不懂做數學功課...(中一級的(英文))

Akari

2013-06-28 1:32 am

請教我做下列題目:

1.The weight of 6 people are56.4kg,89.4kg,78.2kg,88.3kg,76.4kg and 93.3kg.
Given that the limit of the total weight of these 6 people is 490kg.Patrick
estimates the sum by rounding up the weights to the nearest 10kg.Can he
conclude from the estimate whether the total weight exceeds the limit?

2.The general term of a sequence is T(n)= n+2/n+1.Find the value of
T(1)*T(2)*...*T(100).

3.Expand (ay+b)(ay-b).

4.The population of a country was increased in the past 4 years.The annual
percentage increases are 20%,25%,30% and 10% respectively.What is the
overall percentage increase in these 4 years.

5.A rectangular prism,the length,the width and the height of the prism are all
increased by 50%,find the precentage increase of the total surface area and
the volume.

6.A figure A is first reflected about a line L and then translted to obtain the
image A'.If we reverse the order of the transformations,can we claim that we
must obtain the same image A'?

謝謝!(^_^)

回答 (1)

用戶10012

2013-06-28 2:22 am

✔ 最佳答案

1.
Sum of the weights after rounding up to the nearest 10kg
= 60 + 90 + 80 + 90 + 80 + 100 = 500kg that exceeds the limit of 490kg. So we can conclude from the estimate that the total weight exceeds the limit.
2.
T(1) = (1 + 2)/(1 + 1) = 3/2
T(2) = (2 + 2)/(2 + 1) = 4/3 etc.
so T(1)*T(2)*T(3)*..... T(100) = (3/2)(4/3)(5/4)(6/5)......(102/101) = 102/2 = 61.
3.
(ay + b)(ay - b) = (ay)^2 - bay + bay - b^2 = a^2y^2 - b^2.
4.
Overall increase
= (1 + 20%)(1 + 25%)(1 + 30%)(1 + 10%) = (1.2)(1.25)(1.3)(1.1) = 2.145
So overall % increase = (2.145 - 1) x100% = 114.5%
5.
(a) New surface area after the increase = 6 x (1 + 50%)(1 + 50%)
= 13.5
So % increase in surface area = (13.5 - 6)/6 x 100% = 125%.
(b) New volume = (1 + 50%)(1 + 50%)(1 + 50%) = 3.375
so % increase in volume = (3.375 - 1) x 100% = 237.5%
6.
No.
Example : Reflect A(- 5, 3) about the y - axis and then translate upwards by 3 units become A'(5, 6).
But reflect A'(5,6) about the y - axis and then translate upwards by 3 units become (-5, 9)

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