1.) Factorize a2次b+ab2次
2.Round off 405.504 to
(a) the nearest integer
(b)2 decimal places
(c)2 significant figures
3.The total number of stamps owned by John and Mary is 300.If Mary buys 20 stamps from a post office,the number owned by her will be 4 times that owned by John>Find the number of stamps owned by John.
4.In a polar coordinate system,O is the pole. The polar coordinates of the points P and Q are (k,123度) and (24,213度)respectively,where k is a positive constant.It is given that PQ=25.
(a) Is △OPQ a right-angled triangle?
(b)Find the perimeter of △OPQ
Please HELP!!Thank so muych!!!!
數學問題!!!Thank
2012-09-08 8:14 pm
回答 (3)
2012-09-09 3:42 am
✔ 最佳答案
1)a²b + ab²
ab*a + ab*b
= ab(a + b)
=====
2.
(a) 406
(b) 405.50
(c) 410
=====
3.
Method 1 :
Let n be the number of stamps owned by John.
Then, the number of stamps owned by Mary = 300 - n
(300 - n) + 20 = 4n
320 - n = 4n
5n = 320
n = 64
Hence, John owns 64 stamp.
Method 2 :
Let j be the number of stamps owned by John, and m be that owned by Mary.
j + m = 300 ..... [1]
m + 20 = 4j ..... [2]
[1] - [2] :
j - 20 = 300 - 4j
5j = 320
j = 64
Hence, John owns 64 stamp.
=====
4.
(a)
∠QOP
= 213° - 123°
= 90°
Hence, ΔOPQ is a right-angled triangle.
(b)
OP = k
OQ = 24
PQ = 25
In right-angled ΔOPQ :
OP² + OQ² = PQ²
k² + 24² = 25²
k² = 25² - 24²
k² = 49
k = 7 or k = -7 (rejected)
Perimeter of ΔOPQ
= OP + OQ + PQ
= 7 + 24 + 25
= 56
2012-09-08 19:43:32 補充：
The reason of OP² + OQ² = PQ² is Pythagoras' theorem.
參考: micatkie, micatkie
2012-09-09 2:39 am
1)a^2*b+a*b^2
=ab(a+b)
2a)406
2b)405.50
2c)410
3)
Let the number of stamp John own to be x,
then (300-x) is the number of stamp Mary originally own.
(300-x)+20 = 4x
300-x+20 = 4x
320-x=4x
320=5x
x=64
So, John own 64 stamps.
=ab(a+b)
2a)406
2b)405.50
2c)410
3)
Let the number of stamp John own to be x,
then (300-x) is the number of stamp Mary originally own.
(300-x)+20 = 4x
300-x+20 = 4x
320-x=4x
320=5x
x=64
So, John own 64 stamps.
參考: 自己
2012-09-08 9:01 pm
2) a) 406 b) 405.50 c) 400
3) 76
3) 76
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