1) A company purchased 100 T-shirt. The original price of each T-shirt is $10. Later on, the company found that 10 of them are damaged. In order to make 50% profit at least, the company decided to sell the rest at a price of $y each. Find the minimum value of y and the lowest price of each T-shirt. (Correct the answer to the nearest dollar.)
2) If the length of a rectangle is reduced by 20% and its width is increased by 15% , find the percentage change in its area.
3)Michael is going to make an investment. If he wants to have a minimum return of double his principal in 5 years, what should be the corresponding interest rate? Find out one possible interest rate and verify it.
4)If the radius(r) of a sphere increases by 10%, find
a) the percentage change of its total surface area
b) the percentage change of its volume
5)Try to construct a cylinder and a semi-sphere with the same total surface area. Please state the dimensions of the objects and verify youe answers.
6)Given that the slope of the line AB, which is perpendicular to line CD, is 2. Find the coordinates of 2 points possibly being on the line CD. Please verify your answers.
7)Given that a sin x = b cos y = c tan z, what are the possible values of a ,b ,c ,x ,y ,z. Please verify your answers.
8)If the length of the cuboid increases by 10%, the width decreases by 15% and the height increases by 20%, find the percentage change in the volume of cuboid. let l, w and h be the length, width and height of the rectangle.
f3-4 maths
2010-08-24 9:10 pm
回答 (1)
2010-08-25 3:36 pm
✔ 最佳答案
1) Cost of all the 100 T-shirts = $10 x 100 = $1000
Since 10 T-shirts were damaged, the remaining number of T-shirts = 100 – 10 = 90
To make a profit of 50%, total revenue = $1000 / 100 x 150 = $1500
The lowest price of each shirt = $1500/90 = $16.67 at least
y = $16.67 , the minimum price if you want make a profit of 50% (Don’t forget you take the damaged T-shirts into consideration).
2)
Let the original length be 200 m and the width be 100 m;
The area = 200 m x 100 m = 20000 m^2
The new length = 200 x 0.8 =160 m
The new width = 100 x 1.15 = 115 m
The new area = 160 m x 115 m = 18400 m^2
Change in area = 20000 – 18400 = 1600 m^2
Percentage change = 1600/20000 x 100% = 8% (Reduction)
3) Simple interest or compound interest?
What is compounding period? Compounded daily, monthly, semi-annually or annually?
Please specify.
4)
a) the percentage change of its total surface area
surface area of sphere = 4x pi x r^2
new surface area of sphere =4x pi x (1.1r)^2
change in surface area = (4x pi x (1.1r)^2) – (4x pi x r^2) =4x pi x (1.21 - 1)r^2
Percentage change in surface area = change in surface area/original surface area x 100%
[4x pi x (1.21- 1)r^2]/(4x pi x r^2)x100% = [4x pi x 0.121r^2]/(4x pi x r^2)x 100%
= 0.21 x 100%
= 21%
6)
Slope of line AB = 2
Slope of line CD = negave reciprocal of slope CD = -1/2
Two points on CD are A(0, 0) B(2, -1)
Slope of AB = (y2 – y1)/(x2 –x1) = (-1 -0)/(2 -0) = -1/2
7)Given that a sin x = b cos y = c tan z, what are the possible values of a ,b ,c ,x ,y ,z. Please verify your answers.
a = 2, b =2, c = 1
x = 30 degrees , y = 60 degrees z = 45 degrees
Proof:
a sin x = b cos y = c tan z
2 sin 30 degrees = 2 cos 60 degrees = 1 tan 45 degrees
2 (0.5) = 2(0.5) = 1(1)
1 = 1 = 1
8)
Original volume = lxwxh
New volume = 1.1 l x 0.85w x 1.2 h
Change in volume =new vol – old vol
=(1.1 l x 0.85w x 1.2 h) – (lxwxh) = (1.122 – 1) (lxwxh) =0.122(lxwxh)
Percentage change = change in vol/original vol x 100%
= 0.122(lxwxh)/ (lxwxh)x100%
= 12.2%
Insufficient space. Email Question 5 to you.
2010-08-25 07:43:33 補充：
You won't accept Email. Can't Email #5 to you.
收錄日期: 2021-04-29 17:08:53
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100824000051KK00602