Answer:
f = 5.6
Step-by-step explanation:
given the quantities are proportional then the equation relating them is
t = kf² ← k is the constant of proportionality
To find k use the condition t = 0.02 when f = 8
k = [tex]\frac{t}{f^{2} }[/tex] = [tex]\frac{0.02}{64}[/tex] = [tex]\frac{1}{3200}[/tex]
t = [tex]\frac{f^{2} }{3200}[/tex] ← equation of proportionality
when t = 0.0098, then
0.0098 = [tex]\frac{f^{2} }{3200}[/tex] ( multiply both sides by 3200 )
f² = 0.0098 × 3200 ( take the square root of both sides )
f = [tex]\sqrt{0.0098(3200)}[/tex] = 5.6
