<p>I searched in the Thread that contains answers and explanations to many questions in the blue book, but I could not find any for the following questions:</p>
<p>P.337 #6
They are asking about the triangle with the least area.
I would like to know if there is any other approach to solve this problem other than the one I used. Here is what I did:</p>
<p>Since the figure is drawn to scale, I used my eye to look at the areas. I quickly eliminated all answers except (A)"AOX" and (E)"EOX",
then I tried to guess which one has more area than the other, I found that when mentally 'cutting' EOX into pieces, these pieces will easily fill AOX and some will not fit in. This led me to guess that (A)** 'AOX'** has the least area, and luckily, it was correct.</p>
<p>My question is: Is there any algebraic way or any other way to solve this problem????</p>
<p>P.340 #15
Unlike the previous question, I had no luck with this one at all, so I skipped it.
So I really wish to know why the correct answer is (A): X=Y^2 -2</p>
<p>NOTE: If there is a link or sth that explains similar examples or the concept itself, posting it would be greatly appreciated.</p>
<p>Please help me in these also (I could not find an explanation in the explanation thread)</p>
<p>P.368 #5
-I made an educated guess on this one, but I do not undersand how to solve it :(</p>
<p>P.368 #7
I could not find any explanation for this one :(</p>
<p>**P.369 #8 **
I actually found an explanation for this one, but I could not understand it because the one who explained it linked it with trig and periods EDIT: I found an accurate explanation in the second page of an explanation for a different question, I will post it now.</p>
<p>UPDATE
I tried P.374 #7 again and found the solution. Surprisingly, this question is pretty easy. Here is the solution:</p>
<p>The question tells you the following:
if :
The adult’s weight = 4 X (avg. weight of 10 kids)
find:
The ratio (or what fraction is) the adult’s weight to the total weight of all 11 people in the elevator. So the total weight is the sum of his own weight and that of kids.</p>
<p>Solution:
Suppose that each kid weighs exactly 5 kg. , so the average of the kids’ weights will be 5.
Now multiply that by 4 to get the adult’s weight. You will get 5X4 = 20</p>
<p>We are not done yet, we still need to find the total weight, which is the adult’s weight plus that of kids. Remember that we supposed that EACH kid weighs 5, so the total weight of kids is 10 X 5 = 50</p>
<p>And the total weight of 11 people is 50+20=70</p>
<p>Now set the ratio:
20:70
which is equal to
2:7 , which means 2/7, which is the correct answer.</p>
<p>I am surprised that I could not solve this question from the first glance!</p>
<p>You know that the point (-2,0) works in the correct equation. Therefore, if you plug 0 in for y in all the equations, the ones that produce -2 are the only valid answers. These are A,B, and E. Also, you know that x=0 produces TWO values for y. This eliminates E, (as the only solution is y=sqrt(2)). So now the question is whether it is A or B. Since you know that there are there are values of y for x between -2 and 0, you can try a number like -1.</p>
<p>For A, you get -1+2=y^2, or 1=Y^2, and Y= plusorminus 1.
For B, you get -1+2=-y^2, or -1=Y^2, and Y is undefined. </p>
<p>To get the y-intercept, you plug in 0 for x, and solve for y. To get the x-intercept, you plug in 0 for y, and solve for x.</p>
<p>By looking at the equations, you can see that the y intercept will always be the number after equals sign, divided by the number in front of the y. (if you don’t see why this is, solve for the y-intercept with the method above, and you’ll likely see the pattern). </p>
<p>By looking at the answer choices, the only two that have a y-int of 2 are B and D. </p>
<p>The same method can be used for x-intercepts. By plugging in, B gives an x-int of -3, and D gives an x-int of 3. </p>
<p>Hi!
Triple-H, if you are stuck on whether it’s A or B, perhaps you can take into consideration another approach…
We know that the equations of x and y are reversed(we are solving for x instead of y). If you imagine them like this on the graph you can see that the parabola is now opened upwards. This means that y should be positive…x=y^2-2. Hope this helps :)</p>
<p>Because it’s easier to limit the domain. it is definitely from -2 to +inf, but we don’t need to test numbers that high. Here is the math behind p.340 #15:</p>
<p>y = +/- sqrt(x) is a sideways parabola with vertex at (0,0)
y = +/ sqrt(x + 2) is a sideways parabola with vertex at (-2,0)</p>
<p>y^2 = x + 2
y^2 - 2 = x</p>
<p>p. 337 #6</p>
<p>There are two approaches. The trick is to realizing that every triangle is an isosceles triangle. That means that the height of each is entirely dependent on the base. /\OAC is the “default area” to use - as a right triangle, the area is r^2 / 2. If we let r = 1, the area is 1/2. It is of note that if we did not use the isoceles sides but instead used the hypothenuse and found the height via trigonometry, we get 1/2 * sqrt(2) * sqrt(2)/2, which results in the same answer. </p>
<p>The area of an isosceles triangle can be found here: </p>
<p>On the SAT, it is much faster to realize that as the height and base approach each other, the area is maximized. This means that as the highest and base get farther apart, the area reduces. That’s why AOX has the smallest area.</p>
<p>Typo. I meant “Height and base get farther apart,” not “highest and base.”</p>
<p>When the base is small, height is large. As the base increases, the height reduces. The closer the base is in value to the height, the higher the area. As the base becomes large, the height becomes small. I don’t think you’ve taken calculus yet but optimization problems are based around this, and since OAX has the largest difference between height and base, it has the smallest area.</p>