f.4 Maths

2009-02-26 6:53 am
Use the factor method to solve the quadratic equations involved in the following questions.
1.The smallest of three consecutive positive integers is m, and the product of the other two integers is m+10. What are the three numbers?

Use the method of taking square roots to solve the quadratic equations involved in the following questions.
2. The length of a rectangle is 3 times its width. If the area of the rectangle is 129 cm2, find the length of the rectangle, correct to 3 significant figures.

3. A small square of sides 4 cm is cut from each of the four corners of a square card. The remaining part of the card can be folded to from a box without a lid. If the capacity of the box is 400cm3, find the length of each side of the original square card.

Use the quadratic formula to solve the quadratic equations involved in the followiing questions.
4. The sum of two numbers is 4, and the sum of their squares is 8.5. Find the two numbers.

------------------------------------------------------------------------------
This part, you can use any method to solve the quadratic equation involved in the question.

1. A straight river flows along one side of a rectangular piece of land of area 1200 m2. The other three sides of the land are surrounded by a fence of total length 100 m. Find the length and the width of the piece of land.
更新1:

n = (8 2)/4 ------but 8x2 =16 and 16/4=4 , so why n=2.5 or n=1.5 n = 2.5 or n = 1.5 4 - n = 1.5 or 4 - n = 2.5

回答 (1)

2009-02-26 8:06 am
✔ 最佳答案
1.
The smallest integer is m.
Then, the other two integers are (m + 1) and (m + 2).

(m + 1)(m + 2) = m + 10
m2 + 3m + 2 = m + 10
m2 + 2m - 8 = 0
(m - 2)(m + 4) = 0
m = 2 or m = -4 (rejected)

The three numbers are 2, 3 and 4.

2.
Let the width of the rectangle be w cm.
Then, the length of the rectangle = 3w cm

w x (3w) = 129
3w2 = 129
w2 = 43
w = √43 or w = -√43 (rejected)
3w = 3√43 = 19.7

The length is 19.7 cm.

3.
Let the length of each side of the original square card be y cm.
Then, the base of the box is also a square.
Length of each side of the base of the box = (y - 2 x 4) cm = (y - 8) cm
Height of the box = 4 cm

4(y - 8)2 = 400
(y - 8)2 = 100
y - 8 = 10 or y - 8 = -10
y = 18 or y = -2 (rejected)

The length of each side of the original card is 18 cm.

4.
Let one of the two numbers be n.
Then, the other number = 4 - n

n2 + (4 - n)2 = 8.5
n2 + 16 - 8n + n2 = 8.5
2n2 - 8n + 7.5 = 0
n = [8 √(82 - 4 x 2 x 7.5)]/(2 x 2)
n = (8 2)/4
n = 2.5 or n = 1.5
4 - n = 1.5 or 4 - n = 2.5

The two numbers are 1.5 and 2.5

1.
Let the length of the sides opposite to the river be y m.
Then, the length of each of the other two sides with fence = (100 - y)/2

y x [(100 - y)/2] = 1200
y[100 - y] = 2400
100y - y2 = 2400
y2 - 100y + 2400 = 0
(y - 60)(y - 40) = 0
y = 60 or y = 40
(100 - y)/2 = 20 or (100 - y)/2 = 30

The length and the width are 60 m and 20 m respectively.
Or: The length and the width are 40 cm and 30 cm respectively.
=


收錄日期: 2021-04-29 18:17:05
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090225000051KK02023

檢視 Wayback Machine 備份