# Mixture-related Problems

# Number-related Problems

**Addition**

Expressions that can be translated to addition, ( + ): sum, plus, added to, in addition, increased by, and more than.

Verbal expression | Algebraic equivalent |

the sum of x and y | x + y or y + x |

x plus y | x + y |

x increased by y | x + y |

x added to y | y + x |

x in addition to y | y + x |

x more than y | y + x |

# Verbal Problems in Algebra

The following is an attempt to classify the verbal problems.

**Number-related problems**

Number-related problems are considered as the most basic type of verbal problems. It is taken as the base point of analysis for more complex type of problems.

# Problem 05 | Inverse Laplace Transform

**Problem 05**

Find the inverse transform of $\dfrac{2s^2 + 5s - 6}{s^3 - 3s^2 - 13s + 15}$

# Problem 04 | Inverse Laplace Transform

**Problem 04**

Perform the indicated operation: $\mathcal{L}^{-1} \left[ \dfrac{s - 5}{s^2 + s - 6} \right]$

# Problem 03 | Inverse Laplace Transform

**Problem 03**

Find the inverse transform of $\dfrac{7}{s^2 + 6}$.

# Problem 01 | Right Spherical Triangle

**Problem**

Solve for the spherical triangle whose parts are a = 73°, b = 62°, and C = 90°.

# Oblique Spherical Triangle

**Definition of oblique spherical triangle**

Spherical triangles are said to be oblique if none of its included angle is 90° or two or three of its included angles are 90°. Spherical triangle with only one included angle equal to 90° is a right triangle.

**Sine law**

$\dfrac{\sin a}{\sin A} = \dfrac{\sin b}{\sin B} = \dfrac{\sin c}{\sin C}$

# Right Spherical Triangle

**Solution of right spherical triangle**

With any two quantities given (three quantities if the right angle is counted), any right spherical triangle can be solved by following the Napier’s rules. The rules are aided with the Napier’s circle. In Napier’s circle, the sides and angle of the triangle are written in consecutive order (not including the right angle), and complimentary angles are taken for quantities opposite the right angle.