Jade is having a wonderful time riding a carousel. Her distance, $d$ (in feet), from the fence nearest the entrance is given by the equation $d=25\sin\left(\frac{\pi t}{15}\right)+35$, where $t$ is the time in seconds since the carousel started to rotate.  

1. How close can Jade be to the fence? How far?

   Hint (a):

   What are the minimum and maximum values of the function?

2. How much time does it take for the carousel to complete one revolution?

   Hint (b):

   This is the time for one cycle, or the period.
   period $=\frac{2\pi}{b}$

3. When is Jade $60$ feet from the fence for the second time?

   Hint (c):

   Solve $f(t)=60$.

4. Sketch the graph of this situation. Label and scale the axes appropriately.