Answer:
a)[tex]s=\sqrt{1+d^2}[/tex]
b)d(t)=500t
c)[tex]s(t) =\sqrt{1+250000t^2}[/tex]
Step-by-step explanation:
d = Horizontal distance
s = the distance between the plane and the radar station
The horizontal distance (d), the one mile altitude, and s form a right triangle.
So, use Pythagoras theorem
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]s^2=1^2+d^2[/tex]
a) [tex]s=\sqrt{1+d^2}[/tex]
(b) Express d as a function of the time t (in hours) that the plane has flown.
[tex]distance = speed \times time[/tex]
d(t)=500t
(c) Use composition to express s as a function of t.
[tex]s(t) =\sqrt{1+d^2}[/tex]
using b
[tex]s(t) =\sqrt{1+(500t)^2}\\s(t) =\sqrt{1+250000t^2}[/tex]
