Math Questions BB2

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1

<p>New Blue Book Math Problems.</p>

<p>p.400;18
p.401;19
p.418;17
p.424;16
p.456;15
p.457;18,19
p.484;11
p.519; 19,20</p>

<p>I know that it's alot of questions to ask help with, but I've been going through the book and circling the ones that I just couldn't understand on my own, and I have finnaly gathered enough problems I think lol. If someone would be willing to help, me with these, that would be wonderful. </p>

<p>If it's nessicary for me to write the questions down, I will, but Im hoping on someone here have the BB2 by chance.</p>

2

<p>Post the problems and we’ll help.</p>

3

<p>P.401;19</p>

<p>[Imageshack</a> - 40119](<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)
The pyramid shown above has the altitude H and a square base of side M. The four edges that meet at V, the vertex of the pyramid, each have a length E. If E=M what is the value of H in terms of M?</p>

<p>A) m/(square root of Two)
B) (M Square Roots of Three)/2
C) M
D) 2M/(Square Root of Three)
E) (M Square Roots of Two)</p>

<p>P.424 16</p>

<p>n(t) = (t^2)/2) -20t+k
There was a 100 day period when the number of bees in a certain hive could be modeled by the function N above. In the function, K is a constant and N(T) represents the number of bees on day number T, for 0<em><t</em><99. On what number day was the number of bees in the hive the same as it was on day number 10?</p>

<p>A) 20
B) 30
C) 40
D) 50
E) 60</p>

<p>p.456; 15</p>

<p>For all positive integers X, let X! be defined to be (X-1)(X+1) which of the following is equal to 6!-5!</p>

<p>A) 2!+1!
B) 3!+2!
C) 4!+3!
D) 5!+4!
E) 6!+5!</p>

<p>p.457 18</p>

<p>[Imageshack</a> - cylinder](<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)</p>

<p>The Right circular cylinder above has diameter D and height H. Of the following expressions, which represents the volume of the smallest rectangular box that completely contains the cylinder.</p>

<p>A) DH
B) D^2H
C) DH^2
D) D^2H^2
E) (D+H)^2</p>

<p>p.457 19.</p>

<p>The square of X is equal to 4 times the square of Y. If X is 1 more than twice Y, what is the value of X.</p>

<p>A) -4
B) -1/2
C) -1/4
D) 1/4
E) 1/2</p>

<p>p.485 13</p>

<p>If N is a positive integer and 2^N + 2^(N+1) = K what is 2^(N+2) in terms of K?
A) (K-1)/2
B) (4K)/3
C) 2K
D) 2K+1
E) K^2</p>

<p>P.486 16.
On a square game board that is divided into N rows of N squares each, K of these squares lie along the boundry if the gameboard. Which of the following is a possible value for K?</p>

<p>A) 10
B) 25
C) 34
D) 42
E) 52</p>

<p>Those are the ones that I had time to write down for now, that should be enough to hold you guys.</p>

4

<p>anybody wanna do 401 number 20?</p>

<p>A salesperson’s commision is k percent of the selling price. While of the following represents the commision, in dollars, on 2 cars that sold at 14,000</p>

<p>A. 280k
B. 7,000k
C. 28,000k
D. 14,000/ (100+2k)
E. 28,000+k/ 100</p>

<p>the answer is A</p>

5

<p>

</p>

<p>This question was giving me problems until I realized that all you had to do was substitute a number for n. So in the equation I substituted 2 for n. Numbers in the bold are numbers which were substituted. </p>

<p>2^N + 2^(N+1) = K
2^2 + 2^(2+1) = K
4 + 2^3 = K
4 + 8 = K
12 = K</p>

<p>Then it asks us what is 2^(N+2) in terms of K. So again you substitute 2 in for n. To get:</p>

<p>2^(2+2)
2^4
16</p>

<p>So now all we have to do is find an answer choice that gives us 16. I picked B. So</p>

<p>(4K)/3
(4*12)/3
48/3
16</p>

<p>The answer is B.</p>

6

<p>oh wow thanks Harambee on that one, If I see that one again there will be nothing to it.</p>

<p>On number 20, page 401.</p>

<p>It’s quite simple actualy, </p>

<p>14,000$ per car is a total of 28,000.
28,000 Divided by 100 is 280.
Add your K to represent your percent, and you are good to go,
280K.</p>

<p>I didn’t get it at first, but after working it backwards, it made sense.</p>

7

<p>Is anyone brave enough to attempt p.486, number 16?</p>

8

<p>^Think of the board as made up of horizontal rows of squares. Picture the border as the top and bottom rows (all squares on the border) plus the rows in between (2 squares only on the border for each of these rows, and there are n-2 of them).</p>

<p>So, k = 2<em>n + (n-2)</em>2 = 2n + 2n - 4 = 4(n-1)</p>

<p>See if this narrows the choices down to one…</p>

9

<p>What do you sugest subistituting in for N? With the given information could N not be any board with square dimensions? In my drawing, I drew a 4*4 board, and inputed that into the formula you provided, and it did work to derive the number of boarder squares that I have for that drawing, but the problem is, we are not told the dimensions of the board, so please help me with this aspect of the problem.</p>

10

<p>^At this point, you could plug in values for n until you see a number that appears in the answers. Better, since the number of border squares is 4(n-1), then the answer must be a multiple of four.</p>

11

<p>new book pg 424, #16 thanks.</p>

12

<p>Response to question There was a 100-day period when the number of bees … ?</p>

13

<p>Re the gameboard problem: </p>

<p>If you draw a simple board of say, 4 by 4, you will see that the perimeter of the gameboard (k) is not 16, (four squared) but 12. This is because the squares are duplicated at the 4 corners. </p>

