Reflection #7

Well, I missed Tuesday and Friday so I'm kind of lost. I remember doing this last year and it was pretty easy. I understand it a little, but I would still like someone to explain it to me. I understand ellipses, I think, and I know how to turn an equation into standard form:
Ex.
ellipse: 4x^2+16y^2=32
you must make it equal to 1 and to do that all you do is divide by 32
x^2/8+y^2/2=1

So if anyone would mind explaining circles and hyperbolas to me, that would be a lot of help!
Please and thank you ☻

Reflection 7

I definately thought this week was a lot easier than normal. I'm so glad we had the day off for the field trip. We all needed a break! But overall this week was pretty simple. We learned conics this week. I like how working the problems are kinda simular. Also, the formulas are basically easy to memorize.

EXAMPLES: Circles

Standard Form: (x-h)^2+(y-k)^2=r^2
center: (h,k) radius: r

Find the center and radius of each cirlce.
1.) (x-3)^2+(y+7)^2=19
center: (3,-7) radius: squareroot of 19

Find the intersection of the circle.
1.) x^2+4^2-25 and y=2x-2
a) y=2x-2
b) x^2=(2x-2)^2=25
c) x^2+4x^2-8x+4=25
5x^2-8x+4=25
5x^2-8x-21=0
5x^2-15x+7x-21=0
5x(x-3)+7(x-3)=0
(x-3)(5x+7)
x=3 x=-7/5
y=2(x)-2
2(3)-2=4
y=2(-7/5)-2=-24/5

Final Answer: (3,4) (-7/5,-24/5)

Write in Standard form.
1.) Center: (4,3) Radius: 2
(x-4)^2+(y-3)^2=4

I also thought the hyperbolas were mostly simple, but i'm still trying to understand them. But i thought the cirlces were most easiest to understand.

Reflection #6

Last week wasnt too bad. One thing i think that i really dont think i got was distributing a negative exponent to variables being added.

First you start with a problem like this: (x^-2+y^-1)^-1

Then i did this: (1/x^2+1/y)^-1

Then i multiplied each by y and x^2: (x^2+y/x^2y)^-1

From here, im not sure wat to do. Can someone help?

Reflection6

Okay…So this week was pretty bad for me. Logs and exponentials are easy; there are just so many different rules. So solving logs is easy. Log7^49=x switch the 49 and the x and you will get Log7^x=49 which is obviously x=2 to solve a log that can not be simplified into a whole number such as Log8^23=x You get Log8^x=23 which is xLog8=Log23 so your answer is x=Log23/Log8 Pleas correct me if that is wrong. And here is an exponential converted to log form 7^2=49 is Log7^49=2 I pretty much get everything. I just need a good bit of practice on everything. Good luck on the test everyone!

Reflection #6

This week I understood logs the easiest.

Changing base.....piece of cake!

log 12^x=4

you would log both sides:

log 12^x = log 4

then you would put your X in front..

X log 12 = log 4

then you would simply solve for X and get:

log 4 over log 12 unless you could plug them into your calculator and get a whole number

One thing I didn't understand completely was the stuff we learned Wednesday. I guess it's because I haven't fully memorized all the formulas :-/

Reflection #6

Sooo, i pretty much suck at math and not life. Cuz im awesome at life...just thought id throw that out there.
and Ashleigh is helping me with the blog.

At first, well last year, i thought logs were stupid. I still do...but they are soooooo much easier now...Thanks B-rob.
So from what i learned...you dont have to do the change of base formula on every single log ever created...its actually simple to me now!!!

Solving LOGS:

LOG x^9=2

to solve, switch the 9 and 3...you would get x^2=9

x=3

That was the easiest thing to me...and thats pretty much all i understood this week...ha..so help me with THE REST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

peace

reflection 6

This week i thought was pretty easy, but we had alot to do and a fe formulas to remember. Let me start of with the math competition wasnt to bad just a lot of asians. Kinda creepy. In class though we did a lot of problems with exponents and negative exponents.
To solve the problem (a^-2+b^-2)^-1 Then u turn it into a fraction (1/a^2+1/b^2)-1. Now get the same common donominator by multiplying by the donominator. Then you sandwhich the two fraction which means multiply the middle and the bootom and top and you should get b^2+a^2/a^2b^2. I just had a little bit of trouble with the logs because i never did that before but i got the hang of it. I'm just gonna have trouble with the formulas tryin to remember them.

