Question
Download Solution PDFA varies directly as the positive square root of B, and inversely as the cube of C. If A = 15, when B = 27 and C = 2, then find B when A = 9 and C = 2.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A varies directly as the positive square root of B.
A = 15, when B = 27 and C = 2.
Concept used:
If P ∝ Q and P ∝ R, then P ∝ QR and P = H × QR. (Here, H is a constant)
Calculation:
According to the question,
A ∝
So, A ∝
⇒ A = k ×
Now putting A = 15, B = 27 and C = 2 in (1),
A = k ×
⇒ 15 = k ×
⇒ k =
⇒ k =
Now when A = 9 and C = 2,
A = k ×
⇒ 9 =
⇒
⇒ B/3 = 81/25
⇒ B = 243/25
∴ The value of B is
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