|Start||some of you the competent questions are pretty straight forward, be careful you dont psych yourself out
and turn it into harder questions then they are
theres no graphing on the exam
theres no ellipses on the test
I know that makes you happy
cant use calculators, what else would people like to know?
the part one we have the whole take it over in the testing center 2 weeks from now
|0:34||at the end on the final there will be a part one and a part two part one on the final, thats what you really need to make sure to pass thats the real minimum competent part, obbviously if you pass that at then end you pass the minimum competent course even if you didnt pass the first few times around thats where you demonstrate to us that you can move up to calculus|
|1:02||theyre not teaching 125 , im sorry wasnt up to me other questions well i think it would probably be the same as last time, 10 out of 16 im pretty sure, well from memory im pretty sure its 16 points and again you need 10 again thats about the number, you got to get some of them right|
|1:31||other questions you sure? okay so heres what im gonna do im gonna put a bunch of questions on the board that are going to be similar to the minimum competent questions on the test if you can do these you are minimally competence be really happy|
|2:06||so i will give you these four and youll get the basic idea everybody do that one|
|4:37||okay theres some to start off
so if you cant read these well because of my beautiful hand writing
represent log base 8 of 128 as a fraction, interger or radical
whats the largest domain on which log base 5 to the 5-4x is defined
solve for x. 16 to the 3x-5 equals 32 to the x+!
find the equation of a line from 8,pi and 4,1
|5:02||dont be scared on pi, pi is just a number log base a is 20, log base b is 30, simplify log square root of a/ b cubed, i dont know why i said simplify write the equation of a circle with center at 8,-4 and radius 10 represent log base 10 of 1000 as an interger, radical or fraction represent log base 8 of 128, as a interger, fraction or radical|
|5:34||so you take log base 8 of 128
you say thats equal to something so we call it x
you guys can see that over there?
that means that 8 to the x is 128 so now you go how am i suppose to solve 8 to the x, you could solve it by doing logs again but thats not what were looking for
|6:03||this is 2 cubed so 128 must be 2 to the something who wants to give a gues 7 yea work it out, thats what you have scrap paper for so now that we know that 2 to the 3x equals 2 to the 7 then 3x must equal 7|
|6:30||x is 7/3 okay, how do we feel about this one okay if you can do this one, its 2 points if you can practice these i posted one like this a couple days ago theres some other practice problems make sure we do this|
|7:06||8 to what exponent is 128 7/3 cause 8 squared is 64 and 8 cubed is 512, so somewhere between 2 and 3|
|7:34||what is the largest domain of this log base 5 5-4x is defined now it can be log any base it could be natural log it can be any base and the rules of the log are the same it happens, when you take the log it has to be a positive number so whether that says ln or that say log, log base whatever it doesnt matter,=. this|
|8:00||must be greater than 0, 5 minus 4x is greater then 0 so 5 has to be greater then 4x or 5/4 greater then x. or you can flip that around x is less then 5/4, you dont need to use interval notation you can write it as, any number less then 5/4 okay you get that? 2 more points youre up to 4|
|8:30||you can call your mom and say maybe i will be a doctor well she was hoping, cbecause you have to pay for your time got to move to florida i told you i want the good doctors from this class and if one of you become a billionaire thats fine too we can talk|
|9:06||so this is not very different from that
16 to the 3x-5
is 32 to the x+!
so lets get a common base, what base would you like to use?
