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.

please help

clahkie

this has been very helpful! thanks!


www.flocabulary.com

gcf101

2nd ed./ 392 / 10 /
3rd ed./ 312 / 10 / Math Question From 10 Reals Red book (second Edition)

gcf101

Once again:
a very good resource on "Real SATs" questions is on the "Study Hall" web site
http://www.studyhall.com/webpage2000/MainAnsSheet.html

gcf101

2nd ed./ 288 / 25 / Math question

winzton

1st edition/pg.276/question 23

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

md4me

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

optimizerdad

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

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

maybells

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

urgent help required

nilkn

maybells:

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 *maximize* the product of the numbers, then it is very solvable.

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

x(S - x) = Sx - x^2.

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:

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

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

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

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

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

S - S/2 = 2S/2 - S/2 = S/2.

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.

hope this helps,
nilkn

Beejay

nilkn wonderfuly said.

gcf101

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.
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.

gcf101

3rd ed. / 374 / 23 / Two math questions from the collegeboard red book :/

ali153

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

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

(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)

I: Length of arc PQR
II: Perimeter of Triangle OPR
III: Length of Chord PR

I understand how I and II work, but how does the chord length help?

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

Joe_L514

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.