## Equivalent Cartesian Equation of Parametric Equations

**Problem**

Find the Cartesian equation of the curve represented by $x = 4t + 3$ and $y = 16t^2 - 9$, -∞ < *t* < +∞.

A. $y = x^2 + 6x$ | C. $y = x^2 + 4x$ |

B. $y = x^2 - 6x$ | D. $y = x^2 - 4x$ |

**Problem**

Find the Cartesian equation of the curve represented by $x = 4t + 3$ and $y = 16t^2 - 9$, -∞ < *t* < +∞.

A. $y = x^2 + 6x$ | C. $y = x^2 + 4x$ |

B. $y = x^2 - 6x$ | D. $y = x^2 - 4x$ |

**Problem**

Find the equation of a sphere of radius 3 and tangent to all three coordinate planes if the center is on the first octant.

A. $x^2 + y^2 + z^2 - 9 = 0$ |

B. $x^2 + y^2 + z^2 - 6x - 6y - 6z + 18 = 0$ |

C. $x^2 + y^2 + z^2 - 4x - 4y - 4z + 12 = 0$ |

D. $x^2 + y^2 + z^2 - 8x - 8y - 8z + 14 = 0$ |

**Situation**

Given:

Effective Depth,

Compressive Strength,

Steel Strength,

- The beam is simply supported on a span of 5 m, and carries the following loads:
- Superimposed Dead Load = 16 kN/m

Live Load = 14 kN/mWhat is the maximum moment,

*M*(kN·m), at ultimate condition? $U = 1.4D + 1.7L$_{u}A. 144 C. 104 B. 158 D. 195 - Superimposed Dead Load = 16 kN/m
- Find the number of 16 mm diameter bars required if the design moment at ultimate loads is 200 kN·m.
A. 2 C. 6 B. 4 D. 8 - If the beam carries an ultimate concentrated load of 50 kN at midspan, what is the number of 16 mm diameter bars required?
A. 2 C. 4 B. 3 D. 5

**Situation**

The total length of the beam shown below is 10 m and the uniform load $w_o$ is equal to 15 kN/m.

1. What is the moment at midspan if *x* = 2 m?

A. 37.5 kN·m | C. -187.5 kN·m |

B. -37.5 kN·m | D. 187.5 kN·m |

2. Find the length of overhang *x*, so that the moment at midspan is zero.

A. 2.5 m | C. 2.4 m |

B. 2.6 m | D. 2.7 m |

3. Find the span *L* so that the maximum moment in the beam is the least possible value.

A. 5.90 m | C. 5.92 m |

B. 5.88 m | D. 5.86 m |

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Learn or test your concepts and terminology knowledge with this quiz.

**Version**: 0.5

**Number of questions in the bank**: 56 (as of June 23, 2021)

High school math questions | Engineering math questions | Engineering sciences questions | Civil engineering questions |
---|---|---|---|

17 | 12 | 10 | 17 |

In this blog, I will discuss the technique will easily allow us to write the equations of lines **directly** to its general form, without going through the classical methods. All we need is its slope.

**MSTE - Mathematics, Surveying and Transportation Engineering**

**Review Instructor:** Jhun Vert

**Language:** Taglish, more on Tagalog

Get yourself acquainted with the CE board exam problems in MSTE. Experience the level of difficulty you will encounter in the actual board examination and feel the similar time-constraint in solving problems. Learn how to solve the problem in the most efficient way and improve your problem solving strategies from experienced CE review instructor.

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Creating an online course is monumental specially to a small website like MATHalino. Despite being manned by one person from the ground up, the development of this functionality is actually progressing by degrees. I've been conceiving this feature as far as I can recall, way before online courses become a common thing in the Philippines. What makes me unable to implement it *before* comes from three factors.

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**Is this course right for you?**

Although we named this course * Basic Algebra Review*, this is actually designed for those who already completed their Algebra subject in engineering curriculum, hence, review. Problems presented in later topics are not really for beginners and solutions presented here assumed that you already earned the credits of College Algebra from your university.

Beginners however are also welcome to join, but never consider this course as a substitute to the long standing and thoroughly tested university program. Don't forget that your professor is the one holding the authority of the subject. Whenever contradiction arises between my teaching and that of your professor, do not follow me, listen to your professor. You may consider this course, however, as a supplement material to the already rich Algebra materials handed to you in your school.

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