1. A person with no more the $2000 to invest plans to place the money in two investments, telecommunications investment and pharmaceuticals. the telecommunications investment is to be no more than 4 times the pharmaceuticals investment. Write a system of inequalities to describe the situation. Let x = amount to be invested in telecommunications and y=amount to be invested in pharmaceuticals.
2. A steel company produces two types of machine dies, part A and part B. The company makes a $2.00 profit on each part A that it produces and a $6.00 profit on each part B that it produces. Let X= the number of part A produced in a week and Y= the number of part B produced in a week. write objective function that describes the total weeky profit.
3. A refecting telescope has a parabolic mirror for which the distance from the vertex to the focus is 32 feet. If the distance across the top of the mirror is 70 inches, how deep is the mirror in the center.
4. Two LORAN stations are postioned 248 miles apart along a straight shore. A ship record a time difference of 0.00086 seconds between the LORAN signals. (The radio signals travel at 186,000 miles per seconds) Where will the ship reach shore if it were to follow the hyperbola corresponding to this time difference? If the ship is 200 miles offshore what position of the ship?
The solution explains how to use the equations of parabola and hyperbola to solve real world problems.