need help with some math questions

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mahi123

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Sep 9, 2007
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1. x^1/3 = 32/ sqrt x 1/3 is the exponent

2. if 9^x - 9^x-1 = 216, find 4^x x-1 is the exponent

3. find the inverse function of f(x) = 3sqrt (x + 1) ( on the left side of square root it has
3 slightly on top so i guess it means whatever sqrt of x + 1 is it's to the power of 3.

4. rationalize the denominator

5x/sqrt (x) - sqrt (2x-5)

5. prove that x-s-t is a factor of x^3 - s^3 - t^3 - 3st(s + t)

6. express 2 sqrt 18 + sqrt 12 / sqrt 18 + 3 sqrt12 2 and 3 is multiplying

7. if f:x ~~> 2/x, find the value of f(x + a) - f(x) / a

i know this is a lot of questions, but my math teacher is extremely unhelpful and she tells us to do questions that she never taught before. i have no idea how to even start off for those problems so id prefer if someone can give the final answers also rather than hints etc cuz i don't think i can do them on my own. They look complicated and we've never done them in class and i don't know the rules regarding exponets etc. thanks
 
1)
x^1/3=32/sqrt[x^1/3]

for simplicity I will let z=x^1/3. It might make the steps easier to follow
z=32/z^1/2
multiply each side by z^1/2
z[z^1/2]=32
z^3/2=32
square each side
z^3=32^2
take the cube root of each side
z=32^2/3

replace z with x^1/3
x^1/3=32^2/3
cube both sides
x=32^2 answer

========================================
I will redo it without changing the variable
x^1/3 = 32/sqrt[x^1/3 rewrite
x^1/3=32/x^1/6
cross multiply
x^(1/3+1/6)=32
x^3/6=32
x^1/2=32
x=32^2

when you multiply you add exponents

x^2 means x squared
x^3 means x cubed
x^1/2 means square root of x
x^1/3 means cube root of x

x^2/3 means the cube root of x squared
hope this helps
Arthur
rest to follow
 
2)
9^x-9^(x-1)=216
rewrite
9^x-[9^x]/9=216
factor out 9^x
9^x[1-1/9]=216
9^x [ 8/9] = 216
9^x= 216[9]/8
9^x=27[9]
9^x=243
[3*3]^x=3*3*3*3*3
if x=5 we would have 5 sets of [3*3]. the square root of this would give us 5 sets of 3
[3*3]^5/2=243
x=5/2

then 4^x=4^5/2 =2^5=32 answer

Arthur

rest to follow
[3*3]^5/2=243
 
3)
the little 3 means cube root

y=[x+1]^1/3
to find the inverse interchange the x and y and solve for y

x=[y+1]^1/3
cube both sides
x^3=y+1
y=x^3 - 1 answer

Arthur

rest to follow
 
5)
I am going yo assume the [2x-5] is also in the denominator

5/[x^1/2 -[2x-5]^1/2 ]

multiply top and bottom by
[x^1/2 +[2x-5]^1/2]

5[x^1/2 +[2x-5]^1/2] / {[x^1/2-[2x-5]^1/2][x^1/2 +[2x-5]^1/2 ]}

on the bottom
x^1/2*x^1/2=x
[2x-5]^1/2*[2x-5]^1/2=2x-5
the cross terms cancel out

5[x^1/2 +[2x-5]^1/2] /[x-[2x-5]]
5[x^1/2 +[2x-5]^1/2] / [5-x] answer

Arthur

rest to follow
 
5)
prove x-[s+t] is a factor of x^3-s^3-t^3-3st[s+t]

first we will look at [s+t]
[s+t]^3=s^3+3s^2t+3st^2+t^3
you can prove this by expanding the term. Pascals triangle, or the general term for expanding to the nth power.
rewriting
[s+t]^3=s^3+t^3+3st[s+t]

substitute and rewrite the original
prove x-[s+t] is a factor of x^3-[s+t]^3

either divide x-[s+t] into x^3-[s+t]^3 and show there is no remainder, or factor the term

but
x^3-[s+t]^3=[x-[s+t]] [x^2+x[s+t]+[s+t]^2] answer
the term has a factor [x-[s+t]]

