F.5 MATHS....幫幫我！急>u

1) Assume y varies directly as the square of x .When x = 10.y = 50
a) Find the value of When x = -8
y = kx^2 (where k is a non-zero constant)
sub x = 10 and y = 50 into y = kx^2
50 = k(10^2)
k = 1/2
so y = (x^2)/2...(1)
sub x = -8 into (1)
y = (-8)^2 / 2
y = 32//

b) Find the %change in x if y increases by 21%
Let the original values of x and y be x0 and y0, and the new values of x and y be x1 and y1
y1 = 121% y0
y0 = (x0)^2 / 2
x0 = sqrt(2 y0)
y1 = (x1)^2 / 2
121% y0 = (x1)^2 / 2
242% y0 = (x1)^2
x1 = sqrt (2.42 y0)
% change in x
= (x1 - x0)/x0 x 100%
= [sqrt (2.42 y0) - sqrt (2 y0)]/sqrt (2 y0) x 100%
= (sqrt2.42 - sqrt2)(sqrt y0) / (sqrt2)(sqrt y0) x 100%
= (sqrt 2.42 - sqrt 2)/sqrt2 x 100%
= 10%//
2) Assume s varies inversely as t. When t = 6, s = 5
a) Express s in terms of t
s = k/t, where k is a non-zero constant
sub t = 6 and s = 5 into s = k/t
5 = k/6
k = 30
thus, s = 30/t //

b) If t = s + 13 , find the values of s and t
sub t = s + 13 into s = 30/t
s = 30/(s+13)
s(s+13) = 30
s^2 + 13s - 30 = 0
(s + 15)(s-2) = 0
s = -15 or s = 2
when s = -15, t = s + 13 = -15+13 = -2
when s = 2, t = s + 13 = 2 + 13 = 15
Thus,
s = -15, t = -2
or s = 2, t = 15//

2008-06-02 18:58:59 補充：
3) The value of a flat $ V varies directly as its floor area Am² and inversely as its age N years. If a flat with a floor area of 42m² has been built for 2 years, its value is $2835000.
a) Express V in terms of A and N

2008-06-02 18:59:07 補充：
V = kA/N, where k is a non-zero constant
2835000 = k(42)/(2)
k = 2835000 / 21 = 135000
thus, V = 135000A/N //

2008-06-02 18:59:14 補充：
b) Find the value of a flat which has been built for 5 years with a floor area of 75m²
Sub A = 75 and N = 5 into V = 135000A/N
V = 135000 x 75 / 5 = 2025000//

2008-06-02 18:59:33 補充：
4) The monthly electricity cost $ E of a company partly varies directly as the number of working days N in that month and partly varies directly as the average temperature TºC of the month
When N = 25 and T = 22, E = 4216. When N = 18 and T = 32, E = 4700.

2008-06-02 18:59:41 補充：
a) Express E in terms of N and T
E = k1N + k2T, where k1 and k2 are non-zero constants
4216 = 25k1 + 22k2...(1)
4700 = 18k1 + 32k2...(2)
(2) x 25 - (1) x 18:
117500 - 75888 = 450k1 - 450k1 + 800k2 - 396k2
41612 = 404k2
k2 = 103
Sub k2 = 103 into (1)
4216 = 25k1 + 22 x 103
k1 = 78
Thus, E = 78N + 103T//

2008-06-02 18:59:49 補充：
b) Find the monthly electricity cost if the number of working days was 14 and the average temperature was 25 ºC in October.
sub N = 14 and T = 25 into E = 78N + 103T
E = 78 x 14 + 103 x 25 = 3667//

2008-06-02 18:59:52 補充：
c) Find the number of working days in April if the monthly electricity cost of the company was $3723 and the average temperature was 21 ºC in that month.
Sub E = 3723 and T = 21 into E = 78N + 103T
3723 = 78N + 103 x 21
N = 20//

1a)
y=kx^2

when x=10 y=50
50=k(10)^2
k=0.5

y=0.5 x^2

when x=-8
y=0.5 (-8)^2
y=32

1b) let X be the new x Y be the new y
Y=0.5X^2
1.21y=0.5X^2

y=(0.5x^2)/1.21

[(0.5x^2)/1.21 - 0.5x^2]/0.5x^2 x100%

= -17.3553719%

2a) s=kt
when t=6 s=5
5=6k
k=5/6

s=(5/6)t

2b) sub t = s+13 in s=(5/6)t
s=(5/6)(s+13)
6s=5(S+13)
6s=5s+65
s=65

3a) V=xA/N
283500= x42/2
x= 13500

V=13500A/N

3b) V=13500(75)/5
V=202500

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