5. Water flows into a tank at a rate of r(t) = √25-t gallons per minute. Find the amount of water entering into the tank during the time interval from t = 9 to t = 16 minutes.

The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial velocity of the object is v(0) 11 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity. v(t) = = b) Find the object's displacement (in meters) from time 0 to time 3. meters c) Find the total distance traveled by the object from time 0 to time 3. meters

At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000 litres. Unfortunately, the tap on the tank was leaking in such a way that the change in volume at any time (r) hours was proportional to the volume (V) of the tank. This means that AP =-kV . dt Show that V= Ve is a solution of this equation. Given that the volume of the tank after 3 hours is 1900 litres, show that k = 0.1523 correct to 4 decimal places. (iii) By the time Mr Huxley discovered that the tank was leaking, there were only 250 litres of water remaining. At what time and on which day did Mr Huxley discover the leak (Answer correct to the nearest minute)?

A large tank is filled to capacity with 600 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds salt in the tank at time t.