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title: Untitled

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111數學分科測驗
224
-324
1
-14
135
234
-24
3
-35
3
-25
13
-14
48
-42
sqrt(5)/5, 2*sqrt(5)/5
3


1.
10 100 1000 10000
b = log10 100 + log100 1000 + log1000 10000
= 2 + 1 + 0.5 + 1/3 = 3.5 + 1/3

2.
1 -1 1
2  c 3
3 -3 c
c^2 - 6 - c = 0
c = -2, 3

3.
p = (cos(pi/4), y, z)
x = sqrt(2)/2
x^2 + z^2 = 1/2 + z^2 = 6/9 = 2/3
z^2 = 4/6 - 3/6 = 1/6

4.
f = x^3 + 2x^2 - 2x + k
g = x^2 + ax + 1

(x^2 + ax + 1)(x + k) = f
= x^3 + ax^2 +   x
      + kx^2 + kax + k

a + k = 2
ka + 1 = -2
a = 2 - k
k*(2 - k) = -3
k^2 - 2k - 3 = 0
k = -1, 3
a = 3, -1
a^2 < 4


5.

6.
(0,0) (1,0)       (0,1)
(0,0) (3,sqrt(3)) (-sqrt(3), 3)
0 1 0 0
0 0 1 0 = 1/2

0 3 -c 0
0 c 3  0 = (9 + 3) / 2 = 6

a b 1 0
c d 0 1

a = 3
c = sqrt(3)
b = -sqrt(3)
d = 3

3      -sqrt(3)
sqrt(3) 3

2sqrt(3) * sqrt(3)/2, -1/2
                 1/2, sqrt(3)/2
                 
    
7.

8.

9.
1/5 * 1/5 + 4/5 * 1/5 * 1/5
= 9/125
125/9 = 13

10.
1234
EMS
3*4*4=48

--
1234
V

E
 ABC 6

  E
AB C 6
 ABC 6
 C   3
   C 3
   
   E
ABC  6
 ABC 6
 C   3
  C  3
  
11.

      ^
  p   |
      |
------------->

z = cosv + isinv
z^3 = cos3v + isin3v
p theta = pi - 37deg
(-3/5 - cos3v)^2 + (4/5 - sin3v)^2
=(-3/5 - cosv)^2 + (4/5 - sinv)^2

3 cos3v - 4 sin3v
= 3 cosv - 4 sinv

pi - 37 - v = 3v - pi + 37
pi = 2v + 37
(pi - 37) / 2

(1 + cos2U)/2
(1 - cos2U)/2

12
