ice-melting(rate of change)

2008-02-10 4:08 am
A volume of the solid of ice is 192 cm^3.
the ice is now heated and it is melted at a rate
(2t-61) cm^3 per second.
Find the time required to melt the ice. ANS=64s
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The following is my solution, i don't know what's wrong?
Time (s) ice melted
1 2*1-61=-59
2 59+2*2-61=-116
3 -116+2*3-61=-171
4 -171+2*4-61=-224>192
更新1:

Time (s) / ice melted 1 / 2*1-61=-59 2 / 59+2*2-61=-116 3 / -116+2*3-61=-171 4 / -171+2*4-61=-224>192

更新2:

i just want to know what's wrong of my solution!!

更新3:

what is the meaning of -59? is it melting 59 cm^3 of ice in 1 second? or melting 0 cm^3 of ice in 1 second? or condense 59 cm^3 of ice in 1 second?

回答 (2)

2008-02-10 4:33 am
✔ 最佳答案
Volume of ice melted as a function of time is:
V = ∫(t = 0 → t) (2t - 61) dt
= t2 - 61t + C where C is a constant.
At t = 0, V = 0 and therefore, C = 0
So,
V = t2 - 61t
Finally, for melting 192 cm3, time required is:
t2 - 61t = 192
t2 - 61t - 192 = 0
(t - 64) (t + 3) = 0
t = 64 or -3 (rejected)
Therefore time required is 64 s.
參考: My maths knowledge
2008-02-10 4:11 am
XDXD nth is wrong XDXD


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