Question

In: Advanced Math

MAT 117 Problem Set 1 Name: ___________________________ Directions: Show al

MAT 117 Problem Set 1 Name: ___________________________

Directions: Show all work and explain your thinking as you solve these problems or write the explanations. Each problem is worth five points.

1. Below are definitions of different math number concepts. Write the concept that goes with each description. (no explanation needed for this problem only).

Concept	Definition
	Include integers, all fractions pq, where p and q are integers with q≠0, all repeating and all terminating decimals.
	Sometimes referred to as the counting numbers.
	Include the natural numbers and 0.
	A number in the form c x 10ⁿ, where 1≤ c < 10 and n is an integer. Used to represent numbers that are large or small in absolute value.
	Include the natural numbers, their opposites, and 0.
	Can be written as nonrepeating, non-terminating decimals; cannot be a rational number, if a square root of a positive integer is not an integer, it is this number.
	Any number that can be expressed in standard (decimal) form. Include the rational numbers and irrational numbers.

2. Explain the difference between the expressions 6x⁰ and (6x)⁰. If there is no difference, explain why.

Grading: 2 points: Worked out Problem Mathematically; 3 points: Explanation

3. For a recent year, the United States consumed about 1.0 x 10⁴ of petroleum per second. (Source: U.S. Energy Information Administration)

How many gallons of petroleum did the United States use that year?

Show work for all intermittent steps and Explain each step used to get your answer.

Grading: 1 point: Correct Answer; 2 points: Work; 2 points: Explanation

4. State whether the following statement is true and explain why or why not: A trinomial is always a higher degree than a monomial. Give an example proving your answer is correct.

Grading: 2 points: Correct Answer; 2 points: Explanation; 1 point: Example

5. Explain why x+ 7 is a polynomial, but x+7 is not a polynomial.

Grading: 5 points: Complete explanation

Expert Solution

EDIT:

5. is a polynomial, but is not a polynomial, because, in the latter, the exponent of is not a natural number.

2. Anything raised to the power 0 gives 1. So, we have

while

Hence the two expressions are not equal.

Colby Messinger answered 1 year ago

Problem 6. Show that a closed set is a Gδ and open set is Fδ.

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