# Quod Erat Demonstrandum

## 2017/03/19

### 盛水水深

Filed under: Additional / Applied Mathematics,HKCEE,NSS — johnmayhk @ 12:43 下午
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$(H-\sqrt[3]{H^3-h^3})$ 單位。

## 2014/05/20

### 兩個等差數列

Filed under: HKCEE,mathematics,NSS — johnmayhk @ 6:42 下午
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## 2012/07/25

### 根中根

Filed under: Additional / Applied Mathematics,HKCEE,NSS — johnmayhk @ 11:40 上午

$\sqrt{3+\sqrt{8}}=1+\sqrt{2}$

$\sqrt{3+\sqrt{7}}$

## 2011/10/03

### 無題

Filed under: Additional / Applied Mathematics,HKCEE,NSS — johnmayhk @ 7:39 下午

Refer to the figure, the shaded region shown is bounded by the curves $y=\sin (2x)$ and $y=2\cos x$. Find the area of the shaded region.

## 2011/10/01

### 小心切線

Filed under: Additional / Applied Mathematics,HKCEE,NSS — johnmayhk @ 9:02 上午
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Find the equation of tangent to the curve

$x^3+x^2y-2x^2+xy^2-2xy+x+y^3+y=0$ ………. (*)

at (1,0).

## 2011/05/24

### 中四數學教科書某習題

Filed under: HKCEE,NSS — johnmayhk @ 11:21 上午

According to the graph above, find the values of $a$ and $k$.

## 2010/07/22

### 暑期無聊閱讀

Filed under: Additional / Applied Mathematics,HKALE,HKCEE — johnmayhk @ 9:02 上午
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If you worked for a mining company the following might be a typical problem:

There are two intersecting mine shafts that meet at an angle of 123$^o$, as shown in the figure above. The straight shaft has a width of 7 feet, while the entrance shaft is 9 feet wide. What is the longest ladder that can be negotiate the turn? You can neglect the thickness of the ladder members, and assume it is not tipped as it is maneuvered around the corner. Your solution should provide for the general case in which the angle, A, is a variable, as well as the widths of the shafts. (more…)

## 2010/04/15

### 無聊數學教學

Filed under: HKCEE,Junior Form Mathematics,mathematics,NSS — johnmayhk @ 6:05 下午
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【其一】

1. If the equation $k^2x^2 - (k+2)x + 1 = 0$ has real roots and k is a constant. find the range of values of k.

2. If the quadratic equation $k^2x^2 - (k+2)x + 1 = 0$ has real roots and k is a constant. find the range of values of k. (more…)

## 2010/04/05

### 心在線上

L.U. 的一道舊題目，見下：

$y = m_1x + \frac{a}{m_1}$
$y = m_2x + \frac{a}{m_2}$
$y = m_3x + \frac{a}{m_3}$

## 2010/03/28

### 學生問數

Filed under: HKCEE — johnmayhk @ 10:46 下午
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## 2010/03/22

### 無聊：概率問法

Filed under: HKCEE,mathematics — johnmayhk @ 9:45 上午
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“Box A contains 3 white balls and 1 black ball…a ball is randomly drawn from box A…find the proabability that a black ball is drawn…"

1/4

## 2010/03/21

### 三角方程的通解

Filed under: Additional / Applied Mathematics,HKCEE — johnmayhk @ 9:41 下午
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Find the general solution of

$\tan7\theta + \cot2\theta = 0$ … … … … (*) (more…)

## 2010/03/04

### 三角習題的問法

Filed under: Additional / Applied Mathematics,HKCEE,NSS — johnmayhk @ 12:43 下午
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$(1 + \tan 1^o) \times (1 + \tan 2^o) \times (1 + \tan 3^o) \times \dots \times (1 + \tan 44^o) = ?$

（Fig. 1）