Math Question

[Rayleigh]

Hey Ender, thank you for taking time out to solve it via modelling approach. Appreciated.

[Rayleigh]

Hey guys, need help again. The figure consists of a circle and a square overlapping each other partially, ABCO. O is the centre of the circle. If the ratio of the area of the square ABCO to the area of the circle is 4:7, what is the ratio of the shaded part to the whole figure?

 

 

Below is my solution and not sure if it is correct:

 

1. Since the area of circle is 7 units, 1/4 area of circle is 7/4 units or 1.75 units

 

2. Therefore area of the shaded area is 4 - 1.75 = 2.25

 

3. Area of shaded shaded area and circle is 2.25 + 7 = 9.25

 

4. Hence ratio of shaded part to whole figure is 2.25:9.25. Correct?

 

[1fast1]

Hey guys, need help again. The figure consists of a circle and a square overlapping each other partially, ABCO. O is the centre of the circle. If the ratio of the area of the square ABCO to the area of the circle is 4:7, what is the ratio of the shaded part to the whole figure?

 

 

Below is my solution and not sure if it is correct:

 

1. Since the area of circle is 7 units, 1/4 area of circle is 7/4 units or 1.75 units

 

2. Therefore area of the shaded area is 4 - 1.75 = 2.25

 

3. Area of shaded shaded area and circle is 2.25 + 7 = 9.25

 

4. Hence ratio of shaded part to whole figure is 2.25:9.25. Correct?

 

 

Correct, but you need to simplify the ratio. Multiply by 4 to get 9:37.

[Rayleigh]

 

Correct, but you need to simplify the ratio. Multiply by 4 to get 9:37.

 

Thank you thank you.

[Manmaster]

Hey guys, need help again. The figure consists of a circle and a square overlapping each other partially, ABCO. O is the centre of the circle. If the ratio of the area of the square ABCO to the area of the circle is 4:7, what is the ratio of the shaded part to the whole figure?

 

 

Below is my solution and not sure if it is correct:

 

1. Since the area of circle is 7 units, 1/4 area of circle is 7/4 units or 1.75 units

 

2. Therefore area of the shaded area is 4 - 1.75 = 2.25

 

3. Area of shaded shaded area and circle is 2.25 + 7 = 9.25

 

4. Hence ratio of shaded part to whole figure is 2.25:9.25. Correct?

 

Your logic is correct but your figure is wrong.

 

The area of circle is 7/11, not 7 as 7 is a ratio unit. so 7/11 x 1/4 = 7/44

 

Area of shaded area = 4/11 - 7/44= 16/44 - 7/44 = 9/44

 

Area of shaded area and circle = 9/44 + 7/11 = 9/44 + 28/44 = 37/44

 

Hence the ratio is 9/44 : 37/44 = 9:37

[1fast1]

Your logic is correct but your figure is wrong.

 

The area of circle is 7/11, not 7 as 7 is a ratio unit. so 7/11 x 1/4 = 7/44

 

Area of shaded area = 4/11 - 7/44= 16/44 - 7/44 = 9/44

 

Area of shaded area and circle = 9/44 + 7/11 = 9/44 + 28/44 = 37/44

 

Hence the ratio is 9/44 : 37/44 = 9:37

 

There's nothing wrong with his figures. He just used decimals in his proportion without simplifying it to give a whole number ratio. Mathematically correct, but not the preferred representation.

 

And when you write things like area of circle = 7/11, what are the units, or what is it in reference to? This is meaningless without units or context. The area of the circle is 7/11 of the summed areas of the square and the circle (with the overlap basically being double-counted), but this is unwieldy and unnecessary to state.

 

On the other hand, Rayleigh assigning the area of 4 units to the square and 7 units to the circle is perfectly acceptable. The same arbitrary units of area are used for each.

Edited April 30, 2014 by Turboflat4

[Manmaster]

 

There's nothing wrong with his figures. He just used decimals in his proportion without simplifying it to give a whole number ratio. Mathematically correct, but not the preferred representation.

 

And when you write things like area of circle = 7/11, what are the units? This is meaningless without units. The area of the circle is 7/11 of the summed areas of the square and the circle (with the overlap basically being double-counted), but this is unwieldy and unnecessary to state.

 

On the other hand, Rayleigh assigning the area of 4 units to the square and 7 units to the circle is perfectly acceptable. The same arbitrary units of area are used for each.

