F.5 Maths 問題

用戶142711

2008-05-03 6:38 am

(1) It is given that f(X)=X^3 +3X^2 -3. Find the remainder when f(X+1) is divided by (X-1)
A. -3 B. 7 C. 17 D. 24

(2) A right concial container of height 10 cm contains water to the level of 5cm , which the concial container is inverted(a). It is then inverted as upright position(b). Find the depth of water of (b) correct to 2 decimal places.
A. 0.44cm B. 0.75cm C. 1.25cm D. 2.54cm

URGENT!!!!!!!

回答 (1)

sha wan

2008-05-03 7:14 am

✔ 最佳答案

1. f(X)=X^3 +3X^2 -3
f(X+1)=(X+1)^3 +3(X+1)^2 -3
let g(x)=(X+1)^3 +3(X+1)^2 -3
remainder = g(1)
=(1+1)^3 +3(1+1)^2 -3
=8+12-3=17
Answer is C
2. Let V be the Volume of the whole cone
in the inverted cone
ratio of side = 5:10 = 1:2
ratio of volume = 1:8
volume of water =(1/8)V
Let h be the height of "air" cone
Let 10-h be the depth of water in upright position
consider the two cones - cone of air and whole cone
ratio of side = h:10
ratio of volume = h^3:1000
ratio of volume of water to whole cone is
(1000 - h^3):1000
volume of water = [(1000 - h^3 )/ 1000]V

therefore [(1000 - h^3 )/ 1000]V=(1/8)V
[(1000 - h^3 )/ 1000]=(1/8)
(1000 - h^3 ) = 125
(1000 - 125) = h^3
875 = h^3
9.56 = h
depth of water = 10-9.56 = 0.44cm

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