Mathematics, Surveying and Transportation Engineering

Problem
If $\arcsin (3x - 4y) = 1.571$ and $\arccos (x - y) = 1.047$, what is the value of $x$?

Problem
The digits of a three-digit number are in arithmetic progression. If you divide the number by the sum of its digits, the quotient is 26. If the digits are reversed, the resulting number is 198 more than the original number. Find the sum of all the digits.

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?