f.4 maths - Ans.fyi 參考答案

f.4 maths

2012-09-10 12:31 am

I WANT THEIR ANS AND SHOW THE WORKING STEP PLZ~

1. if z varies directly as y^2 and inversely as x. which of the following must be
constant?
A. xy^2z
B. y^2z / x
C. xz / y^2
D. z / xy^2

2. it is given that x varies directly as y and inversely as z^2. if y is decreased by
10% and z is increased by 20%, then x is decreased by ?%.

3. it is given that y is partly constant and partly varies directly as x. when x=2,
y=17 and when x=4,y=11. find x when y=5.

4. if 1/a : 1/b = 2:3 and a:c = 4:1, then a:b:c = ? : ? : ?

5. if a:b =2:3, a:c = 3:4 and a:d = 4:5, then b:c:d = ?:?:?

6. if (x+2y)/(3x-4y) = 5, then x:y=?:?

7. if x:y =3:4 and 2x+5y=598,find x.

8. if 1 australian dollar is equivalent to 4.96 HKD and 100 japanese yen are
equivalent to 5.33 HKD, how many japanese yen are equivalent to 1 australian
dollar?

9. if 9a^2 - b^2 and ab < 0, then a-b / a+b =?

10. tea A and tea B are mixed in the ratio x:y by weight. A costs $80/kg and B
costs $100/kg. if the cost of A is increased by 10% and that of B is decreased by
12%, the cost of mixture per kg remains unchanged. find x:y.

回答 (1)

不用客氣

2012-09-10 7:54 am

✔ 最佳答案

1.
The answer is : C. xz/y²

z ∝ y²/x
Then z = ky²/x where k is constant
xz/y² = k = constant

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2.
x ∝ y/z²
Then x = ky/z² where k is constant.

When y = yo and z = zo, x = xo :
xo = kyo/zo²

When y = yo(1 - 10%) and z = zo(1 + 20%) :
x = kyo(1 - 10%)/[zo(1 + 20%)]
x = 0.625kyo/zo²
x = 0.625xo

% decrease of x
= [(xo - 0.625xo)/xo] x 100%
= 37.5%

=====
3.
y = k1 + k2x
where k1 and k2 are constant.

When x = 2, y = 17 :
17 = k1 + 2k2 ... [1]

When x = 4, y = 11 :
11 = k1 + 4k2 ... [2]

[2] - [1] :
2k2 = -6
k2 = -3

Put k2 = -3 into [1] :
17 = k1 + 2(-3)
k1 = 23

Hence, y = 23 - 3x

When y = 5 :
5 = 23 - 3x
x = 6

=====
4.
1/a : 1/b = 2 : 3
2*(1/b) = 3*(1/a)
2/b = 3/a
a/b = 3/2
a : b = 3 : 2
a : b = 12 : 8

a : c = 4 : 1
a : c = 12 : 3

a : b : c = 12 : 8 : 3

=====
5.
a : b = 2 : 3 = 12 : 18
a : c = 3 : 4 = 12 : 16
a : d = 4 : 5 = 12 : 15

a : b : c : d = 12 : 18 : 16 : 15
Hence, b : c : d = 18 : 16 : 15

=====
6.
(x + 2y)/(3x - 4y) = 5
x + 2y = 5(3x - 4y)
x + 2y = 15x - 20y
14x = 22y
x/y = 22/14
x : y = 11 : 7

=====
7.
x : y = 3 : 4
Then, let x = 3k and y = 4k

2x + 5y = 598
2(3k) + 5(4k) = 598
k = 23

x = 3(23)
x = 69

=====
8.
1 A$ = 4.96 HKD
A$ : HKD = 4.96 : 1

100 Yen = 5.33 HKD
Yen : HKD = 5.33 : 100
Yen : HKD = 0.0533 : 1

A$ : Yen = 4.96 : 0.0533
0.0533 A$ = 4.96 Yen
1 A$ = 93.06 Yen

93.06 Japanese yen are equivalent to 1 Australiandollars.

=====
9.
What is meant by "9a² - b² and ab < 0" ?

=====
10.
(80x + 100y)/(x + y) = [80(1 + 10%)x + 100(1 - 12%)y]/(x + y)
80x + 100y = 88x + 88y
8x = 12y
2x = 3y
x/y = 3/2
x : y = 3 : 2

參考: micatkie

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