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Help!! Grade 10 math question - Printable Version

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Help!! Grade 10 math question - sneaky - 05-17-2012 12:05 PM

A pipe cleaner is 20cm long. It is bent into a rectangle. Use a quadratic model to determine the dimensions that give the maximum area.

She didn't even teach us how to do this and it's part of my homework:-/


RE: Help!! Grade 10 math question - LOON_ATTIC - 05-17-2012 12:13 PM

So let's say this rectangle has 2 sides, x and y
2(x+y)=20
because each "side length" is "repeated" twice
x+y=10
xy=???
where ??? is the area
wut
y=10-x
x(10-x)=?
10x-x^2=?
where x^2 is x squared
I think that does it
you could make it "standard form" with
area=-x^2+10x
or
A(x)=-(x^2)+10x
^as a function "A" or "Area" of x.

I'm gonna check soon to see if it's right
let's say it's a square so 20/4=5 which would be each side, thus x
A=-25+50=25
and 5*5 is 25 it's correct
let's say you have a side that's 6 and another that's 4, 6*4=24
plug in 6
A=-36+60
A=24
and 6*4 is 24 it's correct
4
A=-16+40
A=24

In order to find the largest area, thus the largest value of X, you'd have to find the vertex of the quadratic function, which is -b/2a... well
in this case (-10)/2(-1)=5
that's the x coord, or the side length. The maximum area seems to be yielded is by a square, not a non-square rectangle.
A(x)=-(25)+50=25
the max area is 25 square units

Feel free to shove a rusty pipe up your teacher's ass. I hate teachers who don't teach shit, expect you to pull shit out of your ass and make people hate math. Well, at least my hypothesis is that they make people hate math.

I could write a longass explanation for all I did here if you so desire.

It's stupid how it says it's a pipe cleaner when finding the area would be useless in such a situation. They're trying too hard to make it seem "useful in the real world". Oh well.

Also, something that could come in handy:
If a quadratic equation/function has its first, squared term negative, such as in:
f(x)=-32x^2+4x-94
or
f(x)=-x^2-999999x+9999999999
or
f(x)=-949x^2+9999999999999x+9999999999999999999999999999999
you get a parabola that goes down, somewhat hill shaped. but if it's positive its "arms" go up.
Also, if you square a negative value:
(-5x)^2
that's equivalent to
(-5)^2x^2
which is
25x^2
because -5 * -5 = 25
when you have -x^2, it's usually just like having -1x^2, order of operations applies. You first square x and then multiply it by -1.


RE: Help!! Grade 10 math question - LOON_ATTIC - 05-17-2012 12:16 PM

In case you read it too soon, I fucked up, fixed it.


RE: Help!! Grade 10 math question - sneaky - 05-17-2012 01:27 PM

"I could write a longass explanation for all I did here if you so desire."

[

o_o No,no I think that's long enough.

ThanksxD


RE: Help!! Grade 10 math question - LOON_ATTIC - 05-17-2012 06:11 PM

glad to help
This also does exactly what I did, maybe they explain it better
http://www.purplemath.com/modules/perimetr6.htm


RE: Help!! Grade 10 math question - SoulRiser - 05-18-2012 10:12 AM

Holy crap. They want you to write down such a long explanation for basically dividing it in 4 and then multiplying 2 of the sides together? Laugh