All times are UTC - 6 hours




Post new topic Reply to topic   Page 1 of 1
 [ 11 posts ] 
Author Message

 Post subject: Year 12 Mathematics
PostPosted: January 11th, 2008, 7:29 am 
Squire
Squire
User avatar

Joined: January 10th, 2008, 6:40 pm
Posts: 173
Gender: Male
Status: Offline
I've been given revision to do throughout these school holidays, but i'm having trouble with some of the questions. You would probably need high end mathematical knowledge (Math Studies and Specialist Math). I'll be slowly adding the questions I don't understand on this thread.

Ex 1.A

18) A doorway is to be parabolic in shape and 2m high. At a height of 1m above ground level the width of the opening is 1.6m. How wide is the door at floor level.

__________________
Runescape (TEMP QUIT) - Deathwaltzer - Lvl 93(+5), Total lvl 1600+
Runescape (TEMP QUIT) - Pyro Ritual - Lvl 18, Total lvl 480+
Image
Image
'Your just like your father........MY FATHER WAS A BRILLIANT MAN! YOU DON'T EVEN KNOW!'


Top
 Profile
 

 Post subject: Re: Year 12 Mathematics
PostPosted: January 11th, 2008, 7:51 am 
Village Elder
Village Elder
User avatar

Joined: August 3rd, 2003, 4:24 am
Posts: 5,572
Location: U.K South-London R.S name: Killa Kiaba, Combat lvl: 137,
Gender: Male
Status: Offline

Donor: Guardian (2010)
Kaspertime wrote:
I've been given revision to do throughout these school holidays, but i'm having trouble with some of the questions. You would probably need high end mathematical knowledge (Math Studies and Specialist Math). I'll be slowly adding the questions I don't understand on this thread.

Ex 1.A

18) A doorway is to be parabolic in shape and 2m high. At a height of 1m above ground level the width of the opening is 1.6m. How wide is the door at floor level.



ok i could be completely wrong cus i aint been to school in like 7 years,

but at the top it meets in the middle so the width would be 0, half way down its 1.6, now if the door continues on its path it would be double the size it is half way.

so taking a guess 3.2m

im prob way off or wrong lol

__________________
Never argue with an idiot, they drag you down to their level and beat you with experience
Image


Top
 Profile
 

 Post subject: Re: Year 12 Mathematics
PostPosted: January 11th, 2008, 9:43 am 
Village Elder
Village Elder
User avatar

Joined: April 8th, 2004, 11:07 am
Posts: 2,878
Location: Sweden
Gender: Male
Status: Offline
I'll assume that the doorway is symmetric. Otherwise would the information given, be insufficent for solving this (as far as I know).

Forgive me for using commas instead for periods, we do that in Sweden.

Let's call the height of the door for y and half of the width for x. Imagine the door in a coordinate system like this:

Image

The formula for a parabola is y=ax^2+bx+c, where a, b and c are constants. In this case, as we are assuming that the doorway is symmetric, b equals 0.

As y(0)=2 and y(0,8)=1 (0,8 is 1,6 divided to two), we get the following equation system:

1=a*0,8^2+c (1)
2=a*0^2+c (2)

(2) tells us that c=2.

Put c=2 in equation (1) and get:
1=a*0,8^2+2
-1=a*0,8^2
a=-1/0,8^2
1=-1,5625

Now we know that the equation looks like this:

y=2-1,5625x^2

All what's left now is to find out the x value at y(0)

0=2-1,5625x^2
2=1,5625x^2
x^2=2/1,5625
x=sqrt(1,28)

Since x is only half the width of the doorway, the total width is 2*sqrt(1,28) which is approximately 2,26.


Last edited by Bulker on January 11th, 2008, 11:56 am, edited 1 time in total.
Top
 Profile
 

 Post subject: Re: Year 12 Mathematics
PostPosted: January 11th, 2008, 10:07 am 
Village Elder
Village Elder
User avatar

Joined: August 3rd, 2003, 4:24 am
Posts: 5,572
Location: U.K South-London R.S name: Killa Kiaba, Combat lvl: 137,
Gender: Male
Status: Offline

Donor: Guardian (2010)
lol what bulker said, i really hated parabola's, i mean how many doors have you seen shaped like that its like 1 in 100

__________________
Never argue with an idiot, they drag you down to their level and beat you with experience
Image


Top
 Profile
 

 Post subject: Re: Year 12 Mathematics
PostPosted: January 11th, 2008, 10:21 am 
♫ Hakuna Matata ♫
Village Elder
Village Elder
User avatar

Joined: March 10th, 2006, 2:55 pm
Posts: 5,936
Status: Offline

Donor: Guardian (2009)
great job bulker :)

I think the first thing one should do while solving these kinds of questions is to draw the sketch of it. Sketching really helps! They help you visualize the problem better and then you can start looking at different methods. In this problem I thought of 3 different tactics to tackle the question.
-Coordination System
-Circular Functions

But I guess the first one is the easiest choice :icon_thumright:

killa kiaba wrote:
Kaspertime wrote:
I've been given revision to do throughout these school holidays, but i'm having trouble with some of the questions. You would probably need high end mathematical knowledge (Math Studies and Specialist Math). I'll be slowly adding the questions I don't understand on this thread.

Ex 1.A

18) A doorway is to be parabolic in shape and 2m high. At a height of 1m above ground level the width of the opening is 1.6m. How wide is the door at floor level.



ok i could be completely wrong cus i aint been to school in like 7 years,

but at the top it meets in the middle so the width would be 0, half way down its 1.6, now if the door continues on its path it would be double the size it is half way.

so taking a guess 3.2m

im prob way off or wrong lol

This only works in similar Triangles. I thought of it too, but a parabola is case-specific and can't be changed into a triangle.

