Answer:
a) Given that w=81 and k = 0.375 then r = 6
b) Given that s=27 and k = 224 then w=32
Step-by-step explanation:
Step(i):-
Given that W varies directly as r³
⇒ w∝r³
⇒ w = kr³
where 'k' is proportionally constant
given that w= 24 and r =4
⇒ 24 = k (4)³
⇒ k = [tex]\frac{24}{64}[/tex]
⇒ k = 0.375
Step(ii):-
Given that W varies indirectly as 's'
w ∝[tex]\frac{1}{s}[/tex]
W =k [tex]\frac{1}{s}[/tex]
where 'k' is proportionally constant
28 = k ([tex]\frac{1}{8}[/tex])
k = 28 × 8 = 224
Step(iii):-
a) Given that w=81 and k = 0.375
w = kr³
81 = 0.375 (r)³
r³ = 216
r = ∛216 =6
r =6
b)
Given that s=27 and k = 224
W =k [tex]\frac{1}{s}[/tex]
w = 224 ([tex]\frac{1}{27}[/tex])
w = 32
