『漫游』酷论坛>『海外生活』>[求助]又要大家帮忙了 ..

[求助]又要大家帮忙了，这次是数学题

iou1985@2005-01-23 06:33

The rate at which the volume of a mothball evaporates from solid to gas is proportional to the surface area of the ball. Suppose that a mothball has been observed at one time to have a radius of 0.5 inches and, six months later, a radius of 0.25 inches.


(a) Express the radius (in inches) of the mothball as a function of time t (in months).

(b) How many months from the initial measurement must pass before the mothball disappears completely?
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iou1985@2005-01-23 06:35

还有，问一下大家

如果知道一个curve的式子，怎么找它的 orthogonal trajectories？
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seiyafan@2005-01-23 06:55

1) DV/dt = 4*Pi*r^2

V(t)=4*Pi*r^2*t + C
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1111111@2005-01-23 07:11

I don't agree because your V is always going up
and r cannot be constant, it is changing do to time.
The formula has r as constant.
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iou1985@2005-01-23 07:12

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最初由 seiyafan 发布
1) DV/dt = 4*Pi*r^2

V(t)=4*Pi*r^2*t + C


不是太懂。。。。可以说详细一点吗？
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iou1985@2005-01-23 07:20

啊，书上有答案，答案是

A） r(t)= -(1/24)t+1/2

B） 一年

但是偶不知道怎么找 r(t) 的说
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JanusWang@2005-01-23 07:22

To be frank, I do not think posting your homework on bbs is good. It is a kind of cheating. If there is on network today, how can u survive?
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iou1985@2005-01-23 07:27

有问题应该问，不是吗？

偶的朋友都不知道这题，因为看见这里很多外国的朋友，所以就来请教的说

如果没有网络的话，偶作业也交不了了，因为作业是上网交的。。。
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seiyafan@2005-01-23 09:08

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最初由 1111111 发布
I don't agree because your V is always going up
and r cannot be constant, it is changing do to time.
The formula has r as constant.


Ya, I forgot that. Thanks for pointing out.
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1111111@2005-01-23 14:20

with the answer, finding step is easier

dV/dt = -4pi*r^2 * C
d(4pi*r^3 /3) /dt = -4pi*r^2 * C
(4/3)*3r^2 *dr/dt = -4pi*r^2 * C
dr/dt = C

r(t) = C*t + Ci
r(0) = 1/2 = 0 + Ci =Ci
r(6) = C*6 + 1/2 = 1/4
C = -1/4 * 1/6 = -1/24

I would ask a question too, someone please answer (not hw)
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iou1985@2005-01-24 03:01

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最初由 1111111 发布
with the answer, finding step is easier

dV/dt = -4pi*r^2 * C
d(4pi*r^3 /3) /dt = -4pi*r^2 * C
(4/3)*3r^2 *dr/dt = -4pi*r^2 * C
dr/dt = C

r(t) = C*t + Ci
r(0) = 1/2 = 0 + Ci =Ci
r(6) = C*6 + 1/2 = 1/4
C = -1/4 * 1/6 = -1/24

I would ask a question too, someone please answer (not hw)


原来是这样，偶还以为 dr/dt 是 (0.25-0.5)/6 的说。。。。。


一开始偶还以为体积跟表面积是成比例的，现在才发现是体积的DERIVATIVE跟表面积成比例。。。

谢谢指教的说
(4/3)*3r^2 *dr/dt = -4pi*r^2 * C 的左边好像漏了个Pi, 是吗？
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water1@2005-01-24 03:59

why is it calculus?????????
but's better than physics
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iou1985@2005-01-24 04:26

why isn't it calculus..........?

i dun think it is physics
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1111111@2005-01-24 07:32

yea, I missed the pi

I don't think this is physics.
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