Arthur

rest to follow
 
6)
[2*18^1/2 +12^1/2] /[18^1/2+3*12^1/2]
18^1/2=3*2^1/2
12^1/2=2*3^1/2

[2*3*2^1/2 +2*3^1/2]] / {3[2^1/]2+3*2[3^1/2]}
factor out [2/3] and multiply top and bottom by 2^1/2-2*3^1/2
[2/3] { [3*2^1/2+3^1/2] [2^1/2-2*3^1/2]} / [2-4*3]
after multiplying the top

[2/3]{6^1/2-6*6^1/2]/-10]
[1/15] 6^1/2[6-1]
1/3 sqrt 6 answer

please check the algebra for errors it is late in ny and ?I am prone to make errors

7)
f[x]=x/a
f[x+a]-f[x]/a

f[x+a] replace x with x-a

f[x+a]= [x+a]/a
f[x]=x/a
f[x]/a= x/a^2

f[x+a]-f[x]/a= [x+a]/a -x/a^2
f[x+a]-f[x]/a= [a[x+a]-x]/a^2
f[x+a]-f[x]/a= [a^2+ax-x] / a^2 answer

Arthur
 
mahi123 said:
> i know this is a lot of questions, but my math teacher is extremely unhelpful
> and she tells us to do questions that she never taught before.

Could you give us her email address so we can tell her that's not nice?

> i have no idea how to even start off for those problems so id prefer if someone
> can give the final answers also rather than hints etc cuz i don't think i can do
> them on my own. They look complicated and we've never done them in class
> and i don't know the rules regarding exponets etc. thanks

Are you serious? You want your homework done?
And you haven't done anything, like google "law of exponents"?
Click to expand...
 
mahi123 said:
...my math teacher is extremely unhelpful and she tells us to do questions that she never taught before.
Click to expand...
Then you might want to have your parents conference with the administration, or at least you should conference with your academic advisor.

mahi123 said:
i have no idea how to even start off for those problems so id prefer if someone can give the final answers also rather than hints
Click to expand...
Most legitimate tutors won't "do" students' work for them, nor give out the answers.

You got "lucky" this time. But, since you claim that you've never seen any of this material before, you probably won't be able to copy the solutions sensibly (some of it will be obvious copying, and you won't be able to catch any typoes or errors), and of course the solutions you've been given won't help you learn at all, nor prepare you for the next test. For that, you'd have to study lessons.

If you're interested in learning, then the following may be helpful:

. . . . .Google results for "exponents"

. . . . .Google results for "radicals"

. . . . .Google results for "solving radical equations"

. . . . .Google results for "functions"

. . . . .Google results for "function notation"

. . . . .Google results for "inverse functions"

Once you have studies some lessons (at least two from each link), please review the solutions you have been given. After having learned the material, you should be able to follow what was done.

Eliz.
 
thanks for answering the questions arthur, really appreciate it, only if my teacher was that helpful.

@ denis, i don't think it's easy to learn math online, i try searching online for like exponents, radicals etc, but they're usually just simpler problems without any variables etc or they dont resemble mine.



@ stapel

my teacher is really unhelpful, i don't think talking to anyone abt her will help me, all the other math teachers are good in my school, she's the only bad one, she teaches for the first 15 mins in a 1 hour and 10 mins class, and then she just does her own stuff, if you go for help, she just tells you this you learned in gr 11 even though that same stuff is in gr 12 math curriculum again and she's supposed to teach that stuff throughly but she just tries to finish the lesson quickly.
 
mahi123 said:
i know this is a lot of questions, but my math teacher is extremely unhelpful and she tells us to do questions that she never taught before. i have no idea how to even start off for those problems so id prefer if someone can give the final answers also rather than hints etc cuz i don't think i can do them on my own. They look complicated and we've never done them in class and i don't know the rules regarding exponets etc. thanks
Click to expand...

Well, yes it IS a whole bunch of questions...you have not shown us any work you've attempted to try to solve any of them.

And your request for "final answers also rather than hints" tells me that you don't quite understand our purpose here....and that you aren't really interested in trying to learn how to do the work.

We WILL give you hints and examples to help you solve your problems. MOST of us will NOT give you complete worked out solutions....you can get them from numerous websites if you are willing to PAY for those results. We're volunteers. We would like to help you learn how to do problems on your own. If you are looking for completed solutions to your problems, you can find "answers for pay" websites on the internet.
 
your welcome.

Its difficult to teach in this format because there is no contact with a student to "see" if he or she follows the reasoning.

I hope I made some of your problems clearer

Arthur
 
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