#1**+1 **

I think I can do the first part:

The problem says the max height is 443 feet.

The second height is 443 feet - the radius.

443 feet - 394/2 feet

443 feet - 197 feet = 246 feet

The third height is 443 feet - the diameter.

443 feet - 394 feet = 49 feet

The very bottom height is 0 feet.

hectictar
Mar 16, 2017

#2**0 **

Note.....the max height - the diameter = starting height [ low point]....so

443 - 394 = 49 ft

1. When

t = 0, h = 49 [starting point ]

t = 7.5, h = 246 [first quarter point]

t = 15, h = 443 [second quarter point ]

t = 22.5, h = 246 [ third quarter point ]

t = 30, h = 0 [ back to starting point ]

There are probably several trig functons that would work, but here's one possibility:

2. h(t) = 246 - 197cos[ (pi/15)*t ] where t is in minutes

3. The vertical shift is 246

4. The amplitude is l -197 l = 197

5. There is no horizontal shift in this function

6. The period is 2pi / [pi/15] = 2 * 15 = 30 minutes

The frequency is the reciprocal of the period = 1/30 [it completes one revolution every 30 minutes]

7. See (2)

CPhill
Mar 16, 2017