Mathematics, Surveying and Transportation Engineering

Problem
There are 7 arithmetic means between 3 and 35. What is the sum of all the terms?

Problem
A boat going upstream takes 1.5 times longer than going the same distance downstream. If the water current in the river is 8 kph, calculate the speed of the boat in still water.

Problem
What is the equation of the normal to the curve $x^2 + y^2 = 25$ at (4, 3)?

Problem
What is the radius of the circle $x^2 + y^2 - 6x = 0$?

Problem
When the polynomial $x^4 + bx^3 + 5x^2 + dx + 6$ is divided by $x - 2$ the remainder is 16. When it is divided by $x + 1$ the remainder is 10. Find the value of constant $d$.

Problem
Gas is escaping from a spherical balloon at a constant rate of 2 ft³/min. How fast, in ft²/min, is the outer surface area of the balloon shrinking when the radius is 12 ft?

Problem
Determine the percentage uncertainty in the area of a square that is 6.08 ± 0.01 m on a side.

Problem
In still water, your small boat averages 8 miles per hour. It takes you the same amount of time to travel 15 miles downstream, with the current, as 9 miles upstream, against the current. What is the rate of water's current?

Problem
\$180,000 was spent on the project that yields annual benefit of \$60,000 for a period of 8 years without any salvage value. Determine the benefit-to-cost ratio considering the cost of money to be 7%.

Problem
Which of the following pizzas is a better buy: a large pizza with 16-inch diameter for \$15 or a medium pizza with an 8-inch diameter for \$7.50? What is the cost per square inch of the better pizza?