<p>^I got this one right... but I'm not familiar with this notation. What does the (x+2 ,y , y) mean? </p>
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<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>
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<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>
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<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>
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<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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<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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<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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<p>Ones I still would like an explanation for:</p>
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<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>
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<p>Answer=5</p>
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<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>
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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>
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<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>
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<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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