Math 2 Questions (please help math-wizes)

Archive SAT Subject Test Preparation
1

<ol>
<li> if F: (x,y) –> (x+2y, y)</li>
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<p>^I got this one right… but I’m not familiar with this notation. What does the (x+2 ,y , y) mean? </p>

<ol>
<li> if f(2x+1)=2x-1, then f(x)=</li>
</ol>

<p>b. x-1
c. x-2 (correct)</p>

<p>(working backwards) I thought that you treated (x-1) as x, like you do when: f(x) = 2x+1, g(x) = x^2, where g(f) = (2x+1)^2 ? </p>

<ol>
<li><p>[Imageshack</a> - snapshot201005262.jpg](<a href=“ImageShack - Best place for all of your image hosting and image sharing needs”>ImageShack - Best place for all of your image hosting and image sharing needs)
its inverted, and unclear, but it asks for the area of the triangle in terms of theta. The diameter of the semicircle is 2 btw. (answer = 2sinxcosx)</p></li>
<li><p>the magnitudes of vectors a and b are 5 and 12 respectively, the magnitides of vector (b-a) could NOT be: </p></li>
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<p>A. 5</p>

<ol>
<li> I see this problem type all the time, and I always forget how to do it. 6.31^m = 3.02^n. What is the value of m/n?<br></li>
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<p>D. .8</p>

<ol>
<li> What is the length of the major axis of the ellipse whose equation is 60x^2 + 30y^2 = 150. I plugged it into my Ti 89 and it said undefined at -2, and 2, (i used the table setting) so I logically concluded that the major axis could be greater than 4. However, the answer is 4.47. How come?</li>
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2

<ol>
<li> How many ways can 10 people be divided into two groups, one with 7 people and the other with 3 people?<br></li>
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<p>hard probability question…</p>

3

<ol>
<li>Take the natural log (ln) of both sides. With the LN, you can bring the power (m and n) out as a coefficient to the ln. So, you get:</li>
</ol>

<p>m<em>ln 6.31=n</em>ln 3.02</p>

<p>Manipulate this and use your calculator.</p>

4

<p>^thanks. yeah I always forget that.</p>

5

<ol>
<li>Divide everything by 150, and use the conics program on the TI-84. I forget the properties of the major/minor axes of an ellipse (if you know them, you can use them), but both methods (calculator or by hand) require you set the equation equal to 1.</li>
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6

<ol>
<li>A function of both X and Y</li>
<li>f(x) = x-2 because (2x+1) - 2 = 2x -1
therefore the answer is a C</li>
</ol>

7

<p>^what’s the comma y at the end mean?</p>

8

<p>Ones I still would like an explanation for:</p>

<ol>
<li><p>How many ways can 10 people be divided into two groups, one with 7 people and the other with 3 people? (answer = 120)</p></li>
<li><p>the magnitudes of vectors a and b are 5 and 12 respectively, the magnitides of vector (b-a) could NOT be:</p></li>
</ol>

<p>Answer=5</p>

<ol>
<li>Imageshack - snapshot201005262.jpg
its inverted, and unclear, but it asks for the area of the triangle in terms of theta. The diameter of the semicircle is 2 btw. (answer = 2sinxcosx)</li>
</ol>

9

<p>

</p>

<p>Out of ten choose 7 and out of the remaining 3 choose 3 (10nCr7 * 3nCr3) I believe. Check if this answer is correct.</p>

10

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<p>DOesn’t work… I tried that while I took the test lol. The answer is 120 and what you said gets 14400. </p>

<p>Is there something wrong with my Ti 89? It says nCr(10,7) = 120; and nCr(10,3) = 120.</p>

11

<p><a href=“10nCr7%20*%203nCr3”>quote</a>

[/quote]
</p>

<p>Ahhh that’s right. Makes sense.</p>

12

<p>

that is a multiple choice question; it would be helpful to have the other choices, because there are alot of numbers it can’t be.</p>

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<p>

</p>

<p>good point lol. 5, 7, 10, 12, 17</p>

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<p>well realistically just looking at those 5 numbers you know that 7 is the lowest number that vector(b-a) could be. This would occur when both of the vectors are on one line and in the same direction (12-5=7). Then you also know that 17 is the largest number it could be and this is if the vectors have opposite directions (12-(-5)=17). The numbers in the middle can all be formed when there are different angles between the vectors. So 5 is not possible.</p>

15

<p>Oh okay; I just didn’t know the rule.</p>

16

<ol>
<li>Take the 150 below- 60x^2/150 + 30y^2/150=1
=2x^2/5 + 1y^2/5=1
Here the ellipse is centered around the y-axis(as the denominator for y^2 is greater). Major axis=denominator of y^2=5
Minor axis is denominator for x^2-5/2</li>
</ol>

<p>Funny my answers not 4.47
Are u sure thats the correct answer?</p>

17

<ol>
<li> Since its a triangle in a semi circle,its a right triangle.
Drop a perpendicular to the base(length 2).
Length of perpendicular=radius=1
now in new right triangle base nd perpendicular-1 unit each(coz both r radius)
Length of hypotenuse= 2^1/2(use pythagoras theo)
now (vr still in new triangle)-base can b xpressd in terms of theta as 2^1/2 cos(theta)
and perpendicular as 2^1/2 sin (theta)
now go back 2 big triangle.
the diametr can now be xpressd as 2<em>base of small triangle isnt it?
so diametr=2</em>2^1/2cos (theta)
and perpendicular of big triangle =perpdiculr of small triangle=2^1/2 sin (theta)
apply area of triangle=1/2 base<em>height
=1/2</em>2<em>2^1/2cos (theta)</em>2^1/2sin (theta)
=2sin (theta) cos (theta)!!!
yay!</li>
</ol>

18

<p>

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<p>This was pretty vital in even attempting this question… lol. thanks</p>

19

<p>do help wid d anwer of 29…Its puzzling me too</p>

20

<p>yea pixie I got the ellipse one. y is the major one because the denom is greater. it is y^2 / 5. Major axis = 2a, and 5 = a^2. </p>

<p>(root 5)*2 = 4.47</p>

<p>thanks for the triangle one though</p>