KaiKai T asked in 社會與文化語言 · 1 decade ago

微積分英翻中問題 (急)20點 翻譯就好不用教我算

An efficiency study of the morning shift at a certain factory indicates that an average

worker who arrives on the job at 8:0 a.m. will have produced

Q(t)=-t三次方 6t二次方 24t

units t hours later

a. compute the worker`srate production at 11:00 A.M.

b. At what rate it the worker`srate of production changing with respect to time at 11:00 A.M. ?

solution

a. the worker`s rate of production is the first derivative

R(t)=Q`(t)=-3二次方 12t 24

of the output Q(t). the rate of production at 11:00 A.M. (t=3)is

R(3)=Q`(3)=-3(3)二次方 12(3) 24=33

=33units per hour

b.The rate of change of the rate of production is the second derivative

R`(t)=Q"(t)=- 6(3) 12

of the output function. At 11:00 A.M. ,this rate is

R`(3)=Q"(3)=- 6(3) 12= - 6 units per hour per hour

The minus sign indicates that the worker`s rate of production is decreaasing ; that is,

the worker is slowing down.The rate of this decrease in efficiency at 11:00 A.M. is

6 units per hour per hour

請幫我翻譯 不用告訴我怎樣算

因為我不會打出數字的次方 所以用中文^^"

1 Answer

Rating
  • 欣儀
    Lv 5
    1 decade ago
    Favorite Answer

    有一個效率研究顯示,在某個工廠的早班工人如果在早上8點抵達工作崗位的話,他們的產能是:Q(t) = -t3 6t2 24t   個/ t小時後。a. 計算工人在早上11點的生產速度。b. 在早上11點時,工人的生產速度跟著時間的變動是多少?解答a. 工人的生產速度計算方式是用一階導數算出:Q(t)產出 是  R(t) = Q'(t) = -3t2 12t 24那生產的速度就是 R(3)=Q`(3)=-3(3)2 12(3) 24=33 =33個/小時(11:00AM => t =3)b. 變動的速度就是用二階導數算出:R`(t)=Q"(t)=- 6(3) 12 在11點的時候,這個速度是R`(3)=Q"(3)=- 6(3) 12= - 6 個/小時負數的意思是工人的生產速度正在降低,代表工人開始緩慢了起來。在早上11點生產速度的降低率是6個/小時。

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