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ice-melting(rate of change)

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發問:

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----------------------------------------------------The following is my solution, i don't know what's wrong?Time (s) ice... 顯示更多 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 ---------------------------------------------------- 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: 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?

最佳解答:

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.

其他解答:

XDXD nth is wrong XDXD
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