Consolidated Answers for 10RS Math Problems

Test Preparation SAT Preparation
21

<p>1st edition/pg.276/question 23</p>

<p>Excluding rest stops, it took Juanita a total of 10 hours to hike from the base of a mountain to the top and back down again by the same path. If while hiking she averaged 2 kilometers per hour going up and 3 kilometers per hour coming down, how many kilometers was it from the base to the top of the mountain?
a) 8
b) 10
c) 12
d)20
e) 24</p>

22

<p>if the answer's (C), I can tell you how I did it.</p>

23

<p>As md4me said, it's (C). And this is probably the way he/she did it, too.... :)</p>

<p>If x = distance(km), base -> top of mountain, then
(x/2) + (x/3) = 10 or (5x/6)=10 or 5x=60
so... x=12.</p>

24

<p>Q. IF the sum of 2 numbers is 18.how large will their product be(solve it using parabolas.)</p>

<p>urgent help required</p>

25

<p>maybells:</p>

<p>As the problem is stated, it cannot be solved. There are infinitely many real numbers x,y such that x + y = 18. If, however, the problem aks you to <em>maximize</em> the product of the numbers, then it is very solvable.</p>

<p>Let's generalize and consider numbers that add to be S. In your problem, S = 18. If one number is x, then the other is (S - x). Thus, the product is</p>

<p>x(S - x) = Sx - x^2.</p>

<p>The problem then resolves itself into one of maximizing the quadratic f(x) = -x^2 + Sx. The quadratic term is negative, so therefore this one opens downward and the global maximum occurs at the vertex. There are two ways to find the vertex:</p>

<p>1) Set the derivative equal to zero and solve for x. In this case:</p>

<p>f'(x) = -2x + S
-2x + S = 0
-2x = -S
x = S/2</p>

<p>2) Remember accurately the formula from Algebra II stating that the x-coordinate of the vertex of ax^2 + bx + c is -b/2a. In this case, a = -1, b = S and c = 0; therefore, the x-coordinate of the vertex is</p>

<p>-b/2a = -S/[ 2(-1) ] = -S/-2 = S/2</p>

<p>So, if one number is S/2, then the other number is</p>

<p>S - S/2 = 2S/2 - S/2 = S/2.</p>

<p>Thus, the maximum product occurs when both numbers are exactly half of the target sum. In this case, S = 18, meaning both numbers should be 18/2 = 9.</p>

<p>hope this helps,
nilkn</p>

26

<p>nilkn wonderfuly said.</p>

27

<p>
[quote]
Q. IF the sum of 2 numbers is 18.how large will their product be(solve it using parabolas.)</p>

<p>urgent help required

[/quote]
</p>

<p>It’s kind of late to give a hand 8 months later, but I thought a different interpretation might help with similar questions; no parabolas though were harmed while solving. :D
x + y = 18, y = -x + 18 ------ straight line parallel to y = -x.
xy = m, y = m/x ------- hyperbola.
The bigger m, the farther from the origin (0, 0) the branches of this hyperbola go.
When m reaches its maximum, the right branch of hyperbola is tangent to line y = -x + 18 (if we increase m, hyperbola “breaks away” from that line). Since both graphs y = -x + 18 and y = m/x are symmetrical about y = x, their point of tangency lies on y = x.
y = x and x + y = 18:
x = y = 9.</p>

28

<p>3rd ed. / 374 / 23 / <a href="http://talk.collegeconfidential.com/showthread.php?t=363359%5B/url%5D"&gt;http://talk.collegeconfidential.com/showthread.php?t=363359&lt;/a&gt;&lt;/p>

29

<p>2nd edition: Page 328 #25 (AKA: Nov 1994, Sec 1, #25)</p>

<p>The circle above has center 0, what is sufficient to determine the radius of the circle:</p>

<p>(It is a circle with radii P and R forming a right triangle and a Q on the circumfrence 1/2way between P and R)</p>

<p>I: Length of arc PQR
II: Perimeter of Triangle OPR
III: Length of Chord PR</p>

<p>I understand how I and II work, but how does the chord length help?</p>

<p>(Also, can we make a thread using only the test dates, sections, and numbers? I feel left out since I have the 2nd edition :( )</p>

30

<p>Can anyone explain the answers for pg. 291-292, 18 and 17 and pg 312, #9?
17) If s can't equal 0, then 1/6 / 2s =
The correct answer is s/3
18) X, y, and x+y/2 make up one triangle. On each side, a square is constructed. What is the sum of the lengths of the sides of the resulting 9-sided figure, in terms of x and y?
the correct answer for this one is 9x+9y/2
pg. 312 #9
quoted irish_hopeful
I don't understant third ed. pg 312, #9, with two overlapping circles inside a rectangle. The circles both have area of 10, with centers A and B. Basically, the circles overlap such that the circumference of each goes through the center of the other circle. The left side of circleB's circumference goes through circleA's center...and vice versa.</p>

31

<p>Hello, I couldn't find this problem anywhere else and the studyhall site had confusing page numbers.</p>

<p>10 Real Sat 3rd Edition
Sunday May 2000
Section 7, Question #4
pg. 592</p>

<p>[figure of square ABCD marked with diagonals BD and AC, which go through point P in the middle]</p>

<p>The figure above shows a square and five labeled points. What is the least number of these five points that need to be moved so that all five points lie on the same circle?</p>

<p>a) one
b) two
c) three
d) four
e) five</p>

<p>I don't understand the question--what kind of circle are they asking about? Does it have to be inscribed within the square? If there are no restrictions concerning the circle, I thought the answer could be anything, since you could just draw a big one over all the points and not have to move any at all. </p>

<p>Anyway, the book says the answer is (a).</p>

32

<p>Bump. Please help!</p>

33

<p>I think I know why that is, but not completely sure. You can draw a circle around any square. The points A,B,C,D are all on the same circle(I guess the word would be tangent). The only point you need to worry about is P. So the only point you need to move is P. Hence, the answer is A)1.</p>

34

<p>Please explain question 8, page 654 Official Guide to me. Thanks so much.</p>

35

<p>What does 10RS mean?
What is consolidated?
And what books are these from?</p>

<p>P.s. what exactly is this thread for I dont get it?
pm me the answers plz. I cant get on often. even 1 answer is great</p>

36

<p>Could someone explain p304 #20 in the 3rd edition? Thank you.</p>

37

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

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<p>Question #20 - Page 304, 3rd Edition

</p>

<ol>
<li>Set up a direct variation problem.</li>
<li>48 (9) = 72 (x)</li>
<li>Solve for X and it equals 6.</li>
</ol>

<p>In words… multiply 48 x 9 to get the number of teeth that Gear B moved and divide that by 72 to get 6.</p>

39

<p>What does “10RS” mean? What is the “xiggi” method? Is there any consensus out there regarding the best SAT and SAT subject test preparation method? Any help would be appreciated. My daughter is a sophomore and I want to steer her in the right direction.</p>

40

<p>^Read through the sticky thread.
<a href=“http://talk.collegeconfidential.com/sat-preparation/763933-new-feature-best-sat-prep-forum-faqs-please-read-before-posting.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/763933-new-feature-best-sat-prep-forum-faqs-please-read-before-posting.html&lt;/a&gt;&lt;/p&gt;