned about expotential functions. We had learned lots of it in grade ten precalc. First we sketched out some simple graphs, and talked about them a bit, like what would happen if you changed the a or b value, ect..Then we did some observations , like D= all reals, graphs have no x intercept(no verticaln shifts). And then we did some examples, which were quite easy.