# 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**

Given the following equations:

$$ab = 1/8 \qquad ac = 3 \qquad bc = 6$$

Find the value of $a + b + c$.

A. $12$ | C. $\dfrac{4}{51}$ |

B. $\dfrac{7}{16}$ | D. $12.75$ |

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**Problem**

Which of the following is the derivative with respect to *x* of $(x + 1)^3 - x^3$?

A. 6x + 3 |
C. 1 + 2x - 3x^{2} |

B. 3x^{2} + 2x + 1 |
D. 6x - 3 |

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**Problem**

How many terms from the progression 3, 5, 7, 9, ... must be taken in order that their sum will be 2600?

A. 80 | C. 50 |

B. 60 | D. 70 |

**Problem**

Find the equation of the curve passing through the point (3, 2) and having s slope 5*x*^{2} - *x* + 1 at every point (*x*, *y*).

A. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{31}{3}$ | C. $y = 5x^3 - 2x^2 + x - 118$ |

B. $y = 5x^3 - 2x^2 + x - 31$ | D. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{83}{2}$ |

**Problem**

A coin is so unbalanced that you are likely to get two heads in two successive throws as you are to get tails in one. What is the probability of getting heads in a single throw?

A. 0.168 | C. 0.681 |

B. 0.618 | D. 0.816 |

**Problem**

In the expansion of (2*x* - 1/*x*)^{10}, find the coefficient of the 8^{th} term.

A. 980 | C. 960 |

B. 970 | D. 990 |

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**Problem**

The formula $v = \sqrt{2gh}$ give the velocity, in feet per second, of an object when it falls *h* feet accelerated by gravity *g*, in feet per second squared. If *g* is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 80 feet per second.

A. 80 feet | C. 70 feet |

B. 100 feet | D. 90 feet |

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**Problem**

Earth is approximately 93,000,000.00 miles from the sun, and the Jupiter is approximately 484,000,900.00 miles from the sun. How long would it take a spaceship traveling at 7,500.00 mph to fly from Earth to Jupiter?

A. 9.0 years | C. 6.0 years |

B. 5.0 years | D. 3.0 years |

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**Problem**

A meteorologist is inflating a spherical balloon with a helium gas. If the radius of a balloon is changing at a rate of 1.5 cm/sec., express the volume *V* of the balloon as a function of time *t* (in seconds). Hint: Use composite function relationship *V*_{sphere} = 4/3 π*r*^{3} as a function of *x* (radius), and *x* (radius) as a function of *t* (time).

A. V(t) = 5/2 πt^{3} |
C. V(t) = 9/2 πt^{3} |

B. V(t) = 7/2 πt^{3} |
D. V(t) = 3/2 πt^{3} |

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