PS: Sorry for the geeky posts lol


Top
 Profile
 

 Post subject: Re: Year 12 Mathematics
PostPosted: January 11th, 2008, 11:58 am 
Village Elder
Village Elder
User avatar

Joined: April 8th, 2004, 11:07 am
Posts: 2,878
Location: Sweden
Gender: Male
Status: Offline
Sketching does absolutely make solving many problems much easier.

I was actually going to add an image of the graph, but I thought I would wait until I knew it's exact values, then I forgot about it...

Edited a graph in now though. :D


Top
 Profile
 

 Post subject: Re: Year 12 Mathematics
PostPosted: January 15th, 2008, 12:24 am 
Squire
Squire
User avatar

Joined: January 10th, 2008, 6:40 pm
Posts: 173
Gender: Male
Status: Offline
Thanks alot everyone, Bulker's equations helped me out the most, I was able to understand the question after reviewing it a few times.

Thanks!

__________________
Runescape (TEMP QUIT) - Deathwaltzer - Lvl 93(+5), Total lvl 1600+
Runescape (TEMP QUIT) - Pyro Ritual - Lvl 18, Total lvl 480+
Image
Image
'Your just like your father........MY FATHER WAS A BRILLIANT MAN! YOU DON'T EVEN KNOW!'


Top
 Profile
 

 Post subject: Re: Year 12 Mathematics
PostPosted: January 16th, 2008, 11:47 pm 
O_o
Clan Chat Moderator
Clan Chat Moderator
User avatar

Joined: June 22nd, 2005, 8:18 pm
Posts: 2,755
Gender: Male
Status: Offline

Donor: Prince (2011)
Friend of Hiker
Oddly enough, I learned how to solve such things today in Calculus class; Bulker beat me to it..

I'm glad you got helped =)

__________________
Image
Queen Black Dragon Kill Log


Top
 Profile
 

 Post subject: Re: Year 12 Mathematics
PostPosted: January 19th, 2008, 7:29 pm 
Squire
Squire
User avatar

Joined: January 10th, 2008, 6:40 pm
Posts: 173
Gender: Male
Status: Offline
I got a new question, this is for math studies, I dont understand fully. I tried many times but couldnt break through

5. c) Find the area function A(x), of an isosceles triangle with equal sides x, and base with no numeral, given that the perimeter is 50 cm.

I got as far as:
2x + y = 50
y= 50 - 2x

5. c) Find the area function A(x), of a square with two semi circles on each end, with the top side of the square being x, given that the perimeter is 400 m.

__________________
Runescape (TEMP QUIT) - Deathwaltzer - Lvl 93(+5), Total lvl 1600+
Runescape (TEMP QUIT) - Pyro Ritual - Lvl 18, Total lvl 480+
Image
Image
'Your just like your father........MY FATHER WAS A BRILLIANT MAN! YOU DON'T EVEN KNOW!'


Top
 Profile
 

 Post subject: Re: Year 12 Mathematics
PostPosted: January 19th, 2008, 9:20 pm 
Minor King
Minor King
User avatar

Joined: December 31st, 2003, 3:09 pm
Posts: 806
Location: Canada
Gender: Male
Status: Offline
For the first one, I don't want to just give you the answer, but you could do it really quickly with Heron's formula.
For triangle with side lengths a, b, c:
A = sqrt(s*(s-a)*(s-b)*(s-c))
where s = (a+b+c)/2.

Try plugging in what you have, and you'll get a very nice formula for area.

Spoiler: answer
Hidden: 
We know that two sides are length x, so say a = b = x. Also the third side is essentially given by the perimeter; c = 50 - 2x. Then:

s = 50/2 = 25

and

A(x) = sqrt(s*(s-a)*(x-b)*(s-c))
= sqrt(25*(25-x)^2*(25-50+2x))
= 5*sqrt((25-x)^2*(2x-25))

Which is pretty clean.


For the second one, do you mean that the semi-circles are the same size? Are their diameters the same size as the length of the square? If so, the function will be pretty boring - it'll be fixed.

Spoiler: answer (if the semi-cricles have diameter x)
Hidden: 
x can be solved for, using the perimeter and the fact that the perimeter is simply (2+Pi)x (by summing).
x = 400/(2+Pi)
Then area is simply area of square plus area of circle with radius x/2.
A = x^2 + 2*Pi*r^2
= x^2 + (1/2)Pi*x^2
with x given above.

__________________
Image
Join RVA today!

Check out my goals!
Low Scorer's Goals (F2P)


Top
 Profile
 

 Post subject: Re: Year 12 Mathematics
PostPosted: January 19th, 2008, 11:57 pm 
Squire
Squire
User avatar

Joined: January 10th, 2008, 6:40 pm
Posts: 173
Gender: Male
Status: Offline
I did the first one without the help needed, but here's a picture of the second question to make it much easier

__________________
Runescape (TEMP QUIT) - Deathwaltzer - Lvl 93(+5), Total lvl 1600+
Runescape (TEMP QUIT) - Pyro Ritual - Lvl 18, Total lvl 480+
Image
Image
'Your just like your father........MY FATHER WAS A BRILLIANT MAN! YOU DON'T EVEN KNOW!'


Top
 Profile
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  Page 1 of 1
 [ 11 posts ] 

All times are UTC - 6 hours


Who is online

Users browsing this forum: No registered users and 5 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Jump to:  

Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group
The Village and this web site are © 2002-2012

ThePub 2.0 - Designed by Goten & Jackstick. Coded by Glodenox & Henner.
With many thanks to the Website Team!