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09-27-2009, 04:47 PM #1
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robjdixon
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More maths help (prize available)

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

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Last edited by robjdixon; 09-27-2009 at 05:55 PM.

09-27-2009, 05:52 PM #2
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Elektrotechniker
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Re: More maths help (prize available)

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.

Last edited by Elektrotechniker; 09-27-2009 at 05:54 PM.

09-27-2009, 05:57 PM #3
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robjdixon
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Re: More maths help (prize available)

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
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09-27-2009, 06:00 PM #4
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Elektrotechniker
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Re: More maths help (prize available)

Quote:
 Originally Posted by robjdixon 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

09-27-2009, 06:04 PM #5
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robjdixon
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Re: More maths help (prize available)

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
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09-27-2009, 06:15 PM #6
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Re: More maths help (prize available)

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.

Last edited by Elektrotechniker; 09-27-2009 at 06:18 PM.

09-27-2009, 06:18 PM #7
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Hallucynogenyc
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Re: More maths help (prize available)

Quote:
 Originally Posted by Silvershot 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
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09-27-2009, 06:20 PM #8
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Elektrotechniker
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Re: More maths help (prize available)

Quote:
 Originally Posted by Hallucynogenyc my eyes are starting to feel pain from this post
Next time I will scan the paperwork

09-27-2009, 06:31 PM #9
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nikokapo
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Re: More maths help (prize available)

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:

Last edited by nikokapo; 09-27-2009 at 07:18 PM.

09-27-2009, 07:25 PM #10
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Elektrotechniker
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Re: More maths help (prize available)

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

Last edited by Elektrotechniker; 09-27-2009 at 07:27 PM.

09-27-2009, 07:29 PM #11
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Re: More maths help (prize available)

Quote:
 Originally Posted by Silvershot 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?

09-27-2009, 07:45 PM #12
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robjdixon
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Re: More maths help (prize available)

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.
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Last edited by robjdixon; 09-27-2009 at 07:47 PM.

09-27-2009, 08:10 PM #13
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Elektrotechniker
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Re: More maths help (prize available)

Quote:
 Originally Posted by nikokapo 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?

Last edited by Elektrotechniker; 09-27-2009 at 08:18 PM.

09-28-2009, 07:52 PM #14
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Re: More maths help (prize available)

Wow, you leave homeworks nearly as late as me! :P

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.

09-28-2009, 07:57 PM #15
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robjdixon
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Re: More maths help (prize available)

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

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
Quote:
 @ 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
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11-02-2009, 10:03 PM #16
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Hallucynogenyc
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Re: More maths help (prize available)

Do you guys know of the existence of the WIRIS? It would save you tons of work there!
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Wicked Lasers Evolution Pro 130mW ------------------> Review
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Laserlands 30mW disco laser --------------------------> Review
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DX 200mW Red laser (Dilda) --------------------------> Review
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