This weeks challenge

1. -1008. Set up a linear system and solved for m, then multiplied by 4.
4. 0

 

1. 2K-2=4M & K-M=502
K-1=2M
K=2M+1

2M+1-M=502
M=501
(note K=1002+1, or 1003)

4M = 2004

 

4. ax+by=bx+ay
ax-ay=bx-by
(x-y)a=b(x-y)
Thus if a does not equal b, then x-y MUST be zero, or the equality is false.

 

DUHHH i always make stupid mistakes like that. i bow down.

 

2. Where a1 = X/360, where X is the number of sides, since it is regular and thus the number of sides equally take 'some of the total degrees'

a2 = 1/2(180 - a1) = 1/2(180 - X/360)

Note that a3 = 180 - 2(a2) =180 - (180 - X/360) = 0 + X/360 or just X/360.

Thus the angle we want is simply 180 - 2(X/360) or 180 - X/180.

Sorry for diagram, it was quick MSpaint job.

BTW, if u want it in radians it is as follows:
a1 = X/2pi
a2 = 1/2(pi - a1) = 1/2(pi - X/2pi)
a3 = pi - 2(a2) =pi - (pi - X/2pi) = 0 + X/2pi
Angle we want = pi - 2(X/2pi) = pi - X/pi
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3. x2= 7x+3y
y= [x2-7x]/3=(x)(x-7)/3

y2=3x+7y

(x2)(x-7)2/9=3x+7/3(x2-7x)
(x2)(x-7)2=27x+21x2-147x
(x2)(x-7)2=21x2-120x
(x2)(x-7)2=(x)(21x-120)
(x)(x-7)2=21x-120
x3-14x2+49x=21x-120
x3-14x2+28x+120=0

To solve, I cannot multiply (no calc) so here goes:
x3 -(7)(2)x2 + (7)(4)x + (4)(2)(15) = 0

Looking at it, seems like as the power decreases, the factors of 2 increase. (Look at it, the first term has no 2's, the second has 1, the next has 2 and the last has 3 factors of 2) so might as well try 2 and -2, and I see -2 will work to cancel a lot out, so here goes:

-2*2*2 - 7*2*2*2 - 7*2*2*2 + 2*2*2*15 = 0
- 1 - 7 - 7 + 15 =0
0=0, true. Notice I didnt need a calc.

Thus, -2 works.

Note that solving the equations for y will give you the same equation, but with y's instead of x's.

Thus, final answer: (-2,-2)

Its easier to write on paper then on the computer.

 

Wow...nice job Auraptor! Keep them coming, Im interested in seeing which one you think is the hardest..and do you think this is grade 10 work...??
Thanks,
David

 

Hey, just so you younger guys know - i graduated high school and i'm functioning properly in the real world and i have yet to come across the need to solve any of those problems...! So just remember - don't bust your ass trying to pass that class and learn all the crap - it's not gonna come back to haunt you later on in life...

 

Haha...yea for real...some of this stuff is just useless..but thats life for you, i guess..

 

Hey, don't get me wrong - until recently, my life didn't really have much meaning; maybe this stuff IS required in the rest of the successful world... i'm not putting you guys down - i think it's pretty hot **** that you guys can actually figure this stuff out... i just always wondered what kinda job someone would have to take on for that stuff to be relevant...

 

i think i did that kinda stuff towards the end of 10th grade, what math are u in?

 

Can't be tenth grade. I was in a higer placement school, but not much higher. This was taught to me in 7-8th grade. I though 8-9th grade was the norm for this stuff?

Now if I could only retain half of it!

 

Question 1 and
Question 4 were 8th grade, basic solving of equations, nothing fancy.
Question 2 was geometry, 9th grade
Question 3 was Algieba. 2, (10th) or accel algebra 1 (8th).

Click links for the solution to each, or just scroll up.

IMO, none were anywhere near long, I did them roughly from shortest to longest, but I tried to also explain everything as I went.

The hard one for me was 3, only because to write it all out on the computer, and not mess up was a bit long...it took me almost as long as it did to do the other 3 to do that one. On paper all of them would have taken well less then 15 minutes to write if you were quick about it.

Good luck!

 

I think the important thing here is knowing that I COULD figure them out if I felt like it.

 

i took alg 1 frosh year, geo soph, now im taking alg 2 trig this year. next year its calculus or Matrix, prob, stat.

 

oooo i see, math isnt one of my stronger points. But i have an A in it.

 

nice, my gpa is gonna be sick nasty this quater like a 3.89. I am so cool

 

A number of technical / engineering professions do require skills like this to be successful.

The thing about getting them early in school is that you can determine if you really like this stuff...because that may be criteria for what you want to do in life.

If you don't like them, then do your best to get through the course and move on to something that does resonate with you...NNO's skill with words are evident in his FML writing and his Web site.

 

Don't be offended, but the irony here is numbing. You're taking honors math courses (which, as you state, anyone can take), but your grammar and spelling are deplorable. You guys must go to Madison High.

 

Google 'ieSpell' and install the program. It works to fix those stupid spelling errors. (all you do is right click and it is a option to spell check the text)