All Answers

Thank you soooo much, this helped tremendously. (:

GuestFeb 6, 2014

+118725

Stu:
Thanks Melody,

"b) What are rules for + - / * when you've a negative ^ -1 on a fraction bottom?
I am not sure what you mean but if the +- is not a part of the index you leave it alone."

re: above I meant if we have an exponent of -1 in the below example,
eg. we simplify (-a^ -n)/ (b^ -n) = a^ m-n : to solve does m - -n ever become a +?
I think that you mean
-a^-n / a^-n => -a^-n--n => -a^-n+n => -a⁰ => -1
which was obvious really because the same thing was on the top and the bottom.
like -2/2 = -1 because the 2s cancelled out.

I just did this for someone else, maybe it will also help
140206 neg indices with fractions.JPG

When does an odd amount of - and + exponents simplify an answer as - overall and an even amount of - and + or - and - simplify to +.
Does it apply to exponents or just applied to signs of coefficients and pronumerals? What about in division (top over bottom)?

I don't know, you are making my head spin. (Sorry, I've been at this all day, I am not criticizing your efforts to absorb knowlege)
All the normal rules for minus signs apply. Are you sure you know them all.

Thanks.

MelodyFeb 6, 2014

+118725

Warped Tour Girl:
Can you explain the grouping method of factoring. Can you describe a scenario when the grouping method would be preferred over other methods and show me an equation in this situation?
I need help with this, if you can please help(:

Hi Warped tour girl,
I haven't seen you for a while, welcome back.

I think this is what you want

3x+2x = (3+2)x = 5x
yes, I know that you already know that.

Let's take it a step further.
3(x-7)+2(x-7) = (3+2)(x-7)=> 5(x-7)
or
2x(x-7) + 3(x-7) = (2x+3)(x-7)

taking it back a step Lets try factorising
2x ² - 14x + 3x - 21
I can see that it is equal to
=2x(x-7) + 3(x-7)
=(2x+3) (x-7)

The main time I would really use this is when I am factorising quadratics with a leading coefficient greater than 1
For example let's factorise this one.
2x ²-11x+5
I have to look for two numbers that multiply to 2 x 5 =10 [Since they multiply to give a pos they must have the same sign ]
and add to -11 [ add to a negative so must both be negative]
-2 and -5 don't work
-1 and -10 work beautifully -1 x -10=10 and -1+-10 = -11
now I have to split the -11x into -1x and -10x
so I have
2x ²-1x -10x+5
now I am going to factorise in pairs
x(2x-1) -5( 2x-1)
(x-5)(2x-1)
That is the main time when I would use this technique.

I actually found a video on this just yesterday that I quite like. (all except the man waving his pen around the place )
I'll go see if I can find it.
http://www.youtube.com/watch?v=ZQ-NRsWhOGI
It might be worth a watch.

MelodyFeb 6, 2014

+6252

Quote:
How do you find the domain of a radical function

you note that x ^2k >= 0

so x ^1/(2k) is not defined if x < 0

So look at all the even roots and make sure their arguments are non-negative.

The Real numbers less these intervals where any even roots would have negative arguments is the domain of your function.

RomFeb 6, 2014

+6252

Quote:
3-{1.6x-3[x-3.5 (x+10)]}

the acronym people use to remember the order of operations is PEMDAS

parentheses
exponents
multiplication/division
addition/subtraction

so the first thing we'd do here is

3.5(x+10) = 3.5x + 35

then x - (3.5x + 35) = -2.5x - 35

now we multiply this by 3

3(-2.5x - 35) = -7.5x - 105

now subtract this from 1.6x

1.6x - (-7.5x - 105) = 9.1x + 105

and finally subtract this from 3

3 - (9.1x + 105) =

-9.1x - 102

RomFeb 6, 2014

+6252

http://www.jamesbrennan.org/algebra/polynomials/factoring_by_grouping_.htm

has a pretty good explanation of how to do factoring by grouping.

It's not radically different from factoring by eye. Just a bit more systematic and so it can help with trinomials where the x ² term isn't 1.

