More maths help (prize available)

robjdixon · Sep 27, 2009

Hey guys,
I've had a really tough day today, and am now struggling with the easiest of maths problems. I can see this happening a lot, so I have had the idea of giving a prize at Xmas to the person that I have judged to have helped me the most.

Here are the problems for today:
1.
express 1
---------
(root a)^4/3

in the form a^n

2.
by letting y=x^1/3 find the values of X for which x^1/3 - 2x^-1/3 = 1

3.
express in the form 2^n

a. 2^1/3 + 2^1/3 + 2^1/3 + 2^1/3
b. 2^100 - 2^99
c. 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1

4.
solve the equation

125^3x = 25^x-2
------- --------
5^x+4 3125

5.
find the equation of the straight line that passes through the points (3,-1) and (-2,2). Find point of intersecton of x axis

Thanks guys

Elektrotechniker · Sep 27, 2009

1. (root a)^4/3 ===> a^2/3
2. x^1/3 - 2x^-1/3 = 1 ====> x=8 or x=-1
3. a. 2^1/3 + 2^1/3 + 2^1/3 + 2^1/3 ===> 2^2/3
b. 2^100 - 2^99 ====> 2^99
c. 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 ==>2^33/10
4. 125^3x = 25^x-2 ==> I guess x=-4/7 and what does 5^x+4 3125 mean?
5. y=-3x/5 + 4/5

If you specify what problem 4 stands for I can help ya with it too.

robjdixon · Sep 27, 2009

Thanks bud. Is it too much to ask for you to show a little working.

I edited the post to show 4 more clear. I need to find x.

Also, the prize is a 70-100mW red laser that runs on 1AA battery - pretty unique if I may say so myself

Rob

Elektrotechniker · Sep 27, 2009

robjdixon said:
Thanks bud. Is it too much to ask for you to show a little working.

I edited the post to show 4 more clear. I need to find x.

Also, the prize is a 70-100mW red laser that runs on 1AA battery - pretty unique if I may say so myself

Rob

Ok.. So 125^3x = 25^x-2 ==> x=-4/7

robjdixon · Sep 27, 2009

Thanks.

How would I got about working through the rest?

If you can do those, you get 10 points (5 for answers and 5 for working). I'll keep a tally, and send the laser out for xmas

Elektrotechniker · Sep 27, 2009

1. (root a)^4/3 = a^1/2*4/3 = a^2/3
2. x^1/3 -2x^-1/3 = 1 ==> y -2y^-1 = 1 ==> y -2/y = 1 ==> y^2 -2 = y ==>
(y-2)(y+1)=0 ==> y=2 or y=-1
y=x^1/3 ==> 2=x^1/3 ==> 2^3=x ==> x=8
y=x^1/3 ==> -1=x^1/3 ==> (-1)^3=x ==> x= -1
3. a. 2^1/3 + 2^1/3 + 2^1/3 + 2^1/3 = 4*2^1/3 = (2^2)*(2^1/3) = 2^(2+1/3)=2^7/3 (sorry i wrote it false in last post )
b. 2^100 -2^99= (2^99)*2 - 2^99 = 2^99*(2-1)=2^99
c. 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 = 8*8^0.1= (2^3)*2^0.3=2^3+0.3=2^3.3=2^33/10
4. 125^3x = 25^x-2 ==> 5^3*3x=5^2(x-2) ==> 5^9x=5^2x-4 ==> 9x=2x-4 ==> x=-4/7
5. λ= (2-(-1))/-2-3= -3/5 so y-(-1)=(-3/5)*(x-3) ==> y=-3x/5 + 4/5

I had a hard time writing these in this post but finished them on paper in about 5 min. If you want anything else just shoot it.

Deleted member 8382 · Sep 27, 2009

Silvershot said:
1. (root a)^4/3 = a^1/2*4/3 = a^2/3
2. x^1/3 -2x^-1/3 = 1 ==> y -2y^-1 = 1 ==> y -2/y = 1 ==> y^2 -2 = y ==>
(y-2)(y+1)=0 ==> y=2 or y=-1
y=x^1/3 ==> 2=x^1/3 ==> 2^3=x ==> x=8
y=x^1/3 ==> -1=x^1/3 ==> (-1)^3=x ==> x= -1
3. a. 2^1/3 + 2^1/3 + 2^1/3 + 2^1/3 = 4*2^1/3 = (2^2)*(2^1/3) = 2^(2+1/3)=2^7/3 (sorry i wrote it false in last post )
b. 2^100 -2^99= (2^99)*2 - 2^99 = 2^99*(2-1)=2^99
c. 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 + 8^0.1 = 8*8^0.1= (2^3)*2^0.3=2^3+0.3=2^3.3=2^33/10
4. 125^3x = 25^x-2 ==> 5^3*3x=5^2(x-2) ==> 5^9x=5^2x-4 ==> 9x=2x-4 ==> x=-4/7
5. λ= (2-(-1))/-2-3= -3/5 so y-(-1)=(-3/5)*(x-3) ==> y=-3x/5 + 4/5

