constructing functions - Tilted Forum Project Discussion Community

Locke · 09-08-2003, 05:27 PM

Anyone know this math subject pretty well? If so I have a few questions.

Amanita · 09-08-2003, 05:50 PM

This is extremely vague. Perhaps post some details?

Locke · 09-08-2003, 06:22 PM

The one in particular I'm havng problems with goes like this.

A wire 10 meters long is to be cut into 2 pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle.

( the top quarter of the wire is 4x the bottom 3/4 is 10-4x)

a) Express the total area ,A, enclosed by the pieces of wire as a function of the length,x, of a side of the equilateral triangle.

I just need to know how to set it up. Everything else I can do. Thanks.

cheerios · 09-08-2003, 07:47 PM

this part: ( the top quarter of the wire is 4x the bottom 3/4 is 10-4x) doesn't make any sense to me. as for hte rest of it, well, it's a related rates problem, isn't it?

so, what's the area of a circle? A = πr^2
what about the circumfrence? C = 2*π*r
what's the area of an equilateral triangle? A = 1/2*x*h, where h = the height of the triangle
sin60(degrees) = h/x, so h = xsin60,
so A = 1/2*x*xsin60.
now the trick is to relate all of those, so that you eliminate all the variables besides x.

first step: A = π*r^2 + 1/2*x*x*sin60. only radius isn't meaningful right now, so get rid of using the circumference equation. that's how I'd approach it, anyway. remember that the circumference of your circle will be 10 - 3x, where x is the length of a side of your triangle!

Locke · 09-08-2003, 08:09 PM

The 4x and 10-4x part makes no sense because as I was typing my eyes decided to jump to another question. I do that from time to time. Thanks for the help.

Lebell · 09-09-2003, 04:53 PM

Cheers, the base of the triangle is not x, it is 1/3 x (assuming that the other length is 10-x).

If I worked it out right, the final equation is:

(3+(2)(pi)(sin60))(x^2)/12(pi) - 5x/pi + 25/pi

using the quadradic equation, one could then work out the max/min of the equation to maximize the area.

09-08-2003, 05:27 PM	#1 (permalink)
Locke Insane Location: The reddest state ever. :(	constructing functions Anyone know this math subject pretty well? If so I have a few questions. __________________ CUBS WIN, CUBS WIN!!!! - Pat Hughes "Don't surround yourself with yourself." Yes

09-08-2003, 06:22 PM	#3 (permalink)
Locke Insane Location: The reddest state ever. :(	The one in particular I'm havng problems with goes like this. A wire 10 meters long is to be cut into 2 pieces. One piece will be shaped as an equilateral triangle, and the other piece will be shaped as a circle. ( the top quarter of the wire is 4x the bottom 3/4 is 10-4x) a) Express the total area ,A, enclosed by the pieces of wire as a function of the length,x, of a side of the equilateral triangle. I just need to know how to set it up. Everything else I can do. Thanks. __________________ CUBS WIN, CUBS WIN!!!! - Pat Hughes "Don't surround yourself with yourself." Yes

09-08-2003, 08:09 PM	#5 (permalink)
Locke Insane Location: The reddest state ever. :(	The 4x and 10-4x part makes no sense because as I was typing my eyes decided to jump to another question. I do that from time to time. Thanks for the help. __________________ CUBS WIN, CUBS WIN!!!! - Pat Hughes "Don't surround yourself with yourself." Yes

09-09-2003, 04:53 PM	#6 (permalink)
Lebell Cracking the Whip Location: Sexymama's arms...	Cheers, the base of the triangle is not x, it is 1/3 x (assuming that the other length is 10-x). If I worked it out right, the final equation is: (3+(2)(pi)(sin60))(x^2)/12(pi) - 5x/pi + 25/pi using the quadradic equation, one could then work out the max/min of the equation to maximize the area. __________________ "Of all tyrannies, a tyranny exercised for the good of its victims may be the most oppressive. It may be better to live under robber barons than under omnipotent moral busybodies. The robber baron's cruelty may sometimes sleep, his cupidity may at some point be satiated; but those who torment us for our own good will torment us without end, for they do so with the approval of their own conscience." – C. S. Lewis The ONLY sponsors we have are YOU! Please Donate!

09-08-2003, 05:50 PM	#2 (permalink)
Amanita Loser	This is extremely vague. Perhaps post some details?

09-08-2003, 07:47 PM	#4 (permalink)
cheerios Banned Location: 'bout 2 feet from my iMac	this part: ( the top quarter of the wire is 4x the bottom 3/4 is 10-4x) doesn't make any sense to me. as for hte rest of it, well, it's a related rates problem, isn't it? so, what's the area of a circle? A = πr^2 what about the circumfrence? C = 2πr what's the area of an equilateral triangle? A = 1/2xh, where h = the height of the triangle sin60(degrees) = h/x, so h = xsin60, so A = 1/2xxsin60. now the trick is to relate all of those, so that you eliminate all the variables besides x. first step: A = πr^2 + 1/2xxsin60. only radius isn't meaningful right now, so get rid of using the circumference equation. that's how I'd approach it, anyway. remember that the circumference of your circle will be 10 - 3x, where x is the length of a side of your triangle!