The unit is X of cos. it should be 7/11x where x is the area. By assigning 7 as the area, it is just an assumption, not the real area as we don't know the area.

 

Logically speaking, you can't use the ratio unit of something as the area. 7 is the ratio unit, not the area. I don't want to debate on this anymore as I just wanna represent a clearer way of solving the problem.

[1fast1]

The unit is X of cos. it should be 7/11x where x is the area. By assigning 7 as the area, it is just an assumption, not the real area as we don't know the area.

 

Logically speaking, you can't use the ratio unit of something as the area. 7 is the ratio unit, not the area. I don't want to debate on this anymore as I just wanna represent a clearer way of solving the problem.

 

Whether you want to debate this or not is not relevant. The fact remains that "your way" as you stated in the original post is not only unclear, it is also *wrong*.

 

"The area of the circle is 7/11" has absolutely NO meaning. You did not state the unit of measure. It doesn't even have to be a common unit of measure like square centimetre, square metre or square inch. It can just be an arbitrary unit of area simply denoted "unit". This is completely fine as long as you use the same notation throughout, as Rayleigh did. However, it is NOT acceptable to just leave it hanging as "7/11".

 

And even now, your latest post is hardly clear. You say "x is the area". Area of what?

 

Rayleigh did NOT assign "7" (pure number) as the area. He said "7 units". That makes all the difference in the world. Granted that I would recommend a little more clarity by stating at the outset: "Let the area of the circle be 7 units. Then the area of the square is (4/7)*7 = 4 units". But this is a small point, and his meaning is still far clearer than yours.

 

If you do not know, do not misinform people.

Edited April 30, 2014 by Turboflat4

[Ender]

The numbers 4711 keeps coming in this question.

Edited April 30, 2014 by Ender

[Manmaster]

 

Whether you want to debate this or not is not relevant. The fact remains that "your way" as you stated in the original post is not only unclear, it is also *wrong*.

 

"The area of the circle is 7/11" has absolutely NO meaning. You did not state the unit of measure. It doesn't even have to be a common unit of measure like square centimetre, square metre or square inch. It can just be an arbitrary unit of area simply denoted "unit". This is completely fine as long as you use the same notation throughout, as Rayleigh did. However, it is NOT acceptable to just leave it hanging as "7/11".

 

And even now, your latest post is hardly clear. You say "x is the area". Area of what?

 

Rayleigh did NOT assign "7" (pure number) as the area. He said "7 units". That makes all the difference in the world. Granted that I would recommend a little more clarity by stating at the outset: "Let the area of the circle be 7 units. Then the area of the square is (4/7)*7 = 4 units". But this is a small point, and his meaning is still far clearer than yours.

 

If you do not know, do not misinform people.

The correct way to express this is 4/11x : 7/11x. I just took out the X from both sides for simplicity. Maybe that's my only mistake.

 

X is the total area, dude! U still don't know? If u use (4/7)*7=4 units for square, then your circle must be (7/4)*4=7 units for circle. Why so different denominators for both? In mathematics, what u do on the left side must also be the same for the right side for ratio.

If you *7 on left, you must *7 on right too. If you *11 on the right, you must *11 on the left....your math is simply amazing...hee hee

 

Ok, my way is unclear and wrong, so is my answer....happy bo?

Edited April 30, 2014 by Manmaster

[1fast1]

The correct way to express this is 4/11x : 7/11x. I just took out the X from both sides for simplicity. Maybe that's my only mistake.

 

X is the total area, dude! U still don't know? If u use (4/7)*7=4 units for square, then your circle must be (7/4)*4=7 units for circle. Why so different denominators for both? In mathematics, what u do on the left side must also be the same for the right side for ratio.

If you *7 on left, you must *7 on right too. If you *11 on the right, you must *11 on the left....your math is simply amazing...hee hee

 

Ok, my way is unclear and wrong, so is my answer....happy bo?

 

Total area of what? The entire figure? That's WRONG. Because there is overlap between the square and the circle.

 

When you lack precision in Math, your solution is wrong.

 

A proportion or ratio represents the relationship between two quantities. The quantities may be a pure number, or may be any metric measure such as number, length, area, volume, weight, whatever. It doesn't matter. What matters is that if A has measure a units and the ratio of the measure of A to that of B is x:y, then the measure of B is (y/x)*a units. It is *critical* to mention units as long as you're dealing with any measure that's not pure (dimensionless) number. Kapish?

