Fermat question

[Insectoid]

So, I wrote the Fermat math contest this morning, and almost finished this one question (I assume all participants have written it, and so thus I can post my partial answer). I would have finished if not for my lousy algebra skills.

Anywho,

Fermat 17 wrote:

In the diagram, the perimeter of the semicircular region is 20 (the perimeter includes both the semicircle and the diameter). The area of the region is closest to:
(A) 36.6 (B) 23.8 (C) 49.3
(D) 51.6 (E) 26.7

I came up with 2 equations, where C is the circumference of the semicircle (including the non-existent half) and D is the diameter

1/2C + D = 20
PI * D = C (Assuming the equation for diameter is 2PI*R, not PI*R^2, I always mix them up)

I substituted one into the other, and came up with

1/2(PI*D) +D = 20

1/2PI*D+D = 20
1/2PI*D = 20-D
1/2PI = 20-D/D
1/2PI-20 = -D/D

As you can see, I did something wrong. 1/2PI-20 != -1. Can someone help me out? I'd like to finish this question, even though the contest is over.

[DemonWasp]

code:

From Perimeter, get Radius: P = 1/2 * (2*pi*r ) + 2*r = 20 (pi+2)*r = 20 r = 20 / (pi+2) ~= 3.89 The Area: A = pi * r^2 A ~= 47.5 Therefore the answer is C

[A.J]

DemonWasp wrote:

code:

From Perimeter, get Radius: P = 1/2 * (2*pi*r ) + 2*r = 20 (pi+2)*r = 20 r = 20 / (pi+2) ~= 3.89 The Area: A = pi * r^2 A ~= 47.5 Therefore the answer is C

I am sorry, but you got it wrong...the answer is actually B (since they want the area of half the circle, not the whole thing)...

sry

I REALLY Messed up on fermat....I think I got #25 right...but I did bad overall

[DemonWasp]

Arg, you're right A.J. I knew I was doing something wrong - this is what happens when I find my Thief 3 installs all over again and play until 2am.

[A.J]

yea, I am pretty depressed about fermat too.....

how do you think you guys did?

[Insectoid]

I think I did okay, considering I didn't make it past part B...

[A.J]

oh...i solved all the questions except for #24 (I got the answer, more like a guestimate, but didn't take the chance).....
I found out eventually that I added wrong for one of the part C questions

[syntax_error]

How did you try to do the last questions, as I am not sure where to start with it, any hints would be helpful.

On a side note, does anyone think its a tab bit unfair to have the second group of students write the contest after my group did. Its not like they changed the questions or something, a whole 20 mins waiting in the library of free time after the first group wrote the contest, is more then enough time for texting answers and such no?

[Insectoid]

what? you did in two groups? I did mine all in one group, with the grade 10's doing their test at the same time, in the same room.

[syntax_error]

We had too many students writing the contest, not all could fit in the caf and library combined.

So, the admin set up 2 groups, and I think the reason we couldnt use any classrooms was because we did not have enough teachers for supervision.

[A.J]

we had more than 100 write the 9/10/11 contests ...every year we fit all of them into our cafeteria...

as for the tips, here they are :

21) Realize that since you are maximizing the # of people who ate both, you might have to minimize something else....right down equations, try numbers

22) There isn't really a hint I can give for this one...all I can say is try drawing lines from the origin to the different line segments....also notice that since the shape is being split into 3, each part must have an area of 16 (since the whole thing has an are of 48)

23) Try adding equations together and factoring...that should be a big hint

24) Try looking for sequences of machine inputs that return special variations of (m,n) (i.e. try finding what sequence of 'A's, 'B's and 'C's return (2m, n), etc...)

25) I sort of bashed this out....can't give much of a hint (sorry )

I hope these hints helped