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# [M2] Integration Application Problem

## Integration Application Problem

Thank you very much

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 風之男 學院師父 發短消息 加為好友 當前離線 2# 大 中 小 發表於 2022-3-19 05:56 PM (第 59 天) 只看該作者 [顯示] [隱藏] What have you tried? Please show your workings. UID216418 帖子970 精華0 積分118 閱讀權限40 在線時間1832 小時 註冊時間2011-5-4 最後登錄2022-5-14  查看詳細資料 TOP

## 回覆 2# 風之男 的帖子

Here is working

but my answer is not correct

Thank you for helping

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 風之男 學院師父 發短消息 加為好友 當前離線 4# 大 中 小 發表於 2022-3-19 10:18 PM (第 59 天) 只看該作者 The method looks good. Just a minor arithmetic error right after plugging N=160. Also, it would be better to write an inequality (basically, > instead of =, doesn't change much), as the problem specifically said "exceed". Writing an equation in this instance is also fine. Sidenote, natural log is written as ln (ell-en), not In (eye-en). --- See why do I insist on you to show your work? There is no need to go through the integration part again, as you already know how. [ 本帖最後由 風之男 於 2022-3-19 10:21 PM 編輯 ] UID216418 帖子970 精華0 積分118 閱讀權限40 在線時間1832 小時 註冊時間2011-5-4 最後登錄2022-5-14  查看詳細資料 TOP
 妙妙貓 中級學徒 發短消息 加為好友 當前離線 5# 大 中 小 發表於 2022-3-20 07:53 AM (第 58 天) 只看該作者 I have no idea either, I integrated dN/dt to become N = -80ln(t^2-16t+100) + 88 + 80ln100. And then created an inequality 160 > -80ln[(t^2-16t+100)/100] + 88. But I think I did something wrong because I got to 100e^(-9/10) > t^2-16t+100 and I don't know how to solve it. UID520114 帖子75 精華0 積分6 閱讀權限10 在線時間29 小時 註冊時間2022-1-14 最後登錄2022-5-16  查看詳細資料 TOP

## 回覆 4# 風之男 的帖子

Thank you for your clear explanation.

May I know which part of my working is wrong?

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## 回覆 5# 風之男 的帖子

Sorry for disturbing again.

I have calculated this question for several times, I can't still find the answer.

[ 本帖最後由 luckjoe 於 2022-3-20 09:25 PM 編輯 ]

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##### 引用:

Sorry for disturbing again.

I have calculated this question for several times, I can't still find the answer.

No worries. With your working, I'm not sure how you get 3.8176 - the line right after subbing N=160.
This question is really not the friendliest when it comes to actual arithmetic, so... yeah, I'd say scrap everything after subbing N=160, and try again. It's annoying and unproductive, but gotta suck it up.

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## 回覆 6# 風之男 的帖子

I will try it again

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##### 引用:

I have no idea either, I integrated dN/dt to become N = -80ln(t^2-16t+100) + 88 + 80ln100.
And then created an inequality 160 > -80ln[(t^2-16t+100)/100] + 88.
But I think I did something wrong bec ...
Look at the inequality carefully, isn't it just a quadratic inequality in t, just with a lot of annoying constants?
Hope you know how to solve a quadratic inequality.

Note: I didn't check if you actually arrive at the correct inequality. But based on experience you're quite careful with arithmetic, unlike me lol.

[ 本帖最後由 風之男 於 2022-3-20 09:38 PM 編輯 ]

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