 

If u use (4/7)*7=4 units for square, then your circle must be (7/4)*4=7 units for circle.

 

This is completely correct, and it's what Rayleigh and I have been saying from the start. Are you saying this is wrong?

 

Yes, my math IS amazing. Go look at my other posts.

 

If you hadn't started out with a presumptuous correction of Rayleigh's (largely correct) post, I would've been inclined to be nicer in my replies. But on the other hand, you don't give chances yourself, do you? I still remember the Bitcoin thread where you got embroiled in a flamewar with Unitd (I think). It was clear that you knew a fair bit about economic theory, and I won't dispute that. That thread involved a fair bit of subjectivity, and even then you were trampling all over the viewpoints of others. This thread deals with math, where one can achieve perfect objectivity. Objectively, I am correct, and you are wrong.

 

Now just like I accord respect to your knowledge of economic theory, respect that I very likely know more math than you and let it go.

Edited April 30, 2014 by Turboflat4

[Porker]

 

Total area of what? The entire figure? That's WRONG. Because there is overlap between the square and the circle.

 

When you lack precision in Math, your solution is wrong.

 

A proportion or ratio represents the relationship between two quantities. The quantities may be a pure number, or may be any metric measure such as number, length, area, volume, weight, whatever. It doesn't matter. What matters is that if A has measure a units and the ratio of the measure of A to that of B is x:y, then the measure of B is (y/x)*a units. It is *critical* to mention units as long as you're dealing with any measure that's not pure (dimensionless) number. Kapish?

 

Yes, my math IS amazing. Go look at my other posts.

 

If you hadn't started out with a presumptuous correction of Rayleigh's (largely correct) post, I would've been inclined to be nicer in my replies. But on the other hand, you don't give chances yourself, do you? I still remember the Bitcoin thread where you got embroiled in a flamewar with Unitd (I think). It was clear that you knew a fair bit about economic theory, and I won't dispute that. That thread involved a fair bit of subjectivity, and even then you were trampling all over the viewpoints of others. This thread deals with math, where one can achieve perfect objectivity. Objectively, I am correct, and you are wrong.

 

Now just like I accord respect to your knowledge of economic theory, respect that I very likely know more math than you and let it go.

Radx got how many pubic hair? Your maths amazing also no use :p

[Manmaster]

 

Total area of what? The entire figure. That's WRONG. Because there is overlap between the square and the circle.

 

When you lack precision in Math, your solution is wrong.

 

A proportion or ratio represents the relationship between two quantities. The quantities may be a pure number, or may be any metric measure such as number, length, area, volume, weight, whatever. It doesn't matter. What matters is that if A has measure a units and the ratio of the measure of A to that of B is x:y, then the measure of B is (y/x)*a units. It is *critical* to mention units as long as you're dealing with any measure that's not pure (dimensionless) number. Kapish?

 

Yes, my math IS amazing. Go look at my other posts.

 

If you hadn't started out with a presumptuous correction of Rayleigh's (largely correct) post, I would've been inclined to be nicer in my replies. But on the other hand, you don't give chances yourself, do you? I still remember the Bitcoin thread where you got embroiled in a flamewar with Unitd (I think). It was clear that you knew a fair bit about economic theory, and I won't dispute that. Now respect that I very likely know more math than you and let it go.

Please check with others....I really don't want to argue this.

 

if u say the square is 4 out of 7, it is terribly wrong as the total no. of units is 11.

 

the square is 4 out of 11, 4/11

circle is 7 out of 11, 7/11

 

so if u want to get rid of the denominators, u must do *11 on both sides, so u get 4 units and 7 units. Same actions for both sides!

 

U can't do (4/7)*7 = 4 units for square and (7/4)*4) = 7 units for circle. This defies math principles.

 

Both sides must have the same denominators and also have the same actions on both sides if you are comparing 2 things in ratio.

 

Pls go and re-learn your maths!

[1fast1]

Please check with others....I really don't want to argue this.

 

if u say the square is 4 out of 7, it is terribly wrong as the total no. of units is 11.

 

the square is 4 out of 11, 4/11

circle is 7 out of 11, 7/11

 

so if u want to get rid of the denominators, u must do *11 on both sides, so u get 4 units and 7 units. Same actions for both sides!

 

U can't do (4/7)*7 = 4 units for square and (7/4)*4) = 7 units for circle. This defies math principles.