7, i mean 7 would were but thers another we can do 2? well 4, does 4 work?
|9:32||no, 8, no 2
so this is 2 to the 4
to the 3x-5
equals 2 to the 5
to the x+1
so that means that 4
has to equal 5
hope that works
|10:03||so then you get 1x -20 is 5x +5 so 7x is 25 x is 25/7 6 points all you got to do is stuff like this this is minimum thats why they are minimum competent got to impress us to demostrate your confidence|
|10:32||whats incompetent, incompetent is for example two outs in the bottom of the 9th and you give up a homerun thats it so when i find the equation of a line see if some one were to watch that video 20 years from now it will make no sense|
|11:07||so what do we need? we need a slope and a point. remember the equation of a line y-y1 equals m times x-x1 i know some of you really want to use y=mx+b because you were taught that its just so nice and easy to remember but its actually not a good way to find the equation of a line if you have this kind of information|
|11:32||in fact i dont know why we teach that its not a good formula of a line, its not a good formula at all we need m, m is the slope how bout m is pi-1 over 8-4 or pi-1/4 so if you have 1-pi/-4, thats the same thing and then brace yourself, pick either point it doesnt matter y-1|
times x-1, and your done, 4 points
you can pick either point
you dont have to simplify, pi is not 3.14
pi is pi
e is e, pi is pi
these are numbers
so far so good?
you feeling better?
you think your stomach is getting a little better?
|12:31||8-4 pi-1, 8-4 gives you 1-pi and 4-8 then you would have 1-pi over -4 same thing doesnt matter which point you use doesnt matter which way you find the slope if you work it out youll end up in the same place|
|13:00||you put it in the mx+b formula its not the same
wait theres more
oh my gosh
we ready? how we doing on these?
so far so good?
maybe its not as bad as you thought it would be dont worry i havent done the harder problems yet but thats okay this is just the minimum competent stuff if you can do the minimum competent stuff, youre okay
|13:31||if get it right youll get at least a c in the class on the exam, not the class, the exam log of a is 20 log base b is 30 whats the log of square root of a/b cubed well lets see that is he same as the log square root of a minus the log of b cubed so far so good|
|14:01||square root of a, is a to what power?
1/2, is everyone clear it has to be to the 1/2 powe you sure? okay that means you can now take the powers in front and make this 1/2log a -3logb thats the same as saying a to 1/2
|14:33||is 1/2, cubed root of a is 1/3
4th root of a is a to the 4th, thats why you use the word 4th
you put the 1/2 in front and you get a 1/2 log a
-3logb, now youre gonna substitue
log a is 20
so this is 1/2 of 20
-3 times 30
comes out -8
you get -80, yeA?
|15:01||whered the half come from?
square root of a is a to what power the square root of a is the same as a to the 1/2 so this is the same as log a to the 1/2 and our rule is you put the power in front 1/2 log a
|15:31||did you get -80?
you are doing the minimum competent at this point write the equation of a circle with a center 8,-4 and radius 10, remember the formula for a circle?
its x-h squared +y-k squared equals r squared where hk is the center
|16:01||and r is the readius so this one is very straight forward its just gonna be x-8 squared +y+4 squared eqauls 10 squared you do not have to simplifythat you dont have to multiply it out or anaything, you dont have to make 10 squared into 100|
|16:34||so another words if you have h-h be okay try not to do that well put 100 in for 10 squared isnt accidental but its perfectly fine, yes so you can square root a number out or not, another words you dont have to do more work then that its the minimum amount of work all you have to do is say x minus the whole thing squared|
|17:00||plus y minus the other thing squared
equals the radius squared, this is just the pythagorean theorem
so you can turn it to 100 if you want but its not necessary
so far so good?
log base 10 of 1000 log base 10 of 1000 equals x
|17:30||that means 10 to the x is 1000
10 to the what is 1000
3 if you notice in scientific notation
just count the zeros
the log base 10
1 followed by how many zero is the number of zeros
you doing good so far? yes?
you can just write 3 write a nice big 3 you ready for some harder stuff?
|20:10||there you go, that would keep you busy for a minute|
|20:50||first when you see this, first you want to do is factor that i say wow can i factor that? oh sure|
|21:01||x suqraed times 4x+3
pull out a 3
and thats gonna factor into
x-1 on top
on the bottom
you do the factoring okay?
you gonna ask how i factored that?
