Question

If a varies directly as the square of b, and a=5 when b=7, find a when b=3. when b=3 a=​

Answer 1

Answer:

When $b=3$

$a=\frac{45}{49}$

Step-by-step explanation:

Given

$a=5$

$b=7$

$a$ ∝ $b^2$  [As $a$ varies directly with square of $b$]

∴ $a=kb^2$

where $k$ represents the constant of proportionality.

Plugging in values to find $k$

$5=k(7)^2$

$5=k(49)$

Dividing both sides by 49.

$\frac{5}{49}=\frac{k(49)}{49}$

$\frac{5}{49}=k$

∴ $k=\frac{5}{49}$

When $b=3$

$a=\frac{5}{49}(3)^2$

$a=\frac{5}{49}(9)$

∴$a=\frac{45}{49}$