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I don't think the following questions will be worth a topic on the general forum (or any of the questions I already asked) so I'll just blog them.
I'm currently reviewing for the SAT II Math Level 2 right now and I'm stumped at some of the questions (I forgot everything I learned in precalc).
1. If x^(3/4)+2x=20 then x=?
I forgot how to solve these
2. What is the magnitude of the [addition of] vectors u and v? vector u is just a horizontal line with length of 11 and vector v is line with 50 degrees of elevation with length 7
The wikipedia article didn't make sense to me -_-. I thought the answer would be 11+cos50(7) but it's not.
3. The operation given by (a,b)O(c,d)=(a+bc,bd) is defined on the set of ordered pairs with nonzero second elements. Which of the following is the identity element for this operation?
I don't understand this question at all.
Thanks guys!
 
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On December 26 2008 09:59 Wala.Revolution wrote:
I don't think the following questions will be worth a topic on the general forum (or any of the questions I already asked) so I'll just blog them.
I'm currently reviewing for the SAT II Math Level 2 right now and I'm stumped at some of the questions (I forgot everything I learned in precalc).
1. If x^(3/4)+2x=20 then x=?
I forgot how to solve these
You know you can just type this into a calculator to solve, right? You can bring a TI 89 to the test. This problem isn't doable by hand, I think.
2. What is the magnitude of the [addition of] vectors u and v? vector u is just a horizontal line with length of 11 and vector v is line with 50 degrees of elevation with length 7
The wikipedia article didn't make sense to me -_-. I thought the answer would be 11+cos50(7) but it's not.
Well when you add the vectors, you get a vector with height 7sin(50) and height 11+7cos(50). Use the pythagorean theorem with those two sides to get the magnitude, which is the hypotenuse of the triangle made by the two vectors u and v.
3. The operation given by (a,b)O(c,d)=(a+bc,bd) is defined on the set of ordered pairs with nonzero second elements. Which of the following is the identity element for this operation?
I don't understand this question at all.
The identity element is the element that, when combined with an input, will give you the same input back. IE 1 is the identity element for multiplication, 0 for addition. So what pair (c,d) makes (a+bc,bd) = (a,b) is the question in simpler terms.
Thanks guys!
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On December 26 2008 10:14 huameng wrote:Show nested quote +On December 26 2008 09:59 Wala.Revolution wrote:
I don't think the following questions will be worth a topic on the general forum (or any of the questions I already asked) so I'll just blog them.
I'm currently reviewing for the SAT II Math Level 2 right now and I'm stumped at some of the questions (I forgot everything I learned in precalc).
1. If x^(3/4)+2x=20 then x=?
I forgot how to solve these
You know you can just type this into a calculator to solve, right? You can bring a TI 89 to the test. This problem isn't doable by hand, I think.
I'm sure there's a clever way to do it by hand, although I can't think of one at the moment, but you don't need a calculator--the SAT is multiple choice. (edit: or is this one of the questions where you have to enter the answer? forgot about those.)
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oops read too fast  nvm
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god I cant find a fucking solution to that math problem using just algebra
I'd use the quadratic equation as well (in Holland we just call it the abc formula). Or if you're allowed to solve it by graphic calculator just enter:
y1=x^(3/4)+2x
y2=20
calc -> intersect
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Well, if we're using wikipedia, clicking through a couple of links brought me to: http://en.wikipedia.org/wiki/Durand-Kerner_method, which would work for this problem (u^3+2u^4-20=0; u=x^1/4). I'd be very surprised if the SAT II expects you to know this method, though.
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United States47024 Posts
A calculator is allowed. Use one if you have one. Making things hard for yourself on purpose is dumb.
On December 26 2008 11:19 qrs wrote:Well, if we're using wikipedia, clicking through a couple of links brought me to: http://en.wikipedia.org/wiki/Durand-Kerner_method, which would work for this problem (u^3+2u^4-20=0; u=x^1/4). I'd be surprised if the SAT II expects you to know that formula, but who knows?
The SAT II doesn't expect you to know the Durand-Kerner method, but they do expect knowledge of the rational root theorem, which would apply, once you put the x^{3/4} term on one side, and raise to the 4th power. However, this would take an obscenely inconvenient amount of time if you have a calculator.
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2. What is the magnitude of the [addition of] vectors u and v? vector u is just a horizontal line with length of 11 and vector v is line with 50 degrees of elevation with length
where i and j are unit vectors in the x- and y- directions, respectively:
{11i} + {7cos50i + 7sin50j}
=
11+7cos50i + 7sin50j
the magnitude is found by sqrt((11+7cos50)^2 + (7sin50)^2)
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A is harder than I would expect for SAT
This is how I would approach it:
Let y = x ^ .25
So you have 2y^4 + y^3 - 20 = 0
You can then solve it using long division.
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I'm not sure A can be solved explicitly. I suspect there is a typo.
An identity element for an operation is one for which (x, y) O (identity) = (identity) O (x, y) = (x, y)
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Oh shit, you are right, sorry, I'm retarded, too much wine for dinner.
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On December 26 2008 09:59 Wala.Revolution wrote:
3. The operation given by (a,b)O(c,d)=(a+bc,bd) is defined on the set of ordered pairs with nonzero second elements. Which of the following is the identity element for this operation?
IIRC
you have to find an identity element which means a o n = a, so (a,b) o (n,m) = (a,b)
...
(a,b) o (n,m) = (a+bn, bm)
first element a+bn: n must be 0 that you get just a
second element bm: m must be 1 that you get b
so n would be (0, 1)
but the thing is that the formula isnt commutative
(1) (a,b) o (c,d) = (a+bc, bd)
(2) (c,d) o (a,b) = (c+da, db)
so i'm not sure if it's valid to state an identity element
but nevertheless the identity element would apply for both cases (1) and (2) with n = (0, 1)
could be complete bullshit what i write though, it's a long time ago i did this 
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For the first problem, I wanted to know how to do it algebraically because I really like understanding concepts so I can (hopefully) apply to other situations. That Durand-Kerner Method seems interesting though. Actually, I just took a look at it and I don't understand it at all. XD
I plan to ask and go over many topics with my math analysis teacher once school starts again, but magnitude just length right? So magnitude of vectors a+b would be the direct distance from point A to B where A is the initial point for starting vector and when the second vector starts at the first one, B would be the second vector's end point right? I think that's what Meta and huameng meant.
Third one I understand -_-;; I guess I just got troubled with the language.
Woohoo, thanks.
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you wouldn't be able to do the first one just by hand in a reasonable amount of time, i got the answer using a graphing calculator, and it turned out to be 7.690856
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United States3824 Posts
PEMDAS backwards is the way to go homie
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You do that and tell us how it goes.
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On December 26 2008 09:59 Wala.Revolution wrote:
1. If x^(3/4)+2x=20 then x=?
I forgot how to solve these
Well, if you really want the answer:
Doesn't seem doable by hand. My guess is you'll have to use other tools/guessing.
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On December 26 2008 12:11 Wala.Revolution wrote:
For the first problem, I wanted to know how to do it algebraically because I really like understanding concepts so I can (hopefully) apply to other situations. That Durand-Kerner Method seems interesting though. Actually, I just took a look at it and I don't understand it at all. XD
I'm almost sure the first one has a typo of some sort. The Durand-Kerner Method (or any fixed point method) is something you might see as a math major in college; definitely not a topic for the SATs, so don't worry if you don't understand it.
Does whatever you're working on have an answer listed for the first one? If it does, I can probably figure out what the typo is.
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EPT![[image loading]](http://i41.tinypic.com/vdo1ud.png)
