Answer:
263.12 radians
Step-by-step explanation:
The length of the rear wheel is given by:
[tex]L=2\pi r\\L=40\pi[/tex]
The distance traveled by the lawn tractor in 23 seconds is:
[tex]d=13\frac{miles}{hour} *63360\frac{inch}{miles}*\frac{1\ hour}{3600\ seconds}*23\ seconds\\ d=5,262.4\ inches[/tex]
The angle through which a wheel rotates is given by:
[tex]A=\frac{d}{L}*2\pi \\A=\frac{5,262.4}{40\pi}*2\pi\\A=263.12\ radians[/tex]
The wheel rotates through a 263.12 radians angle.
