<p>I was doing the practice tests from the OLd Offical SAT ii study guide and i have a few problems (Note that this test is also in the ofifcal math 1 & 2 study guide so if anybody has that please tell me the explainations) </p>
<p>okay </p>
<li>Which of the folliwng has an element that is less than any other element in that set? </li>
</ol>
<p>I. The set of positive rational numbers.
II. The set of positive rational numbers r such that r^2 >or= 2
III. The set of positive rational numbers such that r^2>4
anyways the answer is none , but why though why cant it be II?</p>
<p>also</p>
<li>An indirect proof of the statement “If x=2, then sqrt(x) is not a rational number” could begin with the assumption that.
(a) x= sqrt (2)
(b) x^2 = 2
(c) sqrt(x) is rational.
(d) sqrt(x) is not rational.
(e) x is nonegative.</li>
</ol>
<p>Okay for some reason the answer is C, and i have no clue why, arent u supposed to proving that its NOT rational, how do u start by assuming is rational???</p>
<p>One last one</p>
<li>The radius of the base of a right circular cone is 6 and the radius of a parallel cross section is 4. If the distance between the base and the cross section is 8, what is the height of the cone?</li>
</ol>
<p>(A)11
(B)13 1/3
(C)16
(D)20
(E)24</p>
<p>The answer was E. But i dont understand why, shouldnt it be C because its double? </p>
<p>Thanks alot for anybody who answers, oh and btw if you can answer only one then please just do so! and please answer, test is tommorow LOL.</p>
<p>Hey,
I think I know the answer for the 2nd question you posted (but not the others, because I'm only in Algebra 2, lol). An indirect proof starts by assuming the thing you try to prove is the opposite (if it's true, it's false/if it's false, it's true). So in your example, you are trying to prove that sqrt(x) is not a rational number. First, you assume that the statement you are trying to prove is false (sqrt(x) IS a rational number), then you go on to prove that (sqrt(x) IS a rational number) is false. Hope that helped, and good luck.</p>
<ol>
<li>Let the heght of the small cone be x . From similarity between the radii of the small and the large cone you have r1/r2= x/x+8 so : x/x+8=4/6
so x = 16. But 16 is not the right answer since it asks you for the hight of the large cone, that is x+8=24. E is the right answer</li>
<li>In proving similiar statements you first assume the opposite of what you are going to prove (to prove p = 1 you suppose p'=1 ) . Then you try to reach a contradiction to what you assumed. </li>
<li>II. The set of positive rational numbers r such that r^2 >or= 2 . Let A be this set. 2 is and element of this set and there is no other element in A greater than 2 . So I guess you are right. II should be the answer.</li>
</ol>
<p>This is a really rather dumb question (I know I'm setting myself up here), but how much are these test like the real one? I couldn't help but notice that the two test in the book were from 2002 and 1995. Do they change the content from year to year much? Are the tests in the book sig. easier or anything from the average "real" test?</p>
<p>i looked at the problem and i just realized that the set had an infinite number of elements.. which basically means that there can't be one element that is less than all the others. i guess that's one way looking at it. i can see how analyzing too much can be a bummer for that sort of problem.</p>
<p>The reason II is not true in #48 is because the smallest element of that set would have to be sqrt(2), which is not rational (as they specify it must be). So there's no smallest element of that set, for the same reason as I and III.</p>
<ol>
<li>An indirect proof of the statement "If x=2, then sqrt(x) is not a rational number" could begin with the assumption that.
(a) x= sqrt (2)
(b) x^2 = 2
(c) sqrt(x) is rational.
(d) sqrt(x) is not rational.
(e) x is nonegative.</li>
</ol>
<p>Okay for some reason the answer is C, and i have no clue why, arent u supposed to proving that its NOT rational, how do u start by assuming is rational???</p>
<p>Look at the question.. It says "An indirect proof of the statement"....</p>
<p>An indirect proof is proof in which you being with an assumption that is opposite from what you want to prove. Why? Beacuse in the end you'll come to a contradiction which will prove the frist thing you wanted.. :P</p>
<p>So in this case u start of with an assumption that sqrt(2) is rational :P</p>
<p>Just remember this: IF they're looking for an indirect proof than --- u just take the statment which you're given and make na opposite... In this case it's:</p>
<p>-we want to prove that sqrt(2) is irational
-we assumme that opposite, that sqrt(2) is rational</p>
<ol>
<li>As for this one, u probaably forgot to add 16 and 8... because 16 is the height of the smaller cone ;)</li>
</ol>
<p>For 45, "indirect proof" amounts to the use of the technique reductio ad absurdum<a href="reduction%20to%20absurdity">/I</a>, in which the opposite of what needs to be proved is assumed as a premise. The proof then proceeds to show that from the premise a contradiction (both *p and not p) can be established. Any premise that leads to a contradiction is false, hence its opposite (what you are trying to prove) must be true.</p>