The rate of change in the volume of a tank is known to be dV/dt=0.6t*cos(0.08t^2 -1), where V(t) is in gallons per minute and 0<=t<=10 (0 is less than or equal to t which is less than or equal to 10). If the tank has a volume of 14 gallons initially, what is its volume at 10 minutes?

  1. 👍 0
  2. 👎 0
  3. 👁 261
asked by Jamie
  1. dv/dt = 0.6t cos(0.08t^2-1)
    v = 3/8 sin(0.08t^2-1) + c
    Since v(0) = 14, c = 14+3/8 sin(1) = 14.3

    v(t) = .375 sin(.08t^2-1)+14.3
    Now just evaluate v(10)

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    . A water tank is in the form of an inverted frustum as shown in Figure Q5: The radii of the top and the bottom circles are 80 cm and 36 cm respectively. Let h cm be the height of the water in the tank at time t second (s): 80 cm-

    asked by alison on December 26, 2019
  2. ordinary differential equation

    A contains 200 liters of solution in which is dissolved 40 kg of salt. Tank B contains 400 liters of solution in which are dissolved 80 kg of salt. Pure water flows into tank A at rate of 10 liters per second. There is a drain at

    asked by thigan on May 21, 2016
  3. Math

    "A tank holds 1000L of water, which takes an hour to drain from the bottom of the tank, then the volume V of water remaining in the tank after t minutes is: V = 1000(1-(t/60))^2 where t is between 0 and 60 inclusive. Find the rate

    asked by Stuck on February 7, 2010
  4. Fluid Mechanic

    3) Air at standard conditions enters the compressor shown in Fig. Q3 at a rate of 0.3m3/s. It leaves the tank through a 3 cm diameter pipe with a density of 1.8 kg/m3 and the uniform speed of 210 m/s. (a) Determine the rate (kg/s)

    asked by Adam on November 15, 2016
  5. Calculus @ Henry

    I worked some on this earlier, and botched it a bit, so here goes again. A water tank is made by rotating f(x)=2^x-1 between [0,2] about the y-axis. The water tank is initially full, when a hole is opened at the bottom tip so that

    asked by Steve on January 8, 2016
  1. Calculus

    I have a couple of questions and i wanted to know if my answers are correct. Thanks in advanced! 1. Determine the values of x for which the function f(x)=x+2/x-2 is discontinuous Would the answers be x=2 because the function would

    asked by Sarah on April 9, 2014
  2. Related Rates

    Water is leaking out of an inverted conical tank at a rate of 500 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 10 meters and the diameter at the top is

    asked by Tom on October 14, 2006
  3. Calculus

    I am re-posting this question because i wrote the incorrect function last time. An oil tank is being drained for cleaning. After t minutes there are v litres of oil left in the tank, where v(t)=35(25-t)^2, 0

    asked by Sarah on April 9, 2014
  4. Science

    how the volume of air in a tank of compressed air would change if the volume of the tank doubled? My answer was: The volume of the air would increase and it would be more difficult to fit inside of the tank depending on if the

    asked by Steven on November 17, 2015
  5. Function: Rate of Change

    Joe is investigating the rate of change of the function y=cos x on the interval xE[0,2π]. He notices that the graph of y=cos x passes through the x-axis at 45°. He also determines the instantaneous rate of change at x = 0, π,

    asked by Anonymous on May 17, 2012

More Similar Questions