Calling All Math Geniuses!

<p>dchow...5 different triangles is the answer...
6,7,8,9,10</p>

<p>I got several more that involve graphs and picture, so i appreciate anyone with blue book that would kindly explain...
p.367 #3 the answer is c.</p>

<p>p.369#8
there is graph and then they ask, If a f(x+5)=f(x) for all values of x, then f(x)=0. How many different values of x between o and 12?</p>

<p>the answer is b. 9....i only found 8 but i did not really understand what the question was asking so i solved the way i thought it should be solved.</p>

<p>p.371 #12
4 circles have the same center and their radii are 1,2,3,4 respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?
the answer is 3:7</p>

<p>p.373 # 3</p>

<p>I think I kind of understand but someone confirm.</p>

<p>x+ 1/x=2, what is the value of x^2+1/x^2</p>

<p>the answer is 2...</p>

<p>Is it because the first part was multiplied by x(x+1/x)=2(x)
x^2+1/x^2=2x
and then cross out all the (x)s and u get 2...is that right?</p>

<p>p.367 #3. Yea, I've come through these problems, while I was practicing.
For this one, it says f(x)=f(-x), which means (x;y) and (-x;y), the same y for x and opposite of x. Then you should check those graphs and answer should be C.</p>

<p>p398 blue book</p>

<h1>11...why isn't the answer 36? line AB is diameter...im confused...</h1>

<p>400 #18 what is the difference b/w b is less than or equal to a
and b is less than or equal to the function of a</p>

<p>p.426 #12
2x<y<0, which of the following is the greatest value...
i understand why...but how are you supposed to know when to multiply negative 1 to flip the signs?
the book saids -2(x+y)</p>

<p>p.369#8.
The given graph is just portion of whole continuing graph. So imagine it longer till x=15. Then new graph will be as 3 times as the old one. And see how many x-intersect between 0 and 12. Then you should notice that there are 4 between 0 and 5. And the same goes with points between 5 and 10. But there are only one between 10 and 12 (or just simply between 0 and 2). Then you should have 9 in total.</p>

<p>p.371 #12.
Actually this one was much easier for me. First of you should find the areas of both smaller and larger shaded areas.
A. Area of smaller one. If there wasn't a little hole, then it would be pi * 2^2 = 4 pi; Now subtract the area of the circle with radius of 1 to find out the smaller shaded area. 4 pi - 1 pi = 3 pi;
B. Bigger one. You'll actually have to do the same. 4^2 pi - 3^2pi = 7 pi;
Then at last the ratio will be 3:7, which is D.</p>

<p>p.373 # 3
This one is much more interesting. Let me tell you my approach.
x + 1/x = 2, then you need find the value of x^2 + 1/x^2.
Use the first equality.
(x + 1/x)^2 = 2^2 => x^2 + 2 + 1/x^2 = 4. Then x^2 + 1/x^2 = 2. It is easily seen.</p>

<p>p398 #11. I haven't done this one. But I guess I can do it.
It asks you to find the length of that curved path, not line AB.
If the circumference of the circle is 36pi, then radius will be R=18;
To find the length of that curved path, you should notice that if they complement each other, they make full circle, with radius of 18/4 = 4.5.
Then you should use formula 2 * pi * R to find the length, which is 9 pi.</p>

<p>400 #18. Indolent about this problem and even it looks hard, so let's leave it to someone who is a math genius.</p>

<p>p.426 #12 for this one, i guess you should use real examples, which i think is the fastest way. just use small numbers like -2 < -1 < 0; Then you will be sure ti pick up - (2x+y)</p>

<p>thank god for CC, half of you here probably know more than my math teachers..</p>

<p>understand this :"x^3 - 1/x^2</p>

<p>As x gets really huge,</p>

<p>1/x^2 approaches zero.</p>

<p>x^3 - 1/x^2 = x^3 - 0 = x^3."</p>

<p>but don't the other examples work?...</p>

<p>Akati:</p>

<p>If I had exactly 2 cups of flour and added one extra speck of flour, what is the closest amount I have?</p>

<p>(A) 2 cups
(B) 3 cups
(C) 100 cups
(D) 1000 cups
(E) 10000 cups</p>

<p>The answer is A. Why don't the other examples work?</p>

<p>In your problem, the other examples don't work because when x is super huge, x^3 is not even close to x^4 or whatever the other examples were.</p>

<p>Let me restate the question:</p>

<p>Which of the following is closest to x^3 + 0 ?
(A)x^3
(B)x^4
(C)x^5
(D)x^6
(E)x^9</p>

<p>Akati, answer this question and please explain why B,C,D, and E don't work. Read your initial question about why the other choices don't work again.
Then read what you just wrote.</p>

<p>What is pg.400 #18?</p>

<p>I wish I had the blue book right in front of me right now! I can't stand the torture of not knowing the question and not being to help!</p>

<p>Could someone post these questions, for those of us who don't have the blue book?</p>