RomFeb 6, 2014

+118725

140206 neg indices with fractions.JPG

MelodyFeb 6, 2014

+118725

hutson1995:
1-(5/6)

Draw your self 1 pie. (a circle that is)

Now split it into 6 equal pieces.
Each piece is 1/6 of a pie.

Now you have got a whole pie in front of you. take away 5/6 of it.

That is, eat 1/6 of the pie five times => How much pie is left?

MelodyFeb 6, 2014

+118725

kass_:
solve 3x^(1/2)*x^-1

Hi Kass,

Use these facts - you might be able to work it out by yourself

x ^a*x ^b=x ^(a+b)

x ^1/2= sqrt2

140120 negative indices latex info.JPG

MelodyFeb 6, 2014

+1313

Thanks Melody,

"b) What are rules for + - / * when you've a negative ^ -1 on a fraction bottom?
I am not sure what you mean but if the +- is not a part of the index you leave it alone."

re: above I meant if we have an exponent of -1 in the below example,
eg. we simplify (-a^ -n)/ (b^ -n) = a^ m-n : to solve does m - -n ever become a +?

When does an odd amount of - and + exponents simplify an answer as - overall and an even amount of - and + or - and - simplify to +.
Does it apply to exponents or just applied to signs of coefficients and pronumerals? What about in division (top over bottom)?

Thanks.

StuFeb 6, 2014

+118725

Again, I am not intending to leave this here for ever I just wanted to use it again today.

Positive and negative numbers

For multiply and divide it is very simple. If the signs are the same then the answer is positive. If the signs are different the answer is negative. See, simple.

For addition and subtraction it is a bit trickier.
I am a big user of number lines. Until you get used to it you should actually draw your number lines. I am assuming that you know how to do that.
Zero in the middle, positive numbers going off to the right, negative numbers going off to the left.

Say it is 1+6. You start at 1 then go 6 places in the positive direction and you get 7 (yea, I know, you already knew that)
Now -3+8 Start at -3 and go 8 in the positive direction and what do you get?
Now 4 - 9 start at 4 and go 9 in the negative direction and what do you get?
Now -2- 8 start at -2 and go 8 in the negative direction and what do you get?

When you get good at it you can stop drawing the number line but you should still imagine it. If you use a note book, imagine 0 in the crease of the book, the positive numbers will be on the right and the negative numbers on the left.

Now, what about those pesky + - things
for starters, If you see something like 7+(-8) it is exactly the same as 7+ - 8 (You can put the bracket in or take it away - it doesn't matter.)
That goes for 3 - - 6 = 3- (-6) as well.

Now think of a thermometer. 0 degrees is in the middle. The positive numbers are hot numbers. The negative or minus numbers are cold numbers.
Let's think about 4+ + 5 you are adding heat so it must get hotter. So it is 4+5
What about 6+-7 This time you are adding cold. So it has to get colder. It must be 6-7
And 8 - + 3. This time you are taking away heat so it has got to get colder. It must be 8-3
and lastly -1 - - 4. This time you are taking away coldness so it has to get warmer. It must be -1+4

With pluses and minuses you can also think of it like this.
If two signs are so close together that you can put a circle around them without anything getting in the way then,
if the signs are the same you replace them with a positive.
if the signs are different you replace them with a negative.

am going to give you some questions to answer now.

1) Now -3+8 Start at -3 and go 8 in the positive direction and what do you get?
2) Now 4 - 9 start at 4 and go 9 in the negative direction and what do you get?
3) Now -2- 8 start at -2 and go 8 in the negative direction and what do you get?
4) 0-8=
5) -2-+6=
6) 1-4+(-7)=
7) -9++4 =
8) 13+(-5)=
9) -4 x 6 =
10) 3 x -6 =
11) -5 x -3=
12) 20 / -4=
13) -8 / 2=
14) -15 / -5=
15) +4 x +7=

MelodyFeb 6, 2014

+118725

Hi cbasto,

I am not going to answer your exact question but i will give you a lesson on negative numbers.

For multiply and divide it is very simple. If the signs are the same then the answer is positive. If the signs are different the answer is negative. See, simple.

For addition and subtraction it is a bit trickier.
I am a big user of number lines. Until you get used to it you should actually draw your number lines. I am assuming that you know how to do that.
Zero in the middle, positive numbers going off to the right, negative numbers going off to the left.

