2014 DSE Maths 練習卷 1 Q 6,7,11

11.
(a)
y = bx + m

(b)
當 x = 0, y = 32 :
32 = b(0) + m
m = 32
所以 y = bx + 32

當 x = 100, y = 212 :
212 = b(100) + 32
100b = 180
b = 1.8

m = 32, b = 1.8


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6.
設水面上升 h cm。

實心球體積 = 上升的水所佔的體積
(4/3) × π × 5³ = π × (10/2)² × h
h = 20/3

水位上升 = 20/3cm = 6又2/3cm


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7.
連直線BC。

∠CBD = (1/2)∠COD (對同弧圓周角與圓心角)
∠CBD = (1/2) × 80°
∠CBD = 40°

∠ACB = 90° (半圓內圓周角)

∠CTD = ∠ACB + ∠CBD (ΔBCT 外角)
∠CTD = 90° + 40°
∠CTD = 130°