Problem Solving: Examples and Practice Problems

- The pressure at a point below the surface of a body of water varies linearly with the depth of the water. If the pressure at a depth of 10.0m is 199kPa and the pressure at a depth of 30.0m is 395kPa, what is the pressure at the surface?

Solution - The total fixed cost for a company to operate a certain plant is $400/day. It also costs $2 for each unit produced in the plant. Find the equation relating the total cost C of operating the plant and the number of units n produced each day.

Solution - A wall is 15cm thick. At the outside surface, the temperature is 3C and at the inside surface, it is 23C. If the temperature changes at a constant rate through the wall, write an equation for the temperature T in the wall in terms of the distance x from the outside surface to the inside surface.

Solution - A ray of light travels from the left to along the line x + y = 1 and reflects off the x axis. Write the equation for the reflected ray.

Solution - A student is drawing a friction drive in which two circular disks are in contact with each other. They are represented by circles in the drawing. The first has a radius of 10.0cm and the second has a radius of 12.0cm. What is the equation of each circle if the origin is a the center of the circle and the x-axis passes through the center of the second circle?

Solution - Under certain condition, a cable which hangs between two supports can be closely approximated as being parabolic. Assuming that this cable hangs in the shape of a parabola, find its equation if a point 10ft horizontally from its lowest point is 1.0ft above its lowest point. Choose the lowest point as the origin of the coordinate system.

Solution - A 10ft high truck passes under a parabolic arch. Find the maximum distance x that the side of the truck can be from the center of the road.

NEED SKETCH

- A 100gal container receives 10gal/min of water and 20gal/min of salt solution with a concentration of 2lb of salt/gal. What is the salt content after 5 minutes? What is the salt concentration after 5 minutes? After x minutes?