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**ganesh****Moderator**- Registered: 2005-06-28
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**Excellent performance, Devante` and mathsyperson,You are correct.I wonder how you manage to do it in under 10 seconds. **

54. What is the volume of a room of length 12 feet, breadth 12 feet and height 12 feet?

55. How many square meters is a hectare?

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**Devantè****Real Member**- Registered: 2006-07-14
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54. 1728

55. There are 10,000 square meters in a hectare.

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**ganesh****Moderator**- Registered: 2005-06-28
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YOU ARE ABSOLUTELY RIGHT, DEVANTE`.

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**Toast****Real Member**- Registered: 2006-10-08
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Are we allowed to use calculators?

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**ganesh****Moderator**- Registered: 2005-06-28
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NO................................................

All the calculations should be done by the brain

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**ganesh****Moderator**- Registered: 2005-06-28
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56. What is sin²360° + cos²360° ?

57. What are the prime factors of 1001?

58. Is 4096 a perfect square?

59. How much percentage is 4 greater than 3?

60. What is the value of 2^10?

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**mathsyperson****Moderator**- Registered: 2005-06-22
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56. 1, just like any other sin² + cos² thing. In this case it's even easier though, because it's just 0 + 1.

57. 11 and 91. You can recognise that it's a multiple of 11 with the nifty trick I used before, and then divide by 11 to get the 91.

58. 4096 = 2^12 = (2^6)² = 64². So yes. I know my powers of 2 too well.

59. (4-3)/3 x 100% = 33.333...%

60. 2^10 = 1024.

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It wanted to be normal.

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**Devantè****Real Member**- Registered: 2006-07-14
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56. 1

57. 11 and 91 - That's what I got, at least

58. 4096. I have studied the doubling of numbers (especially 2) for a long time. Didn't have to think much

59. 33.333....(recurring)

60. 1024 (I know my doubles and exponents of 2 )

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**ganesh****Moderator**- Registered: 2005-06-28
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Devante`and mathsy,

Your answers are all correct.

I wonder whether you use a calculator.

The prime factors of 1001 are 7, 11, 13.

Very well done, Devante`!

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**ganesh****Moderator**- Registered: 2005-06-28
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61. If 12 numbers is a dozen, what is 12 dozens?

62. What is the significance of 9.8 m/s² ?

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**Devantè****Real Member**- Registered: 2006-07-14
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ganesh wrote:

Devante`and mathsy,

Your answers are all correct.

I wonder whether you use a calculator.

The prime factors of 1001 are 7, 11, 13.

Very well done, Devante`!

No, no calculators. I solve them in my head. Sometimes I say the working out to myself.

61. 12^2 = 144, simple tables

62. To convert between units of force and mass, we need to know the strength of gravity. Usually this is the so-called standard gravity (approximately 9.8 m/s² or 32 ft/s²).

To extend on question 62:

Plugging this value into Newton's second law, *F = ma* (force = mass × acceleration), we see that a one-kilogram mass experiences a gravitational force of 1 kg × 9.8 m/s² = 9.8 newtons. In general, to convert mass in kilograms to force in newtons (at the earth's surface), multiply by 9.8. Conversely, to convert newtons to kilograms divide by 9.8. (32 is the conversion factor for US Customary Units).

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**mathsyperson****Moderator**- Registered: 2005-06-22
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Oh, boo. I can't believe I forgot to split 91. That's annoying. Ah well.

And I agree with both of Devanté's most recent answers. I know my squares almost as much as I know by powers of 2, and I had to use the 9.8 one very frequently for about 2 years of a mechanics course, so I'm not about to forget it.

Why did the vector cross the road?

It wanted to be normal.

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**Devantè****Real Member**- Registered: 2006-07-14
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13?! Ugh, I didn't even think of that. >_>

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**ganesh****Moderator**- Registered: 2005-06-28
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61. 12 dozens is a gross.

62. 9.8 is the acceleration due to gravity. You are right, Devante` and mathsyperson, this is often used in mechanics.

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**Devantè****Real Member**- Registered: 2006-07-14
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For #61, I wasn't sure which you wanted, twelve dozen as a number of gross.

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**ganesh****Moderator**- Registered: 2005-06-28
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63. What are the prime factor(s) of 256?

64. What is the value of 7 x 7 x 7?

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**mathsyperson****Moderator**- Registered: 2005-06-22
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63. 256 = 2[sup]8[/sup]. Yay for powers of 2!

64. 343. Yay for cubes!

Why did the vector cross the road?

It wanted to be normal.

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**Devantè****Real Member**- Registered: 2006-07-14
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63. 2^8

64. 343; knew off by heart

(Powers of 2! or 2? )

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**mathsyperson****Moderator**- Registered: 2005-06-22
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I had a feeling that someone would go pedantic on me. But 2! = 2 so it doesn't matter so ha.

Why did the vector cross the road?

It wanted to be normal.

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**Devantè****Real Member**- Registered: 2006-07-14
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Yes, I love to comment on typos.

At least there isn't a value for '2?'. Or, as far as I know.

Also, 2! = two!?

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**John E. Franklin****Member**- Registered: 2005-08-29
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Is the special number 26 from Avogadro's number?

**igloo** **myrtilles** **fourmis**

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**ganesh****Moderator**- Registered: 2005-06-28
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No, John.

26 is the only number jammed between a perfect square (25) and a perfect cube (27). I had read this somewhere but I don't know how that can be proved.

Avogadro Number is roughly 6.023x10^23.

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**ganesh****Moderator**- Registered: 2005-06-28
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65. What is 2^20?

66. How many prime factors are there in 729?

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**Devantè****Real Member**- Registered: 2006-07-14
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65. 1048576 (a long time ago, we had a competition to see who could get the farthest in doubling from 1 in 2 minutes, plus knowing doubles)

66. 729 = 3x3x3x3x3x3

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**ganesh****Moderator**- Registered: 2005-06-28
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Devante`,

Thats absolutely remarkable performance.

67. How many prime factors does 7776 have?

68. Whats the value of 7!?

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