Answer:
499.338 feet
Step-by-step explanation:
You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.
Distance
The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...
[tex]\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}[/tex]
