Answer:
w≅8.46ft
Step-by-step explanation:
Data
focus=8
vertex=(0,0)
width=?
depth (y)=3ft
parabola equation: [tex](x-h)^{2}=4p(y-k)[/tex]; then for V=(0,0), [tex]x^{2} =4py[/tex], be focus(f)=8in; [tex]x^{2} =4*8*y=32y[/tex] → [tex]y=\frac{x^{2} }{32}[/tex]
we have that y=3ft then [tex]3=\frac{x^{2} }{32}[/tex]; but 1in≅0.083ft so [tex]x^{2} =3*32*0.083=7.968[/tex] → x=±2.82, finally w=3*2.82≅8.46ft