|21:34||what is the largest domain, another words
domain can be anything you want, you can say its 7 if you felt like it
so the question is whats the biggest
section you can do, another words whats the only section you can exclude?
domain can be x to the anything except -5 or -1, because when you plug those in you make the denominator equal to zero the domain is the denominator cant equal t zero
|22:03||because you cant have zero on the bottom of a fraction
have you ever seen a fraction that looks like that?
i dont think so never seen a zero on the bottom before you also probably seen better hand writting then that okay that was a zero, whatever what value, if any does y approach as x approaches infinity this is sort of asking for the horizontal asymptotes the problem with using the word asymptote is
|22:30||its not really an asymptote its end behavior so we want to be mathematically correct so we just say what is this approach as x goes towards infinity so remember the rules you look at the power on top the highest power is 3x squared look at the powers on the bottom, the highest power is x squared since the powers are the same y is going to approach 3 because its 3/1|
|23:00||so far so good?
now if you have a higher power on top then it wouldnt approach anything, youd just say you can either write infinity or it does not exist okay but the number does not exist what dont you understand?
so you look at the highest power for each the numerator and denominator the highest power on top is 3x squared the highst power on the bottom is x squared
|23:30||the power, thats the power the powers are the same the coefficient of this term and the coefficient of this term 3/1 if the bottom is a bigger power, then its just 0 if the top is a bigger power, then it doesnt exist and i put this on the instagram the other day so agin you look at the powers match them up if its the same on top and same on bottom its coefficient over coefficient|
|24:06||x-1 and x+1 dont cancel x-1, and x-1 would cancel remember your rules ill right it down in a second|
|24:32||what if any are the zeros of fx
the zeros is where the numerator equals 0
so where does the numerator equal 0
and what value does the x cross the x axis?
the y axis sorry, let x equal 0
|25:01||when you plug 0 in what are you gonna get on top?
what do you get on top if you plug in zero?
what do you get on the bottom when you plug in 0 so it is 9/5 one more time at what value does f of cross the x axis?
that means your gonna let x=0
|25:32||okay and when x equals 0 y get 9 on top and 5 on bottom, we plug 0 on top youre gonna get 3 times 0 squared +_ 12 times0 plus 9 so thats just 9 and on the bottom you get 0 squared plus 5 look what we get 9/5|
|26:01||whered i get 3 and 1 again?
you look at the numerator the numerator is equal to 0 when this is 0 or thats 0 you set x-3=0 x=3 you set x-1=0 x=1 you can write 9/5 either 9/5 or you can write 0,9/5
|26:32||either one is okay this is where end behavioral rule again|
|27:14||so you have some rational expression you have something times x to the m plus smaller terms on top and something plus x to the n smaller terms on the bottom so x to the m is the highest term on top x ot the n is the highest term on the bottome|
|27:34||we go that part?
now if the top power is bigger then it doesnt change anything the top power is bigger it just goes towards infinity the bottom power is bigger
|28:04||then the y value approaches 0 and if the two powers are the same then you get a/b so here the 2 powers are the same, x squared and x squared so you get 3/1 thats equal to 3|
|28:32||you can write infinity you can write no value
you can write dne, any of of those things
just make clear you know
that it just keeps growing
not that you have no idea what you are doing
even if you do have know idea what you are doing
okay so far so good?
polynomial division im actually gonna put that on the middle board because some sides wont see it very well
|29:08||time to erase|
|29:31||what you want to do is 2x-3 is gonna go into 2x to the 4th +7x to the 3rd plus 16x plus 29 x +21 alright i dont have my glasses on|
|30:07||so far so good?
you look at the left term, you get 2x what do i have to multiply 2x by to get 2x to the 4th i take 2x and multiply what to get 2x to the fourth x to the 3rd
|30:33||x to the 3 times 2x is x to the 4th
x to the 3rd times 3
is 3x to the 3rd
so far so good?
you subtract 2x to the 4th times 2x to the 4th answers 7-3=4 so you get 4x cubed and you bring down the next term
|31:04||so far so good?