Say it is 1+6. You start at 1 then go 6 places in the positive direction and you get 7 (yea, I know, you already knew that)
Now -3+8 Start at -3 and go 8 in the positive direction and what do you get?
Now 4 - 9 start at 4 and go 9 in the negative direction and what do you get?
Now -2- 8 start at -2 and go 8 in the negative direction and what do you get?

When you get good at it you can stop drawing the number line but you should still imagine it. If you use a note book, imagine 0 in the crease of the book, the positive numbers will be on the right and the negative numbers on the left.

Now, what about those pesky + - things
for starters, If you see something like 7+(-8) it is exactly the same as 7+ - 8 (You can put the bracket in or take it away - it doesn't matter.)
That goes for 3 - - 6 = 3- (-6) as well.

Now think of a thermometer. 0 degrees is in the middle. The positive numbers are hot numbers. The negative or minus numbers are cold numbers.
Let's think about 4+ + 5 you are adding heat so it must get hotter. So it is 4+5
What about 6+-7 This time you are adding cold. So it has to get colder. It must be 6-7
And 8 - + 3. This time you are taking away heat so it has got to get colder. It must be 8-3
and lastly -1 - - 4. This time you are taking away coldness so it has to get warmer. It must be -1+4

With pluses and minuses you can also think of it like this.
If two signs are so close together that you can put a circle around them without anything getting in the way then,
if the signs are the same you replace them with a positive.
if the signs are different you replace them with a negative.

MelodyFeb 6, 2014

+118725

Damian:
5a + 2b = -5
7a + 3b = -6

Just call them equations 1 and 2
Multiply the first one by 3 to get equ 3
multiply the 2nd one by 2 to get equ 4

then do it by elimination method. (with subtraction to eliminate b)

Here is a different one that I did yesterday.
Yours is very similar I think.
Ignore the writing at the top.
The instructions that I have given you will get you to equation 4 I think.
See if you can make sense of it.
140205 Elimination method LaTex.JPG

MelodyFeb 6, 2014

+118725

I want to organise this better but I need to use this now so I am just going to put it here.

140205 Elimination method LaTex.JPG

MelodyFeb 6, 2014

+118725

Guest:
Since the curtain has to be the length of the window to the floor, then 4 ft (height of window) plus 2.5 (distance from bottom window to ground) is 6.5 ft. So the curtain length is 6.5 ft

Sounds good to me.

MelodyFeb 6, 2014

Since the curtain has to be the length of the window to the floor, then 4 ft (height of window) plus 2.5 (distance from bottom window to ground) is 6.5 ft. So the curtain length is 6.5 ft

GuestFeb 6, 2014

+6252

Quote:
The cadmium isotope 109Cd has a half-life of 462 days. A sample begins with 1.0×1012109Cd atoms. How many are left after (a) 29 days, (b) 850 days, and (c) 5400 days?

You know that radioactive decay is a decaying exponential function of the form

I(t) = I ₀e ^-at, here t is in days, and a is a rate constant to be solved for given the half life.

Half life means the time until half of the original radioactive atoms are present. So let t _h be the half life. Then

1/2 I ₀ = I ₀ e ^-at_h

1/2 = e ^-at_h

ln(1/2) = -a t _h

a = -ln(1/2)/t _h = -ln(1/2)/462

Now that you have a you can just plug in the time to answer questions a-c

RomFeb 6, 2014

+118725

KAOcmoa:
how do i plug in a fraction?

6 and a half

6 fraction button 1 fraction button 2 fraction button

MelodyFeb 6, 2014

+118725

Princess Sophie E:
A ladder rests with its foot on smooth horizontal ground and its upper end against a smooth vertical wall.
The ladder is uniformed and weighs 300N and inclined to the wall at an angle x. What horizontal force must be applied to the foot of the ladder to prevent it from slipping if
a) x=30degrees
b) x=arctan(3/4)

Hi Sophie,

I think this question might be the same as the one I like Serena answered. Please don't post questions twice.
If i am wrong then I apologize.

MelodyFeb 6, 2014

+118725