maths problems( urgent!! )

[匿名]

2009-11-11 11:51 am

1. the question is:
what would be the difference in length between a rope stretched tightly round the Earth and another rope always held 1m above?
the answer is 2pi m because i found if the difference between the radii of two circles is 1cm, the circumferences will be differ by 2pi cm.
However, I don't understand why the radius of the upper circle decreses by 1m if the rope is held 1m above.

2. Show that the distance found by the 3-second rule differ from the distance found by the formula by less than 2.5%.
distance found by the 3-second rule=308
distance found by the formula=315
I am confused about if (315-308)/308x100% or (315-308)/315x100% is correct.

回答 (1)

用戶10012

2009-11-11 3:49 pm

✔ 最佳答案

1) Let radius of inner circle = r, so circumference = 2pr , where p = pi
Radius of outer circle will be ( r + 1) since it is 1m away from the inner circle, and its circumference = 2p(r + 1) = 2pr + 2p,
so difference in length = 2pr + 2p - 2pr = 2p which is independent of r, that means no matter what is the radius of the circles, different in length will be 2p meters if they are 1m apart.
2) This is a matter of English. 3- second rule differ FROM formula means taking the formula figure as the reference of comparison. Answer should then be (308 - 315)/315 x 100% = - 2.22% ( decrease). If it is formula differ FROM 3 - second rule, answer will be (315 - 308)/308 x 100% = + 2.27% ( increase).
Understanding of the following formula is important:
% change = ( NEW value - ORIGINAL value)/ORIGINAL value x 100%.

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