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1. A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet?
2. A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate?
3. Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.
4. The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water?
Solving the linear equation.
Describe explicitly, including the generators, all intermediate fields between Q(x) and Q, where x is a primitive 5th root of unity.
Define the term equation and then explain what it means to solve an equation. Give an example of an equation and its solution. Explain why it is the solution.
Given a 1-variable linear equation 10z-4=86. Explain the techniques, and show the steps used for solving this equation. Check if the solution is correct.
Solve for the unknown variable
Compute equations for the vertical and horizontal asymptotes
Find the coefficients of the objective function
Solve the following equation
Use compound interest to find the amount.
Demostrate the complete proof of the Cauchy-Schwarz inequality and the triangle inequality.
Provide a numerical answer to each of the following questions and also show the calculations you used to find the answers. How many different ways can 30 runners place in an Olympic qualifying marathon?
Transportation problem
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