# Compose a 250 words assignment on week 11 question. Needs to be plagiarism free!

Compose a 250 words assignment on week 11 question. Needs to be plagiarism free! The real-life application of Pre-Calculus Pre-Calculus is an important that covers areas such as exponents, algebra and logarithms. One of the areas where this course can be applied in real life is the use of differentiation in calculating the maximum or minimum volume of a container, say a box. For example, differentiation can be used to calculate the maximum volume of an open ended box that can be cut from a square plastic piece measuring 20M by 20M.

Assuming the height of the intended box is h, with length l and width w, then volume of the box can be given by:

But length and width can be expressed as and

The volume becomes:

The maximum value of h lies 0 ≤ .h .≤ 10

In order to get the maximum value of h, the expression above can be differentiated to get

Dividing through by 4 yields

Using the quadratic formula

or . but is outside the open interval (0, 10)

The most ideal value of h thus becomes

The maximum height of the box will be 3.333M, and the width and length will be 13.333M each. The maximum volume will thus be (13.33313.333592.58M3

This is a real life example of how pre-calculus can be applied. In this example, this approach can help maximize profits and minimize waste.

After studying this course, the most important piece of knowledge I am taking away is algebra and how it is applied. Throughout the course, algebraic expressions have been used to describe various phenomena. These expressions are important when dealing with real life problems. This knowledge is critical for understanding future mathematical concepts beyond pre-calculus.

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