Answer:
see explanation
Step-by-step explanation:
(a)
given [tex]\sqrt{2x-6}[/tex] + 2 = 10 ( subtract 2 from each side )
[tex]\sqrt{2x-6}[/tex] = 8 ( square both sides )
2x - 6 = 64 ( add 6 to both sides )
2x = 70 ( divide both sides by 2 )
x = 35
As a check
[tex]\sqrt{70-6}[/tex] + 2 = [tex]\sqrt{64}[/tex] + 2 = 8 + 2 = 10 correct
(b)
given T= 8, then substitution into the formula gives
8 = 1.25[tex]\sqrt{l}[/tex] ( divide both sides by 1.25
[tex]\sqrt{l}[/tex] = 6.4 ( square both sides )
l = 6.4² = 40.96 feet
(c)
note that (g - f)(x) = g(x) - f(x), hence
x - 10 -(4x + 4) = x - 10 - 4x - 4 = - 3x - 14
