Question

. A is inversely proportional to the cube of B. If A=3 then B=2. If A=8/9, then find the value of B

Answer 1

A is inversely proportional to the cube of B

⇒ A = k/B³ where k is a constant

Find k:

When A = 3, B = 2

3 = k/2³

k = 3 x 2³

k = 24

Therefore the equation is A = 24/B³

Find the value of B when A = 8/9 :

A = 24/B³

8/9 = 24/B³

8B³ = 24 x 9

8B³ = 216

B³ = 216 ÷ 8

B³ = 27

B = ∛27

B = 3

Answer: The value of B is 3.

Answer 2

Answer:

The value of B is 3

Step-by-step explanation:

Given:

A is inversely proportional to the cube of B

⇒ A = t/B³ where t is a constant

Now , we'll find t

According to 1st condition A = 3, B = 2

∴3 = t/2³

t= 3 x 2³

t= 24

Therefore the equation becomes A = 24/B³

Now we'll find the value of B according to 2nd condition when A = 8/9

A = 24/B³

8/9 = 24/B³

8B³ = 24 x 9=216

B³ = 216 ÷ 8

B³ = 27

B = $27^{1/3}$

B = 3

∴The value of B is 3.

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