Answer:
When [tex]b=3[/tex]
[tex]a=\frac{45}{49}[/tex]
Step-by-step explanation:
Given
[tex]a=5[/tex]
[tex]b=7[/tex]
[tex]a[/tex] ∝ [tex]b^2[/tex] [As [tex]a[/tex] varies directly with square of [tex]b[/tex]]
∴ [tex]a=kb^2[/tex]
where [tex]k[/tex] represents the constant of proportionality.
Plugging in values to find [tex]k[/tex]
[tex]5=k(7)^2[/tex]
[tex]5=k(49)[/tex]
Dividing both sides by 49.
[tex]\frac{5}{49}=\frac{k(49)}{49}[/tex]
[tex]\frac{5}{49}=k[/tex]
∴ [tex]k=\frac{5}{49}[/tex]
When [tex]b=3[/tex]
[tex]a=\frac{5}{49}(3)^2[/tex]
[tex]a=\frac{5}{49}(9)[/tex]
∴[tex]a=\frac{45}{49}[/tex]