<p>Anyways, while I'm here, I might as well provide my 2 cents.</p>

<p>Here's two more ways to go about p.373 #3
1. Look at the problem, x + 1/x = 2. See if you can determine a numerical solution right away. Just by looking at it, I can tell x=1 (They are almost always integer answers), so you just plug and chug from there.
2. First, get either x or 1/x by itself. You should have either x = 2 - 1/x, or 1/x = 2 - x. For the first equation, you can write it as x = (2x-1)/x and for the second one you can write it as x = 1/(2 - x). Do some multiplication to the first, and you get x^2=2x-1, which you can bring to one side, forming x^2 - 2x +1=0. Do the same thing for the second one, and you get 2x - x^2 =1, which when brought to one side, is x^2 - 2x +1 = 0 again. Now factor this quadratic, and you get (x-1)^2=0, which as you can see, x=1. Now plug and chug into the other equation to get 2.</p>

<p>WoW you guys are my saviors thank you so much...dchow i understand the question lol....it just took 10-20 times to register...</p>

<p>p.400 #18 is a graph of y=f(x)
The shaded region is bounded by the x axis, the line x=4, and the graph of y=f(x). point (a,b) lie in shaded region which of the following are true?</p>

<ol>
<li> a less than or equal to 4</li>
<li>b less than or equal to b</li>
<li>b less than or equal to function of (a)</li>
</ol>

<p>i know number one is right.... and number 2 does not work...the book however says 3 works....so the answer is 1 and 3</p>

<p>my question is what is the difference b/w choice 2 and 3...why does number work?</p>

<p>p398 #11
is a circle with center O and diameter ab. The 2 semicircles have diameters OA and OB. If the circumference of the circle is 36pi, what is the length of the curved path from A to B through o?</p>

<p>the answer is 18pi..please explain</p>

<p>p. 426 #12
2x<y<0, which of the following is the greatest value...
a. -2x
b. -(2x+y)
c.2x
d.0
e. -y</p>

<p>i understand why the answer is correct...but how are you supposed to know when to multiply negative 1 to flip the signs?
the book answer is -2(x+y)</p>

<p>I hate math. This thread depresses me.</p>

<p>p.400 #18
It looks like I need to see the graph of f(x) to be of any help. Sorry.</p>

<p>p.398 #11
This one's easy if you know your terms. What's a circumference? It's the perimeter of the circle. Try and draw the figure. You have a circle whose diameter is AB. This diameter divides the circle in half. The question asked the length of the curved path from A to B, which means they are asking the length of the circular path that goes from A to B, which happens to be half the circle's length, so 1/2 of 36 pi, or 18 pi is the answer.</p>

<p>p.426 #12
Here's a tip: When working with these kinds of questions, use real numbers that are easy to work with.
As for the multiply -1, you're not supposed to know this. You work with what's given to you. This is essentially a "which of the following expressions fits the question" question. There are an infinite ways to write this question, all of which could have different answers. For all I know, they could have left out the negative sign on b, thus changing the answer, which would be a</p>

<p>p.426: "how are you supposed to know when to multiply negative 1."</p>

<p>Well, the way I did it, I just multiplied by -1 until I could eliminate all the answers. So first I multiplied by -1. -2x>-y>0, so the answer is not D or E. Then in 2x<y<0, i="" can="" eliminate="" c.="" then="" in="" choice="" b="" multiplied="" it="" out:="" -2x-y.="" since="" y="" is="" negative="" (2x<y<0),="" -y="" positive,="" so="" -2x-y="">-2x, so the answer is B.</y<0,></p>

<p>p.400 yeah, i need a graph. Also your choices don't make sense. "b is less than or equal to b" What are you talking about?</p>

<p>dchow:
its supposed less than a
sorry for the confusion
i do not how to post a graph...the only way is to look at book argh....anyone w/ the book want to help...</p>

<p>you did not answer my question
for p.426 HOW do you know when to multiply -1</p>

<p>Look at my post, YOU DON'T, because this is basically an "eliminate all wrong answers until you find the right one" type of question. You just have to use what they gave you. There's no need to start doing something random when the choices are already given to you. Basically, you multiply by -1 when the choice includes a -1, and don't multiply when there isn't a - sign in the choice.
As I said before, there are an infinite ways to write this question, all of them having different answers.
When you see "Which of the following..." just use what they gave you, which is what you're supposed to do. There's no need to come up with stuff if it isn't there.</p>

<p>blue book explanation told you to multiply -1 and then solve from there...that is why i asked how do you when to do it...</p>

<p>How do you know when to do it?</p>

<p>Well, honestly, what else would you do? If you look at the choices, -2x, -y, you know that you will probably have to multiply by -1 and see what happens. My thinking goes like this: I have to use process of elimination (which makes the most sense in this question). I see -2x and -y. Those involve multiplying by -1. So, I'll multiply by -1 and see what happens.</p>

<p>That's the best way to explain it. Sometimes you can look at a problem, look at the choices and just know what to do. </p>

<p>I've basically repeated It'sGr82BeAGator.</p>