reflection 6

Yeah i think ima go with everyone else on this week. It was pretty easy. I really
actually understand logs.

log base 2 of 8=x

2 exponent x = 2 exponent 3

the 2's cancel out

and x=3



the only thing about logs that i dont understand, and i think some of them were on the worksheet that we did in class a while back, is the ones where the base is higher than the other number.

like..

log base 14 of 7=x

i dont even know if that makes sence or not, ha..but its just when the base is bigger than the other number, thats the ones i dont get.

reflection #6

this week was pretty easy, since we learned about logs.

log(base 2)8=x
exponential form:2^x=8 x=3

log(base 3)9=x; 3^x=9 x=2

i understand logs, but im having trouble with exponential problems...

reflection 6

chapter 5 was pretty much the easiest chapter, and there's not that much to get confused about, just remembering to switch up the numbers within the log

log 5 of 25 = 2
5^2 = 25

4^3 = 64
log 4 of 64 = 3


im good for this chapter, and hopefully there will be others as easy as this

Reflection #6

alright this past week we learned how to use logs in many ways. like how to expand, condense, and the change of base. the thing that i understood the most is to expand and condense here are some examples of how to work these problems:

Expand log base 2 x y^2
=log base 2 x + 2 log base 2 y
you take the log with the same base and expand it when things are multiplied you add them when you dived you would subtract.

Condense log 45-2 log 3
=log 45/3^2
=log 45/9
=log 5

one of the things i don't quite understand is the formulas, I'm getting confused on witch formula to use when.
some help would be nice and much appreciated.

Reflection #6

This week was REALLY easy. Since i learned logs last year, they are so easy. If you ever have to find the base of a log it is really easy, because it is the number under the log. But if there is not number, then it is assumed that the base is 10.

PUT IN EXPONENTIAL FORM:

log base of 2 ^ 4 = x

you would end up with 2^x=4 (that is exponential form)
and to solve, you would set the exponents = to each other. (x=4)

______________________________________________________________

The easiest thing is when you have to condense and expand the logs.


Example:

1. CONDENSE

2log base of 3 ^ x + log base of 1

(if it is (+) then you multiply, if it is (-) then you divide)
(the number in front of the log becomes an exponent)

log base 3^ x^2 log base 1


2. EXPAND

log base 2 log base 3/ log base 1


log base 2 + log base 3 - log base 1

__________________________________________________________

The thing that i didn't get was the formula things. I don't know when to use the formulas and which ones to use. I also still don't get how to do the negative exponent things. The one that is always on the quiz. If you can help i would appreciate it. Thanks.

Reflection 6.

Chapter five is the easiest for me I would say, besides the little things that I get confused on. One thing I understood really well in chapter 5 was how to put a log in exponential form.
When putting a log in exponential form all you do is switch the closest numbers by the equal sign. It's kind of like inverses.

Example:

logb^x=a
Switch x and a.
b^a=x

This can be helpful when sloving logs.

Example:

logx^4=2

First to solve this you have to put it into exponential form.
x^2=4
What raised to 2 equals 4? 2
x= +/- 2

----------------------------------------------

Now for something I didn't understand. I didn't understand the last thing we learned at all. It was when they gave you a word problem and you had to find time and rate and stuff? I just don't get what to do at all.. I understand how to find the exponential function but nothing else.
If someone could explain it to me in an easy way that would be helpful:)

Reflection SIX

I liked this week in advance math it was probally one of the easiest weeks because logs are quite simple. I think I did good on all my quizzes this past week. The only thing that seems hard that whole week was the exponential functions word problem things. Hopefully the test Monday is easy and we will learn something fun this up coming week. The change of base and log properties were simple. Im going to show an example of change of base.

