Math 2 Questions (please help math-wizes)

<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>
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<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[x]) = (2x+1)^2 ? </p>

<ol>
<li><p>Imageshack</a> - 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)</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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<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>

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

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

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

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

<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>

<p>
[quote]
47. How many ways can 10 people be divided into two groups, one with 7 people and the other with 3 people? </p>

<p>hard probability question...

[/quote]
</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>

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

[/quote]
</p>

<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>

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

[/quote]
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<p>Ahhh that's right. Makes sense.</p>

<p>
[quote]
37. the magnitudes of vectors a and b are 5 and 12 respectively, the magnitides of vector (b-a) could NOT be:

[/quote]

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>

<p>
[quote]
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.

[/quote]
</p>

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

<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>

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

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

<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>
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<p>
[quote]
Since its a triangle in a semi circle,its a right triangle.

[/quote]
</p>

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

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

<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>