A, r and T are three variables.
A is proportional to T2 A is also proportional to r3 T = 47 when r = 0.25
Find r when T = 365 Give your answer correct to 3 significant figures.
Answers
Given : A, r and T are three variables. A is proportional to T²
A is also proportional to r³
T = 47 when r = 0.25
To Find : Value of r when T = 365
Solution:
A is proportional to T² => A = k₁T²
A is also proportional to r³ => A = k₂r³
k₁T² = k₂r³
=> T² = (k₂/k₁)r³
T² ∝ r³
=> T² = kr³
T = 47 when r = 0.25
=> 47² = k (0.25)³
=> 47² = k (1/4)³
=> k = 47² * 4³
T² = kr³
=> T² = 47² * 4³ r³
T = 365
=> 365² = 47² * 4³ r³
=> r = 0.98
Value of r when T = 365 is 0.98
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