a math problem

[ElFenix]

you have a circular piece of grassy field. you also have a cow. you want the cow to eat exactly half of the grass in the field. if you tie the cow to a post along the edge of the field, how long does the rope have to be, in terms of 'r', radius, to allow the cow access to exactly half of hte field?

 

[mitmot]

pi

 

[dullard]

Need more information. Is the cow a point mass? If not, what is the distance from the teeth to the point where the cow touches the leash? How many teeth are needed for the cow to eat?

 

[imported_Tick]

Originally posted by: ElFenix
you have a circular piece of grassy field. you also have a cow. you want the cow to eat exactly half of the grass in the field. if you tie the cow to a post along the edge of the field, how long does the rope have to be, in terms of 'r', radius, to allow the cow access to exactly half of hte field?

(PI*Ro*Ro)/2=(PI*Rn*Rn)

Ro is original radius
Rn is new radius.

 

[vshah]

Originally posted by: dullard
Need more information. Is the cow a point mass? If not, what is the distance from the teeth to the point where the cow touches the leash?

i think we assume yes and zero

 

[leftyman]

Holstien or Angus?

 

[imported_Tick]

Originally posted by: dullard
Need more information. Is the cow a point mass? If not, what is the distance from the teeth to the point where the cow touches the leash? How many teeth are needed for the cow to eat?

I'm assuming the cow is a point mass. I'm just guessing he's not in calc 2.

 

[vshah]

Originally posted by: Tick

Originally posted by: ElFenix
you have a circular piece of grassy field. you also have a cow. you want the cow to eat exactly half of the grass in the field. if you tie the cow to a post along the edge of the field, how long does the rope have to be, in terms of 'r', radius, to allow the cow access to exactly half of hte field?

(PI*Ro*Ro)/2=(PI*Rn*Rn)

Ro is original radius
Rn is new radius.

but the rope is tied along the edge of the field, not in the center.

 

[dullard]

Originally posted by: Tick
I'm assuming the cow is a point mass. I'm just guessing he's not in calc 2.

We can assume that I guess.

 

[ElFenix]

Originally posted by: Tick

Originally posted by: ElFenix
you have a circular piece of grassy field. you also have a cow. you want the cow to eat exactly half of the grass in the field. if you tie the cow to a post along the edge of the field, how long does the rope have to be, in terms of 'r', radius, to allow the cow access to exactly half of hte field?

(PI*Ro*Ro)/2=(PI*Rn*Rn)

Ro is original radius
Rn is new radius.

i think that would be the formula if you had the cow tied to a post inside the field. the cow is tied to the edge of the field.

 

[imported_Tick]

Originally posted by: vshah

Originally posted by: Tick

Originally posted by: ElFenix
you have a circular piece of grassy field. you also have a cow. you want the cow to eat exactly half of the grass in the field. if you tie the cow to a post along the edge of the field, how long does the rope have to be, in terms of 'r', radius, to allow the cow access to exactly half of hte field?

(PI*Ro*Ro)/2=(PI*Rn*Rn)

Ro is original radius
Rn is new radius.

but the rope is tied along the edge of the field, not in the center.

.....My reading is teh suck.

 

[ElFenix]

Originally posted by: dullard
Need more information. Is the cow a point mass? If not, what is the distance from the teeth to the point where the cow touches the leash? How many teeth are needed for the cow to eat?

yes, point mass, 0 distance from the teeth to the leash, the cow eats by osmosis.

 

[vshah]

you'll have to calculate the the area of a pie slice of the rope length, plus the area of the two sections cut off by chords of rope length. the size of the pie slice will have to be calculated (i think) by creating an equilateral triangle with the two chords & finding the third side

that total area needs to equal the area of the field /2

hmm

 

[imported_Tick]

This requires thinking...

I'll get back to you on that.

 

[dullard]

Originally posted by: vshah
you'll have to calculate the the area of a pie slice of the rope length, plus the area of the two sections cut off by chords of rope length. the size of the pie slice will have to be calculated (i think) by creating an equilateral triangle with the two chords & finding the third side

that total area needs to equal the area of the field /2

Link since I'm not typing it out.

 

[imported_Tick]

Originally posted by: vshah
you'll have to calculate the the area of a pie slice of the rope length, plus the area of the two sections cut off by chords of rope length. the size of the pie slice will have to be calculated (i think) by creating an equilateral triangle with the two chords & finding the third side

that total area needs to equal the area of the field /2

area field/2=area arc of circle with length of rope+2 area of chord slice of circle. OP, do you have those formulas?

 

[vshah]

Originally posted by: dullard

Originally posted by: vshah
you'll have to calculate the the area of a pie slice of the rope length, plus the area of the two sections cut off by chords of rope length. the size of the pie slice will have to be calculated (i think) by creating an equilateral triangle with the two chords & finding the third side

that total area needs to equal the area of the field /2

Link since I'm not typing it out.

cool, thanks 🙂

 

[imported_Tick]

Originally posted by: dullard

Originally posted by: vshah
you'll have to calculate the the area of a pie slice of the rope length, plus the area of the two sections cut off by chords of rope length. the size of the pie slice will have to be calculated (i think) by creating an equilateral triangle with the two chords & finding the third side

that total area needs to equal the area of the field /2

Link since I'm not typing it out.

That's the general, and more dificult form. THis is the case where the second circle's radius is entirely within the first circle.

 

[sao123]

Originally posted by: vshah

Originally posted by: dullard

Originally posted by: vshah
you'll have to calculate the the area of a pie slice of the rope length, plus the area of the two sections cut off by chords of rope length. the size of the pie slice will have to be calculated (i think) by creating an equilateral triangle with the two chords & finding the third side

that total area needs to equal the area of the field /2

Link since I'm not typing it out.

cool, thanks 🙂

I smell an integral between 2 curves.

 

[imported_Tick]

Originally posted by: sao123

Originally posted by: vshah

Originally posted by: dullard

Originally posted by: vshah
you'll have to calculate the the area of a pie slice of the rope length, plus the area of the two sections cut off by chords of rope length. the size of the pie slice will have to be calculated (i think) by creating an equilateral triangle with the two chords & finding the third side

that total area needs to equal the area of the field /2

Link since I'm not typing it out.

cool, thanks 🙂

I smell an integral between 2 curves.

This can be done without calc.

 

[dullard]

Originally posted by: Tick
That's the general, and more dificult form. THis is the case where the second circle's radius is entirely within the first circle.

But once you have the general form, it is easy to plug in the simplification (d=R1 in that link) and chug it out.

 

[OdiN]

Sell the cow and buy a lawnmower

 

[vshah]

Originally posted by: OdiN
eat the cow and buy a lawnmower

fixed....mmm

 

[captains]

crop circles

 

[Billzie7718]

I think I figured it out. Give me a minute to rework this and verify.