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A mixed tank contains 100 gal of water with a salt concentration of 1.2lb/gal. Water containing salt at concentration of 2lb/gal enters at rate of 5 gal/hr. An open valve allows water to leave at 4gal/hr. Set up a differential equation with initial condition to determine the amount of salt as function of time.
Finding the dimensions of a rectangle using second derivative test - Find length and width should the rectangle have so that its area is a maximum?
Prove that if f is a differentiable function with f´(x) > 1 for all x, then there is at most one c such that f(c) = c. [Use the Mean Value Theorem]
You are the director of communicable diseases in a city health department, responsible for a large urban community. It is early spring in 2003. For the past two years, your department has been working to control the spread of the West Nile Virus and ..
A box with its base in the xy-plane has its four upper vertices on the surface with equation z=48-3x^2-4y^2. What is the maximum possible volume.
A certain university has a computer room with 222 terminals. Each day there is a 4% chance that a given terminal will break and a 70% chance that a given broken terminal will be repaired. In the long run, about how many terminals in the room will ..
for a sailboat to reach a destination directly upwind it is necessary to tack left and right to the direction of the
How much would the driver's hourly wage need to be in order for the optimum speed to violate a constraint limiting the speed to 80 mph? This is similar to previous problem except that you are solving for the wage given the speed.
Assuming that there is no cost to enter the .sweepstakes, find the expected value of the amount won for one entry. Round to the nearest tenth.
A point P is moving in the xy-plane. When P is at (4, 3), its distance to the origin is increasing at a rate of √2 cm/sec. Determine the rate of change of the x-coordinate of P at that moment.
What systems of equations can be solved by graphing or using substitution or elimination? Which method do you like best and why would it be different method. How would you answer this question?
A Norman window is shaped like a rectangle whose length is twice its width, surmounted by a semi-circle. Write a polynomial that gives its area.
A particle is moving along the curve y= 3 sqrt{4 x + 9}. As the particle passes through the point (4, 15), its x-coordinate increases at a rate of 5 units per second. Find the rate of change of the distance from the particle to the origin at this ..
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