F.4 Maths

2014-05-27 6:18 pm

The base diameter of a cyclinder is equal to its height. If the total surface area of the cylinder is 54 π cm^2, find its base radius and volume.
(Give your answers in term of π if necessary.)

The mass m g of a radioactive substance after t years s given by m = 6(2)^-0.19t.
(a) Find the mass of the substance after 3 years.
(b)At least how many years later will the mass of the substance be less than 1/20 of its current mass? (Give your answercorrect to the nearest integer.)

更新1:

我也是計得這答案，∴At least 37 years.,仁但正確答案是23years.

回答 (4)

[匿名]

2014-05-28 10:58 pm

✔ 最佳答案

(b)
The mass of the substance at the beginning
= 6 (2)^(-0.19*0)
= 6 g

∵m < 1/20
∴m < 6*(1/20)
m < 3/10

m < 3/10
6 (2)^(-0.19t) < 3/10
2^(-0.19t) < 1/20
log [ 2^(-0.19t) ] < log (1/20)
-0.19t log 2 < log 1 - log 20
-0.19t log 2 < - log 20
0.19t log 2 > log 20
t > ( log 20 ) / ( 0.19 log 2 )
t > 22.74726804
∴At least 23 years.

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YA HOO！知識＋管理員

2014-05-27 11:23 pm

還沒有..

不過在以前一題數學問題裏看看那題的意見時，

大概知道 Stardust 今年的應屆考生，

那題好像是計 Area 的 0.0

2014-05-27 23:08:37 補充：
https://hk.knowledge.yahoo.com/question/question?qid=7014030100010

2014-05-28 18:46:18 補充：
...

作答時沒太留意1/20 of its current mass 的current mass 0.0

current mass = 6

咁1/20 of its current mass = 1/20 * 6 = 3/10 ...

我會刪了我的回答 =.=

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知足常樂

2014-05-27 10:53 pm

你地兩位應屆考生認識了對方沒有？

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Stardust

2014-05-27 8:09 pm

Let base radius be r
2(πr²)+2πr*2r=54π
2πr²+4πr²=54π
6πr²=54π
6r²=54
r²=9
r=3

∴base radius is 3 cm

volume
=π(3)² *2(3)
=9π*6
=54π cm²

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收錄日期: 2021-04-20 15:18:12
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