now we do it again 2x times what is 4x cubed so 2x squared times 2x is 4x cubed plus 6x squared
|31:30||16x squared -6x squared is 10x squared bring down the next term 2x times what is 10x square 5x you get 10x squared plus 15x subract|
|32:01||and bring down the 14x
bring down the 21
a little crocked
and what do i have to multiply 2x to get 14x, i have to mulitply by 7
and when i subtract
there is no remainder
thats very good theres no remainder, what if there is a remainder?
then i would just add that number divide it by 2x+3
|32:33||if i had 8, it would be plus 2x+3
i have a quarter of you paying attention, thats okay
howd we do on this one?
so suppose the ramainder suppose the remainder was 10
|33:04||then you would have, the next term would be 10/ 2x+3 if you had a remainder of 10 you can have a remainder then you can just ignore it you just add so you would have plus something over 2x+3|
|33:30||that would be your remainder whatevers left okay want to try another problem i know how much you want to do this|
|34:22||how bout that? solve that for x i noticed many of you made the same mistake on this so first thing youre gonna do is take the log of both sides|
|34:43||then you put the 3x+2 infront so 3x+2 times log 6 equals x log 9 many of you forgot the perenthesis that wwould get you a wrong answer|
|35:00||remember the 3x+2 is multiplied by the log 6, not just the log 2 distribute the log 6, and you get 3x log 6 plus 2 log 6 equals x log 9 okay remember what you do next you put all the terms that containx on one side|
|35:32||and all the terms that do not contain x on the other side so we can get 2 log 6 is x log 9 minus 3x log 6 so its always the same thing, first you distribute group all the terms that contain x on one sides and all the terms that do not contain x on the other side|
|36:03||factor out the x you get 2 log 6 is x times log 9 minus 3log6 and divide you get 2log 6/ log9 minus 3 log 6 some of you will have -2log6 and you would have the bottom terms reverse, thats okay so go through it again|
|36:31||take the log of both sides take the power in front that power goes in perenthesises and distribute to get 3x, times the log plus 2 times the log thats this term everything with x goes on one side everything without and x goes on the other side|
|37:01||then you factor out x
then you divide
how out word problem?
we love word problems
|39:07||you can use yeast in beer, in alochol if your over 21 or bread or all sorts of things okay lets see so a(t) the amount at time t how much|
|39:30||will you have after 24 hours 2 part question were gonna use growth formula y=a times b to the x this is any this is any exppnentail growth|
|40:00||and we use this equation of course were gonna use t instead of x and use a of t instead of y, but well fix that at the end so what do we know? we know that initially theres 20 grams 5 hours later theres 30 grams the question is how much is there 24 hours later okay|
|40:31||so at time 0 were gonna have 20, so 20 a times b to the 0 anything to the 0 is 1 except for 0 so a is 20 you can fill in one of the variables in our equation instead of having a times b to the x, you have 20 times b to the x now we also know when x is 5 y is 30|
|41:01||you have 30 is 20 times b to the 5 so 3/2 b to the 5 b is 3/2 to the 1/5 the equation because y=20|
|41:31||times 3/2 1/5 to the x or x/5 since i asked for a of t this would be a of t is 20 times 3/5 t/5 3/2 we just changed the letters do we understand that? the first one helps figure out a the second one helps us firgure out b|
|42:02||and now we just plug in
and now if i want to find out how many there are after 24 hours
say a of 24 hours
howd we do on these?
|42:33||you have to write a of 24? no
you can write a
we just need to know what you are doing
one last quick one
can i cover this?
ill uncover it in a minute
|43:42||if you deposit 2000 dollars
in the bank or a user fund, something
at 8% compound continuously
how much will we have after 10 years?
remember the formula is just the future amount present amount e to the rt
|44:01||plu in the future amount
t is 10
you can stop that what we need to do
how would you figure that out without a calculator?
or a log table thats the answer