SOLUTION: The volume of water, V, in kiloliters (kl), in the Stratford water tower on a given day at t hours after midnight can be modelled using the sinusoidal function: V(t)=50000sin[15(t-

Algebra ->  Test -> SOLUTION: The volume of water, V, in kiloliters (kl), in the Stratford water tower on a given day at t hours after midnight can be modelled using the sinusoidal function: V(t)=50000sin[15(t-      Log On


   

Question 1062726: The volume of water, V, in kiloliters (kl), in the Stratford water tower on a given day at t hours after midnight can be modelled using the sinusoidal function: V(t)=50000sin[15(t-3)] +100000
a. Determine the maximum and minimum values for the volume of water in the tank
b.At what time will the volume of water be maximum? At what time will the volume of water be at minimum
c. What will the volume of water be at 10:30 am?
d. During what time period will the volume of water be more than 130 000 kl?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+V%28t%29+=+50000%2Asin%28+15%2A%28+t-3+%29+%29+%2B+100000+
+V%280%29+=+50000%2Asin%28+15%2A%28-3%29+%29+%2B+100000+
+V%280%29+=+50000%2Asin%28+-45+%29+%2B+100000+
( is the angle in degrees or radians? I'm guessing degrees )
+V%280%29+=+%28-1%2Fsqrt%282%29+%29%2A50000+%2B+100000+
+V%280%29+=+-35355.34+%2B+100000+
+V%5B0%5D+=+64644.66+
----------------------------
(a)
The sine function varies from +-1+ to +1+
+V%5Bmin%5D+=+50000%2A%28-1%29+%2B+100000+
+V%5Bmin%5D+=+50000+
and
+V%5Bmax%5D+=+50000%2A%281%29+%2B+100000+
+V%5Bmax%5D++=+150000+
--------------------------------
(b)
+V%5Bmax%5D+=+50000%2A%281%29+%2B+100000+
+sin%28+15%2A%28+t-3+%29+%29+=+1+
+15%2A%28+t+-+3+%29+=+90+
+t+-+3+=+6+
+t+=+9+
The volume is maximum at 9 AM
and
+V%5Bmin%5D+=+50000%2A%28-1%29+%2B+100000+
+sin%28+15%2A%28+t-3+%29+%29+=+-1+
+15%2A%28+t-3+%29+=+270+
+t+-+3+=+18+
+t+=+21+
The volume is minimum at 9 PM
---------------------------------
(c)
+t+=+10.5+
+15%2A%28+t-3+%29+=+15%2A%28+10.5+-+3+%29+
+15%2A7.5+=+112.5+
+sin%28+112.5+%29+=+.9239+
+V%2810.5%29+=+50000%2A.9239+%2B+100000+
+V%2810.5%29+=+46195+%2B+100000+
+V%2810.5%29+=+146195+ kl
-------------------------------------
(d)
+V%28t%29+=+130000+
+130000+=+30000+%2B+100000+
+50000%2Asin%28+15%2A%28+t-3+%29+%29+=+30000+
+sin%28+15%2A%28+t-3+%29+%29+=+.6+
+15%2A%28+t-3+%29+=+36.8699+
+t+-+3+=+2.458+
+t+=+5.458+
+.458%2A60+=+27.48+
+.48%2A60+=+29+
and
+15%2A%28+t+-+3+%29+=+180+-+36.8699+
+15%2A%28+t+-+3+%29+=+143.13+
+t+-+3+=+9.542+
+t+=+12.542+
+.542%2A60+=+32.52+
+.52%2A60+=+31.2+
-------------------------
The volume is greater than 130, 000 kl between
5:27:29 AM and 12:32:31 PM
--------------------------
Lots of math! check it carefully