CE maths (urgent) 30 points

用戶29701

2012-08-08 6:37 am

Please show the steps of the following questions =]
1.

show the steps in solving (1+sin a - cos^2 a) / [(1+sin a)cos a]

(ans = tan a)

2.

What is the sum of all the positive terms in the geometric sequence 4, -2, 1,...
Show the steps
(Ans=16/3)

3

If a solid metal hemisphere of radius r is melted and recast into 3 identical solid right circular cones of height h and base radius r,

Then what is the ratio r : h?

(Ans = 3:2)

4 Let An be the nth term of an arithmetic sequence. If a1 = a2-6 and a1+a2+a3+...+a28 =1624, then a1 =?

(Ans=-23)

回答 (1)

sioieng

2012-08-08 8:13 am

✔ 最佳答案

1.
(1 + sin a - cos²a) / [(1 + sin a) cos a]
= [1 + sin a - (1 - sin²a)] / [(1 + sin a) cos a]
= [1 + sin a - 1 + sin²a)] / [(1 + sin a) cos a]
= (sin a + sin²a) / [(1 + sin a) cos a]
= [(1 + sin a) sin a] / [(1 + sin a) cos a]
= sin a / cos a
= tan a

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2.
Thesum of all positive terms
= 4 + 1 + (1/4) + ......

It is the sum to infinitive terms of a geometric sequence
with first term (a) = 4 and common ratio (r) = (1/4)

The sum of all positive terms
= a / (1 - r)
= 4 / [1 - (1/4)]
= 4 / (3/4)
= 4 x (4/3)
= 16/3

======
3.
Volumeof the hemisphere = 3 x (volume of the solid circular cones)
(1/2) x (4/3)πr³ = 3 x [(1/3)πr²h]
(2/3)r = h
r/h = 3/2
r : h = 3 : 2

=====
4.
Let d be the common difference of the arithmetic sequence.

a1 = a2 - 6
a1 = (a1 + d) - 6
d = 6

a1 + a2 + a3 + ...... + a28 = 1624
n[2a1 + (n - 1)d]/2 = 1624
28[2a1 + (28 - 1)*6]/2 = 1624
2a1 + 27*6 = 116
2a1 = -46
a1 = -23

參考: sioieng

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