5 條 中5 maths

1.z和x^3成正比
z=kx^3,當中k為非零常數
代x=2,z=4
4=k(2^3)
k=1/2
z=1/2x^3
當x=1/2時,
z=1/2(1/2)^3
=1/16
ans:a
2.h^3正比g+10
h^3=k(g+10),當中k為非零常數
代g=10,h=10
10^3=k(10+10)
k=50
h^3=50(g+10)
當h=15時,
15^3=50(g+10)
g=57.5
ans:b
3.f隨d和e^2聯變
f=kde^2,當中k為非零常數
代d=2,e=3,f=6
6=k(2)(3)^2
k=1/3
f=1/3de^2
當d=1/3,f=9時,
9=1/3(1/3)e^2
e^2=81
e=9或-9(rej.)
ans:d
4.n=k1+k2m,當中k1和k2為非零常數
代m=4,n=8
8=k1+4k2......(1)
代m=6,n=2,
2=k1+6k2......(2)
(1)-(2),
6=-2k2
k2=-3
代k2=-3入(1)
8=k1+4(-3)
k1=20
n=20-3m
當m=-1時,
n=20-3(-1)=23
ans:b
5.QSR為等邊三角形
<QRS=60
<QRP=60-32=28
<QSP=28(<s in the same segment)
ans:a
6.<PQR=90(< in semi-circle)
PQ=QR(given)
<QPR=<QRP(base <s,isos.triangle)
<QPR+<QRP+90=180(< sum of triangle)
2<QRP=90
<QRP=45
45+<RQS=112(ext.< of triangle)
<RQS=67
ans:d

sorry for english only
1.
z = kx^3 where k is a constant
4 = k(2^3)
k = 1/2
z = (x^3) / 2
z = [(1/2)^3]/2
z =1/16

2.
h^3 = k(g+10) where k is a constant
10^3 = k (10+10)
k = 50
h^3 = 50(g+10)
15^3 = 50(g+10)
3375 = 50(g+10)
g = 57.5

3.
f = k(de^2) where k is a constant
6 = k(2x9)
k = 1/3
f = (de^2)/3
9 = [(1/3)e^2]/3
27 = (1/3)e^2
81 = e^2
e = 9 or -9 (neglected)

4.
n = c + km where c, k are constant
8 = c +4k ... (1)
2 = c + 6k ... (2)
(1) - (2)
6 = -2k => k = -3
c = 20
n = 20 - 3m
n = 20 -3(-1)
n = 23

5.
angle SPR = angle SQR = 60
consider triangle PSR
angle SPR + 32 + angle PSR = 180
angle PSR = 88
angle QSP = angle PSR - angle QSR
angle QSP = 88 - 60 = 28

6.
angle QSR = 180 - 112 = 68
angle QPR = angle QRP = 45
consider triangle RQS
68 + 45 + angle RQS = 180
angle RQS = 67

這裡有一至六題啊,五題？