Nathan's Calculus Project Final

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Tecnologia Educação

I c e a n d D u mm i e s : Comprehensive Calculus Problems from a Noteworthy Calculus student from a Prestigious High School in a Warm Climate where the people are fun

Practical Design: The Ice Column ,[object Object],Related Rates The Problem:

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Reflection: ,[object Object],[object Object]

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Based on the readings and content for this course.docx Based on the readings and content for this course, which topic did you find most useful or interesting? How will you use it later in life? What makes it valuable? Ans: Well, there are many small but significant things in real life, that I understand, are related to maths. For example the screen size of a TV or a laptop. When we say 14 inch laptop we mean the diagonal of the screen is approximately 14 inches. This is a direct application of Pythagorean Theorem. And depending on the shape of the room determines the formula for area that I use. For example, if our room was a perfect square (which none of them are) I would utilize the formula a = s^2, since our rooms our rectangle, the formula we more commonly use is a = lw. Again I understand the amount of money we spend on gas can be modeled by a mathematical function. When we throw a ball up, the time taken for it to come down can be modeled by a quadratic equation. There are so many things. I won't pick up any particular thing. But after this course, I am able to look at many things in a more analytical way. I can understand the mathematical logic behind them. So all these are valuable to me Do you always use the property of distribution when multiplying monomials and polynomials.docx Do you always use the property of distribution when multiplying monomials and polynomials? Explain why or why not. In what situations would distribution become important? Provide an example for the class to practice with. Ans: The property of distribution is one important tool in solving the polynomial multiplications. For example: 3x*(x+5) = 3x*x + 3x*5 = 3x^2 +15x But this property is used only when one of the bracketed terms contains two or more terms of different order. For example in the above case, the bracket consists of two different order terms, x and 5. Let’s take another case: 3x*(x+2x) This can be solved in two ways. 3x(x+2x) = 3x*x + 3x*2x = 3x^2 +6x^2 = 9x^2 Or we can say: 3x(x+2x) = 3x*3x = 9x^2 So in the 1st method we used the distribute property. But in the 2nd case we did not. So it depends on the particular problem and looking at the different terms we can decide whether or not to use distributive property. Explain how to factor the following trinomials forms.docx Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation Ans: Actually I am not very sure how to answer this. For me x2 + bx + c and ax2 + bx + c are not different from each other. The 1st one is a special case of the second expression where a=1. To factor the expression ax^2 + bx + c we first need to factor the middle term bx cleverly. Now it's to be understood that not all trinomials can be factored. But some of them can be. Basically, we have to write b in the form b= p+q so that p*q= a*c. This is the only trick. Then ...

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Nathan's Calculus Project Final

1. I c e a n d D u mm i e s : Comprehensive Calculus Problems from a Noteworthy Calculus student from a Prestigious High School in a Warm Climate where the people are fun

2.

3.

4.

5.

6.