Question

25. 1 It is given that A is directly proportional to r where r> 0 and A = 75 when r = 5. Find (a) the value of A when r = 4, (b) the value of r when A = 147, (c) the change in the value of A when the value of ris doubled. r​

Answer 1

Answer:

Given:

A is directly proportional to R2

R is inversely proportional to T

Formula:

If x is directly proportional to y, then x α y

If x is inversely proportional to y, then x α 1/y

Calculation:

A α R2      ----(1)

R α 1/T

⇒ R2 α 1/T2      ----(2)

From equation (1) and equation (2)

A α 1/T2

⇒ A = k/T2                           (K = constant)

100 = k/52

⇒ 100 = k/25

⇒ k = 100 × 25

⇒ k = 2500

Again,

A = k/T2

200 = 2500/T2

⇒ T2 = 2500/200

⇒ T2 = 25/2

⇒ T = √25/2

⇒ T = 5/√2

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