I had a hard time writing these in this post but finished them on paper in about 5 min. If you want anything else just shoot it.

my eyes are starting to feel pain from this post

Elektrotechniker · Sep 27, 2009

Hallucynogenyc said:
my eyes are starting to feel pain from this post

Next time I will scan the paperwork

nikokapo · Sep 27, 2009

I'm working on them, gimme some minutes and I'll give you definitive answers

Okay, took two shots of the paper with my D90, of course improved with PS CS4 for visibility (I know they look like crap, we're going for clarity with numbers and the pencil I used is crappy).

Silvershot, you missed both denominators on ex. 4. so the previous answer is not correct (though it is correct for the equation without the denom.

).

All answers down there, also, the graph is just to complement, do it with a ruler and it'll look much better.

(BIG ass resolution)

1:

2:

Elektrotechniker · Sep 27, 2009

I didn't know ---- meant denominator.

nikokapo · Sep 27, 2009

Silvershot said:
Guess what. we did the same thing. And was not my fault that problem 4 was wrong typed by rob. 5^x+4 3125 is confusing. w/e

Of course we did the same thing, dude, a math problem has specific solutions.

2+2 = 4 anywhere.

The confusing part was that 5^x + 4...I had to to the procedure all over again for that.

It's not a competition, I'm not saying the mistake was your fault. However you did miss the linear function's root on ex. 5.
I gave him the procedures since getting just the final answer won't teach him how to do the excercise.
Nevertheless, rob, next time you should ask for help with solving them, not just asking for full answers. Math is learnt the hard way

EDIT: Oops, seems you've edited your post, do you want me to edit mine or leave your last answer unquoted?

robjdixon · Sep 27, 2009

Sorry about 4 silver shot - I was in a manic rush. For this one, I shall give 10 points each, as you both gave different ways of answering that were both very helpful.

Edit:
@ niko, when I asked for help, I meant the solutions, not the answers - my maths teacher is sneaky, and doesn't collect in the homework, but sets a test with similar questions at the start of the lesson, so people that copied the answers are found out.

Elektrotechniker · Sep 27, 2009

nikokapo said:
Of course we did the same thing, dude, a math problem has specific solutions.

2+2 = 4 anywhere.

The confusing part was that 5^x + 4...I had to to the procedure all over again for that.

It's not a competition, I'm not saying the mistake was your fault. However you did miss the linear function's root on ex. 5.
I gave him the procedures since getting just the final answer won't teach him how to do the excercise.
Nevertheless, rob, next time you should ask for help with solving them, not just asking for full answers. Math is learnt the hard way

EDIT: Oops, seems you've edited your post, do you want me to edit mine or leave your last answer unquoted?

although I posted a solution earlier, you took the time and wrote a better explanation on paper. I thought he wanted answers only because he was in a hurry. That's why I said, we did the same thing.
I don't mind about the edited post. As for the ex. 5. He asked the equation of the straight line didn't he? so I find λ( factor management, slope) and considering the line passes from each of the points, no matter which one you use, it's the easiest way to find the equation( imo ), plus I wrote him how to do it, the solution.

@ rob, why don't you do these exercises on your own, so you practise your maths?

charliebruce · Sep 28, 2009

Wow, you leave homeworks nearly as late as me!

If I saw them scanned in, I might be able to help more quickly (I hate having to interpret "computer maths". Is this all Y11 GCSE work or is it beyond the curriculum? My school do the curriculum in an odd order however, so I'd guess our work doesn't line up accurately.

robjdixon · Sep 28, 2009

This is A level maths. I'm doing the whole A level this year though, so going 2 times as fast as everyone else.:thinking:

The reason I left it this late was that I thought my genius brother was coming home from uni for a few days, and he might be able to help me

@ rob, why don't you do these exercises on your own, so you practise your maths?

If you want, I can scan in the pages and pages of questions that I could do, but like I said, I got a few wrong, and it snowballed, so I lost it.

Next time (if there is a next time) I'll scan it. And if there isn't a next time, I'll just draw niko and silvershot randomly, and give one the red, and the other something else

Rob

Deleted member 8382 · Nov 2, 2009

Do you guys know of the existence of the WIRIS? It would save you tons of work there!

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