tides go up and down in a 148houperiod The average depth of

tides go up and down in a 14.8houperiod .The average depth of a certain river is 7 m and ranges from 4 to 10 m. The variation can be approximated by a sine curve. write an equation that gives the approximate variation y , if x is the number of hours after midnight and high tide occorse at 5 am.

A y= 7 sin ( (pie x/7.4) -5pie) B 3 sin ( (pie x /7.4)- ((1.3pie)/7.4)) ) C 3 sin ( (pie x/7.4) -(5pie/7.4) ) D 7 sin ( (pie x/7.4)- ( 5pie/7.4)

Solution

period = 14.8

2pi/B = 14.8

B = pi/7.4

amplitude = 10 - 4 /2 = 3

phase shift = 1.3 pi /7.4

hence, equation is

y = 3 sin ( pix / 7.4 - 1.3pi / 7.4 )

option b is correct