 

Both sides must have the same denominators and also have the same actions on both sides if you are comparing 2 things in ratio.

 

Pls go and re-learn your maths!

 

Point out to me EXACTLY where I said (verbatim) in any of my posts not quoting you: "the square is 4 out of 7".

 

If you can't, you're just being an idiot arguing a strawman.

[Manmaster]

 

Point out to me EXACTLY where I said (verbatim) in any of my posts not quoting you: "the square is 4 out of 7".

 

If you can't, you're just being an idiot arguing a strawman.

Quote:

 

Rayleigh did NOT assign "7" (pure number) as the area. He said "7 units". That makes all the difference in the world. Granted that I would recommend a little more clarity by stating at the outset: "Let the area of the circle be 7 units. Then the area of the square is (4/7)*7 = 4 units". But this is a small point, and his meaning is still far clearer than yours.

 

End Quote.

 

You've stated very clearly in your aforesaid post (4/7)*7 = 4 units. Do u know what does this mean?

 

This means that the area of square is 4 out of 7 parts or units and you can get rid of the denominator by multiplying the total no. of parts or units (7).

 

This is TERRIBLY wrong! If you get this important part wrong, your whole logic is wrong.

 

The area of the square is (4/11)*11 = 4 units.....Got it? Just like the area of the circle is (7/11)*11 = 7 units.

 

Don't try to be a smart aleck again, you will end up looking amazingly stupid with your amazingly maths (DIS) ability.

[RadX]

it would be good to see parties coming and discussing the issue and not adding end lines that border on the personal affronts. This gets nobody anywhere.

 

Manmaster in particular posts challenges and drew first blood. Respect the views of others and what they have posted. We do not condone shoving your bloody views unto others.

 

This will be my final warning before I impose any form of issuance with regard to maintaining the peace here.

 

 

[1fast1]

Quote:

 

Rayleigh did NOT assign "7" (pure number) as the area. He said "7 units". That makes all the difference in the world. Granted that I would recommend a little more clarity by stating at the outset: "Let the area of the circle be 7 units. Then the area of the square is (4/7)*7 = 4 units". But this is a small point, and his meaning is still far clearer than yours.

 

End Quote.

 

You've stated very clearly in your aforesaid post (4/7)*7 = 4 units. Do u know what does this mean?

 

This means that the area of square is 4 out of 7 parts or units and you can get rid of the denominator by multiplying the total no. of parts or units (7).

 

This is TERRIBLY wrong! If you get this important part wrong, your whole logic is wrong.

 

The area of the square is (4/11)*11 = 4 units.....Got it? Just like the area of the circle is (7/11)*11 = 7 units.

 

Don't try to be a smart aleck again, you will end up looking amazingly stupid with your amazingly maths (DIS) ability.

 

WHAT?! Do you even understand what a ratio is? If you don't look it up.

 

A ratio of 4:7 of two quantities A and B means that A is (4/7) of B and B is (7/4) of A.

 

A is ALSO 4/(4+7) = 4/11 of the TOTAL of A and B, and B is ALSO 7/(4+7) = 7/11 of the TOTAL of A and B, which is what you're harping on and on about in your stubborn ignorance.

 

But that doesn't change the earlier part which is also completely accurate.

 

You are completely unjustified in calling ME disabled in math. That would be the pot calling the kettle black. I suggest you stop trying to "help" people in your ignorance, since you can't seem to see/admit your error after it's been amply pointed out to you.

 

EDIT: post edited in deference to RadX's wishes.

Edited April 30, 2014 by Turboflat4

[RadX]

 

WHAT?! Do you even understand what a ratio is? If you don't look it up.

 

A ratio of 4:7 of two quantities A and B means that A is (4/7) of B and B is (7/4) of A.

 

A is ALSO 4/(4+7) = 4/11 of the TOTAL of A and B, and B is ALSO 7/(4+7) = 7/11 of the TOTAL of A and B, which is what you're harping on and on about in your stubborn ignorance.

 

But that doesn't change the earlier part which is also completely accurate.

 

Looks like you're the one who's SEVERELY disabled in basic math. I suggest you stop trying to "help" people in your ignorance, since you seem not only too stupid, but also too obstinate, to see/admit your error after it's been amply pointed out to you.

 

 

ok bro...move on. We remain as he observers here and we can see where the challenges to the cerebrum remain.