Change of Base:

Steps:

1. Take the log (base what you want of both sides)
2. Write as an exponential
3. Move exponent to the front
4. Solve for variable
5. Write as a fraction or whole number if possible. If not possible leave in log form

Ex: 1. 5^x = 10
2. log 5^x = log 10
3. xlog 5 = 1
4. Answer: x = 1/log 5

One the other hand I did not get the exponential function type word problems. I think they just come with practice. The formula's are really big and you have to take the right numbers out the word problem part.

Reflection #6

I do understand how to do change of base:

**Only use when there is no other way to change the base of a log or solve for x in an exponential
First, write as an exponential if it is not already
Second, take the log of both sides (base 10)
Third, move exponent (x) to front
Forth, solve for variable by division
Fifth, write as log fraction (simplify further if whole number only, plug in calc.)

Example:
log base 3 of 7
3^x=7
log of 3^x=log of 7
x log of 3=log of 7
x=log of 7/log of 3

5^x=10
log of 5^10=log of 10
**Note: log of 10 = 1
x log of 5=1
x=1/log of 5

Now, I don't understand...well, actually, I think I understand most of everything. I'm still working on memorizing the formulas, but I think I'm getting there. If anyone wants to give me pointers on how the learn them, that would help, but besides that, I think I'm good to go this week.

REFLECTION #6

Well this week was an okay week. I mean I thought some things were kinda hard and confusing but I did my best to try and catch on and understand them better. Anyway Monday we took a quiz on exponents which I thought was pretty easy. I think I'm finally getting the hang of those things now. And Tuesday we learned about Log Properties. We basically learned how to expand and condense logs and how to solve log problems for x. Then on Wednesday we learned Change of Base which is used when a log can't be further solved and when you want to change the base of the logarithm. by the way I do not like logs :) Then on Thursday we learned the really really hard stuff. We learned a whole bunch of formulas that are used for different types of word problems.

Anyway, I thought expanding and condensing logarithms were the easiest things we learned this week. I understood it very well so I guess I will explain that. First of all, before you can expand or condense logarithms, you have to know your log properties:

1.) Addition is the same as multiplication:
log base b MN = log base b M + log base b N

2.) Subtraction is the same as division:
log base b M/N = log base b M - log base b N

3.) Exponents go in front:
log base b M^K = K log base b M

4.) When the exponent becomes the answer:
log base b of b^k = k
or
b^log base b^k = k


Alright now here are some examples:
Ex 1.) Condense.

1/2 log base 6 of 9 + log base 6 of 5 >> (number in front becomes exponent)

log base 6 of 9^1/2 + log base 6 of 5 >> (9 raised to the 1/2 is the square root of 9 which is 3)

log base 6 of 3 + log base 6 of 5 >> (bases are the same and it is addition so you multiply 3 & 5)

and your final answer is >>> log base 6 of 15


Ex 2.) Expand.

log (M/N^3)

(it is division so you know it will be subtraction)>> log M - log N^3

(the exponent 3 gets moved to the front) >> log M - 3 log N


Another thing I understood really well this week was solving log equations for x.
Here's an example:

Ex 3.) Solve.

log base 3 of x + log base 3 (x + 2) = 2 >> (first combine the two logs)
log base 3 of x(x + 2) = 2
3^2 = x(x + 2) >> (3 is the base. raise it to what's behind the equal sign which is 2)
9 = x^2 + 2x >> (distribute)
x^2 + 2x - 9 >> (move 9 over then use completing the square to solve)

complete the square:

x^2 + 2x = 9
x^2 + 2x + 1 = 9 + 1 (divide linear term by 2 and square it. add 1 to both sides)
(x + 1)^2 = 10
(take the square root of both sides)
x+1 = +/- square root of 10
(then subtract 1 over)
final answer is x = -1 +/- square root of 10 (*I don't think you have to put it in point form.)


***Now for what I didn't quite grasp at all this week. I don't understand any of the formulas that we learned on Thursday. I don't know which one to use for which type of word problem. They all seem the same to me in some ways and I get confused with that. If anyone understands this at all and wouldn't mind helping me out, that would be greatly appreciated :)

Overall, I thought this week was a little tougher than the previous weeks.

Reflection #6

Okay, this week went by really quick. In class, we learned a lot more about logs and then later we learned about exponential functions. I'll describe how to do different formulas for exponential functions. Here are some examples.

a. If I put $300 in an account earning 1.4% compounded semiannually, how much money do I have after 3 years?

