**Problem**

A 50-m steel tape that is is 0.02 m too long was used to measure the distance between two points *A* and *B*. If the measured distance was 160.42 m, calculate the correct distance between *A* and *B*.

A. 160.356 m | C. 160.844 m |

B. 160.484 m | D. 160.563 m |

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**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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**Problem**

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

A. 0.5 | C. 1.5 |

B. 1.0 | D. 2.0 |

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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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- 408 reads

**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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- 191 reads

**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 |