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— FPzero —
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Posted on 08-21-07 08:25:03 PM; last edit by FireCatgirl0 on 08-21-07 08:51 PM Link | Quote
I've got a math summer assignment and most of it is done BUT... I'm stuck on some problems and can't remember how to do them. Help please?

Simplify.
#1.
(x3-x+1)/x1/2

Solve for x.
#2.
2cos(x)+1=0

#3
3sec2(x)-4=0

#4
sin2(x)=3cos2(x)

#5
log2(x)+log2(5)=6

#6
e2x-7ex+10=0

#7
ln(x)-ln(3)=2

That's all of them. If you could explain how you did them that would help me remember how they are done.

HTML math is tedious...

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Pozeal
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Posted on 08-21-07 08:45:32 PM; last edit by Katzeal on 08-21-07 08:46 PM Link | Quote
welll... slash means divided by. that means
Xcubed minus X plus1 divided by Z times one half.

LMAO, I hardly know algebra, I was in pre algebra last year.

I'm probably wrong >.>

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Posted on 08-21-07 09:04:39 PM; last edit by Kattwah on 08-21-07 09:10 PM Link | Quote
It's a layout... that I worked hard on. ^_^
----------------------------------------------------

Originally posted by Katzeal
I'm wrong >.>
Quite in fact.

Anyways... first one.

Turn that (1/x1/2) into an (x-1/2). Factor out an (x-1/2) from the whole expression and you should be able to figure out what to do from there.

~~~~~

As for the trigonometric stuff...

Two and Three: The basic idea is to isolate the trigonometric function, and then solve. So for the first one, isolate the cos(x) turning it into...

cos(x) = -1/2

Now, just find a value on the unit circle that has a cosine that equals -1/2. In this case, it would be 2pi/3 and 4pi/3.

~~~~~

Four: This requires you to remember your trigonometric properties. (sin2(x) + cos2(x) = 1)

It should be easy to solve for that.

~~~~~

Five is all about logrithmic properties. In this case, remember that logm(a) + logm(b) = logm(a * b).

~~~~~

Six is tricky. What we have here is an example of a hidden quadradic equation. So, if you expand it, you get (ex - 2)(ex - 5). Set both of the expressions in the parenthesis equal to 0 and solve like you would any normal equation. (For the record, ln(e) = 1, ln(ex) = x)

~~~~~

Seven. Going back to log properties, ln = loge, and logm(a) - logm(b) = logm(a / b)

Hopefully this should put you on the right track...

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Posted on 08-21-07 09:21:02 PM Link | Quote
ARGH, I hated those kinds of problems SO much.

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Post 190/9597
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Posted on 08-21-07 09:24:39 PM; last edit by FireCatgirl0 on 08-21-07 09:25 PM Link | Quote
Kattwah:
Thanks. I've gotten most of them done. However, I made a mistake on the first problem. I didn't enclose the x3-x+1 in parentheses. I fixed it but I think you saw the problem before I did. If you did see the change and I'm just saying words then feel free to ignore this part.

Also, on number 3, I've isolated the trig function so the problem now reads sec2(x)=(4/3) but I'm stuck on where to go next. Figure out what sec2(x) equals on the unit circle? Or change it into 1+tan2(x)=(4/3)?

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Posted on 08-21-07 09:35:28 PM Link | Quote
Simplicity v1.1
Never doing trig in my life ever again if I can get away with it.

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Posted on 08-21-07 09:37:29 PM; last edit by Kattwah on 08-21-07 09:38 PM Link | Quote
It's a layout... that I worked hard on. ^_^
----------------------------------------------------

Oh...

Well, for the first one now... there honestly doesnt seem to be much to simplify... You could multiply the top and bottom by x1/2, but that seems to be it.

As for the other problem, sec2(x) = (secx)2. Just take the square root of both sides and solve normally.

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Posted on 08-21-07 09:50:29 PM Link | Quote
Simplicity v1.1
What?

English, motherfucker, do you speak it?

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— FPzero —
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Post 191/9597
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Posted on 08-21-07 09:52:03 PM Link | Quote
Okay, that solved the last of them. Now time to move on to my AP Government assignment . Read Hardball by Chris Matthews and write a five-page paper about quotes form the book and their connection to a list of political maxims.



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Posted on 08-21-07 09:52:09 PM Link | Quote
It's a layout... that I worked hard on. ^_^
----------------------------------------------------

Originally posted by Ranko
What?

English, motherfucker, do you speak it?
What?

Now it's a crime to know more than one language? ;D

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