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標題: 一條問題 - Applications of Differentiation : Rate of Change [打印本頁]

作者: oscar 時間: 27/7/2005 11:19 AM
標題: 一條問題 - Applications of Differentiation : Rate of Change
In the figure, ABCD is a square of side a cm. P is a variable point on AB such that angle ADP = α and angle BCP = θ. If θ increases at a rate of 1 rad./sec when θ = π/6, find the rate of change of α.

(Copied from New Progress in Additional Mathematics 3 Exercise 15.5 Question 17)

作者: 抹茶可樂 時間: 27/7/2005 08:36 PM
(First we find out the relationship between αandθ)
AP+PB=AB
ADtanα+BCtanθ=AB
Since AD=BC=AB
tanα+tanθ=1
(It implies that the sizes of angles are indepedent to the length of square)

When θ=π/6, PB=atanπ/6=√3a/3
tanα=AP/AD=1-1/√3

(secα)^2．dα/dt+(secθ)^2．dθ/dt=0
[1+(tanα)^2]dα/dt+[1+(tanθ)^2]dθ/dt=0
[1+(1-1/√3)^2]dα/dt+[1+1/3](1)=0
(7/3-2/√3)dα/dt=-4/3
dα/dt=-4/(7-2√3) rad/sec

(α is decresing)

[ Last edited by 落雷 on 2005-7-27 at 08:40 PM ]

作者: oscar 時間: 29/7/2005 11:42 AM

Originally posted by 落雷 at 2005-7-27 20:36:
(First we find out the relationship between αandθ)
AP+PB=AB
ADtanα+BCtanθ=AB
Since AD=BC=AB
tanα+tanθ=1
(It implies that the sizes of angles are indepedent to the length of square)

Wh ...

係喎...
我唔記得將sec^2 α轉做1+tan^2 α添...
唔該晒！[E-Hap]

作者: 細薯 時間: 29/7/2005 01:04 PM
我唔識ge．．>_<
CE ga﹖

作者: oscar 時間: 29/7/2005 10:03 PM

Originally posted by smallpotato226 at 2005-7-29 13:04:
我唔識ge．．>_<
CE ga﹖

當然啦...
不過係中五先教....
我都係學定先je...

作者: JOHNLAM17 時間: 29/7/2005 10:53 PM

Originally posted by oscar at 2005-7-29 10:03 PM:

當然啦...
不過係中五先教....
我都係學定先je...

你好勁ar....
我一望到a.maths第一課(mathematical induction<--唔記得左個名)就唔想再望=.=
不過果d 唔知咩(q字頭的)equations 就易d

作者: oscar 時間: 29/7/2005 11:45 PM

Originally posted by JOHNLAM17 at 2005-7-29 22:53:

你好勁ar....
我一望到a.maths第一課(mathematical induction<--唔記得左個名)就唔想再望=.=
不過果d 唔知咩(q字頭的)equations 就易d

第一課係MI？唔係Quadratic Equations and Absolute Values咩？
其實MI都係prove je...
學學下就會覺好easy
Quadratic Equations係A Maths最容易...唔識就...

作者: 細薯 時間: 31/7/2005 12:53 PM
MI 最易 bor....
唔使溫ge....
(個人覺得)

作者: oscar 時間: 31/7/2005 10:47 PM

Originally posted by smallpotato226 at 2005-7-31 12:53:
MI 最易 bor....
唔使溫ge....
(個人覺得)

我覺得最易係Quadratic、MI同Binomial
最難係Coordinate同Circle...(因為成日都唔記得d formulae...)

作者: 丫奴 時間: 3/8/2005 08:28 AM

Originally posted by smallpotato226 at 2005-7-29 01:04 PM:
我唔識ge．．>_<
CE ga﹖

我地學校中四已經教ｒａｔｅ　ｏｆ　ｃｈａｎｇｅ．．．．．

作者: 細薯 時間: 3/8/2005 11:48 AM

Originally posted by 丫奴 at 2005-8-3 08:28 AM:

我地學校中四已經教ｒａｔｅ　ｏｆ　ｃｈａｎｇｅ．．．．．

咁你地D A.Math.咪教得好快?

作者: 丫奴 時間: 3/8/2005 12:00 PM

Originally posted by smallpotato226 at 2005-8-3 11:48 AM:

咁你地D A.Math.咪教得好快?

好煩就真－，－

作者: oscar 時間: 3/8/2005 02:06 PM
照道理應該教緊Locus/Vector

作者: dolphin_ice 時間: 4/8/2005 12:43 PM

Originally posted by oscar at 2005-8-3 02:06 PM:
照道理應該教緊Locus/Vector

its is form5 for UK to learn these @@|||

作者: 細薯 時間: 4/8/2005 03:41 PM
我地差1/2 內容才教完......=.="

作者: oscar 時間: 5/8/2005 12:55 AM

Originally posted by smallpotato226 at 2005-8-4 15:41:
我地差1/2 內容才教完......=.="

差一半什麼內容才教完什麼？
Locus?

作者: 細薯 時間: 9/8/2005 03:41 PM

Originally posted by oscar at 2005-8-5 12:55 AM:

差一半什麼內容才教完什麼？
Locus?

Vector
Differentiation
Application of differentiation
Intergration(all)

作者: 火火火火火 時間: 10/8/2005 08:22 AM
哎.....我連第二課書都未教(circle個d)
只有自己屋企自習,有小小唔明呀.....
我差一課,唔知趕唔趕得到課程呀.哎

作者: oscar 時間: 10/8/2005 11:47 PM

Originally posted by 火火火火火 at 2005-8-10 08:22:
哎.....我連第二課書都未教(circle個d)
只有自己屋企自習,有小小唔明呀.....
我差一課,唔知趕唔趕得到課程呀.哎

我聽我校的Form4-->Form5，他們A. Maths只教到Straight Lines...
慢爆....

作者: 火火火火火 時間: 11/8/2005 08:23 AM
我校連Straight Lines都未教,
要中五教十幾課書...
我諗都教唔晒...

作者: oscar 時間: 11/8/2005 11:45 AM

Originally posted by 火火火火火 at 2005-8-11 08:23:
我校連Straight Lines都未教,
要中五教十幾課書...
我諗都教唔晒...

嘩...什麼先生來的...
教得還比龜慢...

作者: 火火火火火 時間: 12/8/2005 08:37 AM
= =
中四大半個學期都係教第一册
話要顧住ｄ唔明既學生
重要補課先教完第二册第一課
問你死未．．．．．．

作者: oscar 時間: 12/8/2005 10:25 AM

Originally posted by 火火火火火 at 2005-8-12 08:37:
= =
中四大半個學期都係教第一册
話要顧住ｄ唔明既學生
重要補課先教完第二册第一課
問你死未．．．．．．

我諗你準備定自修好d啦...

作者: 火火火火火 時間: 13/8/2005 08:14 AM
...............
不過我都開始緊,
但冇時間開第三册
＝　＝

作者: dolphin_ice 時間: 13/8/2005 10:15 AM

Originally posted by 火火火火火 at 2005-8-12 08:37 AM:
= =
中四大半個學期都係教第一册
話要顧住ｄ唔明既學生
重要補課先教完第二册第一課
問你死未．．．．．．

快塭補習啦！
咁樣唔掂！

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