The depth of water, d metres at a port entrance is modelled by the function:
d(t)=sin( (2pi x/13) + pi/2)) +1.7 (t= time in hrs since 12 noon)

The ship needs 1.2 m of water to sail into or out of port. She needs two hrs to get from the entrance of the port to the jetty; 1 1/2 hrs to unload and 2 hours to depart the jetty and sail back to the port entrance.

Use exact values to calculate the earliest time HMAS King is able to complete its activities and be back at the port entrance?

Question

The depth of water, d metres at a port entrance is modelled by the function:
d(t)=sin( (2pi x/13) + pi/2)) +1.7   (t= time in hrs since 12 noon)

The ship needs 1.2 m of water to sail into or out of port. She needs two hrs to get from the entrance of the port to the jetty; 1 1/2 hrs to unload and 2 hours to depart the jetty and sail back to the port entrance.

Use exact values to calculate the earliest time HMAS King is able to complete its activities and be back at the port entrance?

anonymous · Answer

and here x represents...?

anonymous · Answer

time sorry

anonymous · Answer

sin( (2pi x/13) + pi/2)) +1.7   ?
The parentheses count is incorrect.  There are 2 left parens and 3 right parens

anonymous · Answer

whoops, remove one at the end of pi/2

anonymous · Answer

to solve this problem u need to differentiate the d(x) and put d'(x)=0 and find x(or 't' in this case),see how many points u get,those r critical points,put these values in the equation and check which gives the minimum time and that will be ur solution

anonymous · Answer

oh yepp thanks bikas

anonymous · Answer

A Mathemtica solution with comments is attached.