<p>If you want to think of it algebraically: k = n^2 -4</p>

<p>So look at your answer choices, add four and see if you have a perfect square.<br>
A) 10+4=14 no
B) 25+4=29 no
C) 34+4=38 no
D) 42+4=46 no
E) 52+4=56 YES The gameboard is 8 by 8 and has a perimeter of 52.</p>

<p>As for a trick or tip that will work…sometimes you plug in numbers just to make the problem more real. In this problem, it asks for just a possible correct answer so you can’t just plug whatever you picked in to some formula. I picked four as a value for n just to make it easier to see the relationship between n and K, which, it turns out is the pretty straightforward k= n^2 - 4. But this doesn’t help you unless you can make the logical leap to k+4= a perfect square (any perfect square).</p>

<p>I have this problem filed under “logic” but what math isn’t a logic problem? ;)</p>

14

<p>The bee problem</p>

<p>The function is a quadratic, even though it doesn’t look like it at first. Replace t^2 / 2 with (1/2)t^2 and you’ll get a quad in the standard form of ax^2 + bx + c.</p>

<p>Don’t worry that you don’t know the value of c (which is “k” in your problem). You don’t need it.</p>

<p>Remember, quads are parabolas and parabolas are symmetrical. </p>

<p>They ask you about when you’ll get the same answer as when t=10. So we are looking for that OTHER value of x that is on the other side of the axis of symmetry. Find the vertex, and thus the x value for the axis of symmetry, with the formula:</p>

<p>-b/2a</p>

<p>b= -20
a= 1/2</p>

<p>20/1 = 20 (that’s easy!)</p>

<p>Since the vertex is the x value of the axis of symmetry, it is the midpoint of the two values. One of them is 10 (given) and they ask you for the other.</p>

<p>The vertex is 20. Day 10 is -10 from the midpoint and the same y value will appear +ten from the vertex.</p>

<p>20+10= 30</p>

15

<p>^^ You’ve lost me on this one for two reasons: </p>

<ol>
<li><p>Perimeter is 4n, not n^2.</p></li>
<li><p>Even if it were, 56 is not a perfect square.</p></li>
</ol>

<p>Or am I missing something here?</p>

16

<p>The triangle question:</p>

<p>We’ll have to use the Pythagorean theorem at least twice to get the answer. First, you’ve got to find the value of the line that goes from the bottom of the ‘h’ line to one of the lines that connect to the vertex (the ones that start from the edges of the squares). Once you’ve picked the place, use the Pythagorean theorem to find it:</p>

<p>m^2 + m^2 = c^2 = 2(m^2). c = m<em>sqrt(2). The thing is, this is the value for 2 of the lines I described earlier (the ones that connect from the bottom of ‘h’ to one of the edges of the square). So, just divide it by 2. m</em>sqrt(2)/2</p>

<p>Now, you simply use the theorem again to find h.</p>

<p>(m*sqrt(2)/2)^2 + h^2 = m^2. Remember, E=M, that’s why I did m^2 instead of e^2, to make it possible to subtract and what not.</p>

<h2>2(m^2)/4 + h^2 = m^2. That’s basically .5(m^2) + h^2 = m^2, so subtract the .5(m^2) from the m^2 to get h^2 = .5(m^2). That’s also h^2 = m^2/2, and h = m/sqrt(2).</h2>

<p>The board problem:</p>

<p>Simply look for a pattern.</p>

<p>Basically, saying that a board with N rows and N squares in each row is saying you can make boards of 2x2, 3x3, 4x4, etc.</p>

<p>Draw a 2x2. You get 4 squares on boundaries.
Draw a 3x3. You get 8 squares on boundaries.
Draw a 4x4. You get 12 squares on boundaries.</p>

<p>There seems to be a pattern here, and that is to add 4 every time you go up one number in ‘n’. That also means the total amount of squares for the boundaries following the rules given by the question must be a multiple of 4. Look at the answer choices; only 52 is a multiple of 4.</p>

17

<p>Oh GOSH! so sorry. Totally my spaz…</p>

<p>The term perimeter isn’t really apt because it’s not really asking what the perimeter is as how many squares there are around the outside. It wouldn’t be 4n, but 4n-4 since four are counted twice. </p>

<p>The problem doesn’t require you to square anything. That’s where I spazzed and I was thinking of another (similar) problem that I had worked out for someone else.</p>

<p>E) 52 + 4 = 56, which is the only one divisible by four.</p>

<p>The CORRECT algebraic expression would be: k = 4n - 4 NOT n^2 - 4</p>

<p>Mea culpa</p>

18

<p>1) triangle comprising h,e,b with b=segment from center of base to bottom vertex of e. b= sqrt{2}(m/2)=m/sqrt{2}. This is b/c right triangle from center of base to vertex of e, to middle of base edge has two edges of length m/2, and the other is b. Now, right triangle with h, e and this b has sides m, m/sqrt{2}, and h. So, h=m/sqrt{2}.</p>

<p>2) n(t)=n(10) ==> n(t)-n(10)=0. t^2-40t+300=0 ++> (t-10)(t-30)=0. t=30</p>

<p>3) x!=(x-1)(x+1)=x^2-1. 6!-5!=11. x!+y!=x^2+y^2-2. plug==> B</p>

<p>4) base is DxD. Height is H, HD^2</p>

<p>5) x^2=4y^2 and x=2y+1 <==> y=(x-1)/2. This means 4y^2 = (x-1)^2. So we need x^2=(x-1)^2. x=1/2</p>

<p>6) plug</p>

<p>7) multiple of 4 as mentioned.</p>