# Mathematics, Surveying and Transportation Engineering

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

**Problem**

A circle has an equation of $x^2 + y^2 + 2cy = 0$. Find the value of $c$ when the length of the tangent from (5, 4) to the circle is equal to one.

A. 5 | C. 3 |

B. -3 | D. -5 |

**Problem**

Calculate the acute angle between two intersecting surfaces whose equations are as follows:

$$2x - 4y - z = -5$$

$$3x + 4y + 5z = -6$$

A. 62.4° | C. 42.6° |

B. 64.2° | D. 46.2° |

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- Read more about If arcsin (3x - 4y) = 1.571 and arccos (x - y) = 1.047, what is the value of x?
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**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.

A. 9 | C. 15 |

B. 12 | D. 18 |

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**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 |