# Mathematics, Surveying and Transportation Engineering

**MSTE - Mathematics, Surveying and Transportation Engineering
Common name: Math**

Algebra, Trigonometry, Statistics, Geometry, Calculus, Differential Equations, Engineering Mechanics, Engineering Economy, Surveying, Transportation Engineering

**Problem**

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

A. 133 | C. 665 |

B. 608 | D. 171 |

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**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.

A. 30 kph | C. 40 kph |

B. 50 kph | D. 20 kph |

**Problem**

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

A. $4x + 3y = 0$ | C. $3x + 4y = 0$ |

B. $3x - 4y = 0$ | D. $4x - 3y = 0$ |

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**Problem**

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

A. 6 | C. 4 |

B. 9 | D. 3 |

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**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 $d$.

A. 7 | C. -5 |

B. -7 | D. 5 |

**Problem**

Gas is escaping from a spherical balloon at a constant rate of 2 ft^{3}/min. How fast, in ft^{2}/min, is the outer surface area of the balloon shrinking when the radius is 12 ft?

A. 1/2 | C. 1/3 |

B. 1/5 | D. 1/4 |

**Problem**

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

A. 0.27% | C. 0.26% |

B. 0.25% | D. 0.29% |

**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?

A. 4 miles/hr | C. 2 miles/hr |

B. 3 miles/hr | D. 5 miles/hr |

**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%.

A. 1.99 | C. 1.57 |

B. 2.21 | D. 2.63 |

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**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?

A. medium pizza: \$0.07/in.^{2} |
C. medium pizza: \$0.15/in.^{2} |

B. large pizza: \$0.07/in.^{2} |
D. large pizza: \$0.15/in.^{2} |