[求助]又要大家帮忙了，这次是数学题

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?

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

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

引用

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？

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?

引用

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.

引用

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？

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

i dun think it is physics