Page 25 - PBD Plus Matematik T5 (EG)

Matematik Tingkatan 5 Bab 1 Ubahan
25. Selesaikan. TP 4
Solve.
Contoh
Diberi P berubah secara langsung dengan punca kuasa dua Q dan secara songsang dengan R. Jika P = 50
apabila Q = 0.09 dan R = 3, hitung
Given P varies directly as the square root of Q and inversely as R. If P = 50 when Q = 0.09 and R = 3, calculate
(i) nilai R apabila P = 100 dan Q = 0.16,
the value of R when P = 100 and Q = 0.16,
(ii) nilai Q apabila P = 250 dan R = 1.4.
the value of Q when P = 250 and R = 1.4.
√Q 500√Q 500√Q
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P ∝ (i) P = (ii) P =
R R R
k√Q
P = 100 = 500√0.16 250 = 500√Q
R R 1.4
k√0.09 √Q = 0.7
50 = R = 2
3 Q = 0.49
k = 500

(a) Diberi x berubah secara langsung dengan y dan secara songsang dengan z. Jika x = 0.06 apabila y = 3
2
dan z = 10, hitung nilai y apabila x = 0.24 dan z = 0.1.
Given x varies directly as y and inversely as z. If x = 0.06 when y = 3 and z = 10, calculate the value of y when x = 0.24 and z = 0.1.
2
y 2 y 2
x ∝ x =
z 15z
ky 2 y 2
x = 0.24 =
z 15(0.1)
k(3) 2 2
0.06 = y = 0.36
10 y = ±0.6
1
k =
15

(b) Diberi x berubah secara langsung dengan y dan secara songsang dengan punca kuasa tiga z. Jika
x = 0.25 apabila y = 4 dan z = 8, hitung
Given x varies directly as y and inversely as the cube root of z. If x = 0.25 when y = 4 and z = 8, calculate
(i) nilai y apabila x = 0.5 dan z = 64,
the value of y when x = 0.5 and z = 64,
(ii) nilai z apabila x = 30 dan y = 1200.
the value of z when x = 30 and y = 1200.

y 0.125y 0.125y
x ∝ 3 (i) x = 3 (ii) x = 3
√z √z √z
ky 0.125y 0.125(1200)
x = 3 √z 0.5 = 3 √64 30 = 3 √z
k(4) y = 16 3 √z = 5
0.25 = 3
√8 z = 125
k = 0.125

Cuba jawab Praktis SPM 1, K1: S5

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