急! CE Maths(Section A)(應該唔係pp)

👨🏻‍🏫 學術台數學

[匿名]

2009-01-12 9:27 am

有三題,

1. The number of sides and the number of vertices of a polyhedron are 15 and 10 respectively. Find the number of faces. (3marks)

2. 請看圖
可能有d 唔清楚, graph= y = 4^x3-6^x2-9x+3
[IMG]http://i104.photobucket.com/albums/m167/indifferentwind/q2.jpg[/IMG]

3. 都係看圖
[IMG]http://i104.photobucket.com/albums/m167/indifferentwind/q3.jpg[/IMG]

要full step, thx~

更新1:

回煩惱即是菩提 : 這是老師就CE課程給我們做的一些練習, 程度是Section A的, 而且應該是他自行出, 或從其他練習題抽出來的, 故應該不是 past paper 的題目。我都有東西想問一下, 請問 Euler formula 應該是中一至中五裡哪一年學的?? 好像沒多印象呢... Orz

更新2:

In Q.3 (a), why OX = 24cm?? sorry about that...

回答 (5)

mathmanliu

2009-01-12 9:54 am

✔ 最佳答案

Q1.
By Euler formula: V-E+F=2, thus 10 - 15 +F=2 =>F= 7
Q2.
8x^3- 12x^2 - 18x - 5=0
=> 4x^3 - 6x^2 - 9x + 3 = 11/ 2
By the given graph, find the x values such that y=f(x)= 11/2
Thus, I guess x= - 0.5 , -0.5 and 2.5 and they are exact roots.

Q3.
a). In △ODX: OX=24, OD=12 , thus ∠DOX= 60 degrees, so is ∠COY
Therefore, ∠XOY= 60 degrees
b). Arc length of XMY= 2π*24 * 60/360 = 8π
Area of OXMY=π*24^2 * 60/360= 96π
c) Circumference = arc length of XMY= 8π=>radius of the cone r = 4
Height of the cone h = √(24^2 - 4^2)= 4 √35
Volume = (1/3) π*r^2*h= 4√35π / 3

2009-01-12 01:55:54 補充：
Correct:
Q3:
c) V= (1/3)π*r^2*h= 16√35π / 3

2009-01-12 02:08:09 補充：
請解釋一下:CE Maths(Section A)(應該唔係pp)
的意思,OK!?

2009-01-12 02:42:49 補充：
應屬立體圖形部分,不知中幾吔! (中三嗎?)

2009-01-12 02:44:36 補充：
From fig5(a), OX=OM=AD= 24

參考: me

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