Question

Given that b is inversely proportional to a^2 and b=32 when a =1.Find an equation connecting a and b, then find b when a=8

Answer 1

Answer:

1/2

Step-by-step explanation:

b is inversely proportional to a^2, which means,

$b = \frac{k}{ {a}^{2} }$

where, k is a constant.

Now, when b=32 and a=1,

$32 = \frac{k}{ {1}^{2} } \\ k = 32$

Now, the equation becomes

$b = \frac{32}{ {a}^{2} }$

Now, to find b when a=8,

$b = \frac{32}{ {8}^{2} } \\ b = \frac{32}{64} \\ b = \frac{1}{2}$

The equation connecting a and b is b=32/a²

When a=8, b=1/2