To solve this, you use these terms and formula:

A0 (what you start with) = 300

r (rate as a decimal) = .014 semiannually (2x a year)

t (time) = 3

Formula: A(t) = A0 (1+r)^t

Plugin: A(t) = 300 (1 + (.014/2))^3 (divide by 2 because it is two times a year)

Answer: A(t) = $306.34

b. Do this again, but this time, figure it if it were compounded continuously?

You would use these terms and formula:

P0 (what you start with) = 300

r (rate) = .014

t (time) = 3

Formula: P(t) = P0 e^rt

Plugin: P(t) = 300 e^.014 (3)

P(t) = 300 e^(.014 * 3)

Answer: P(t) = $312.87

Now, the only thing I didn't understand this week was the whole lim n > infinity ( 1 + 1/n)^n = e. does this have anything to do with the 72 rule? or are they two separate formulas?

reflection 6

Ok, this week was... interesting. First off, the football team won again, so yay to them. umm...... not really that much happend this week that i can remember :( let's see....... the pep rally was awesome, and so was the football game. idk if yall could hear the band at the pep rally, i mean, it was a super loud pep rally, which is how it should be. umm...... hmm...... mahna mahna....... we had a math tournament this weekend, which didnt really go well. i mean, Sarah beat Tir on the one of the tests, and the potpourri team won 3rd. the party at Mrs. Carrie's house was pretty cool, we got to see LSU almost lose :/ but thank God for Chad Jones w/ his 93 yard return for a TD, and his defensiveness on the second to last defensive stand for LSU, when MSU was by the goal line. and then the movie game :D remember, "sex=Forgetting Sarah Marshall", always. and the game of mafia we played b4 us band ppl left was fun, especially when i died, so i started movin around on the sofa by Dustin and made Edee think that Dustin was mafia almost every time. u gotta admit, it was funny :P and then the brownies WERE ROLLIN, gotta love my mom's brownies :D and im just ramblin here to hit the word requirement fyi :P and then we had our band night out, ate at La Carreta's and got to see Tebow get OWNED, and i really hope that he aint healthy for the LSU game, but not die. and then movies at my house.... scary movies...... not good ones...... DONT EVER WATCH PULSE IF U DONT LIKE GHOSTS, WATCHIN PPL COMMIT SUICIDE, OR RANDOM MOMENTS OF SCARES THAT POP OUT AT U!! just warnin ya.
ok, enough of my ramblin, back to math......
this week was pretty easy, i mean it was just logs and exponent stuff, it wasnt really hard....

i mean take log100=x
all u gotta do is put it in exponential form so that u get 10^x =100
then u just set the bases equal to get 10^x=10^2
then, u just use the exponents to get x=2
and then ur done

but one thing i didnt really understand this week was when are you supposed to use the A(t)=A(base o) b^(t/k) and that stuff

Reflection 6

Well for starters this week went by really quick. I'm glad that we learned logs because they are super easy to understand. We learned how to solve for exponents, properties of logs, many different formulas, etc. I like how we take more quizes now because it helps my grade out by a lot. But for this week i found i understood log propeties the most.
EXAMPLES:
log M + 2 log N = log MN^2
in this problem addition is just like multiplication.

log 12 - log 3 = log 12/3 = log 4
in this problem subtraction is just like division.

Those problems were examples of condensing a log. Here are some examples
of expanding logs.

log base b (M/N) = log base b M - log base b N
for this you go from division to subtraction.

log 2N^2 = log 2 + 2 log N
for this you go from multiplication to addition.

We also learned a few new formulas. Here is an example of one.

If i invest $100 in a blank account earning .08% compounded monthly how
much money will i have after 3 years?

FORMULA: A(t)=A (1+r)^t
A = $100
r = .08% = .0008 monthly
t = 3

= 100(1+.0008/12)^3
Calculator plug in: 100 X (1+9.0008/12))^3

= $100.02

Overall this week was mostly easy. I still have trouble with that SAME problem she gives us on every quiz, but i think i sorta understand. Hopefully this coming week will be just as easy.