Problem 4 Determine whether $ab$. $$ ... [FREE SOLUTION]

Chapter 1: Problem 4

Determine whether $ab$. $$ a=(3.2)^{2}, b=10 $$

Short Answer

Expert verified

$a > b$

Step by step solution

Calculate the Value of 'a'

First, we need to calculate the squared value of 3.2. The formula is $a = (3.2)^2$. Let's compute this: $a = 3.2 \times 3.2 = 10.24$.

Compare Values of 'a' and 'b'

Now we have $a = 10.24$ and $b = 10$. We need to compare these two values to determine the relationship between them. Since $10.24 > 10$, we conclude that $a > b$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Comparison of Values

When we talk about comparing values, we essentially try to figure out which one is larger, smaller, or if they are equal. In mathematical terms, comparisons use symbols like ">", "<", or "=". For example, in our exercise, we compare the calculated value of $a$, which is $10.24$, with $b$, which is $10$. By evaluating these numbers, we can see that $10.24$ is greater than $10$.
Thus, the comparison is written as $a > b$.

\">" means "greater than."
"<" means "less than."
"=" means "equal to."

Comparing values is an everyday task in math, helping us make decisions, ranging from which ingredient quantity is higher in a recipe to which product is more expensive.

Squaring Numbers

Squaring numbers is a mathematical operation where a number is multiplied by itself. This is represented by the exponent "2".
So, when you see $(3.2)^2$, it means 3.2 is multiplied by itself: $3.2 \times 3.2$.
In our example, squaring 3.2 results in $10.24$.

The square of a positive number is always positive.
Squaring can help us determine areas (e.g., of squares) and is crucial in equations involving exponents.

Squaring numbers is foundational in both algebra and geometry, making it essential to understand how to compute squares accurately.

Problem-Solving Steps

When tackling mathematical problems, following structured steps can be extremely helpful. Let's break it down using our problem as an example:

Step 1: Understand the Problem - Identify what is being asked. Here, we need to determine the relationship between two quantities.

Step 2: Solve for Known Values - Calculate any values that need determining. For this exercise, we calculate $a = (3.2)^2$ to get $10.24$.

Step 3: Compare Using Calculated Values - Once values are known, compare them as required. We compare $a$ and $b$, leading us to the conclusion that $10.24 > 10$.

Adopting a methodical approach to problem-solving aids comprehension and reduces errors. These steps aren't just for math; they're practical in various aspects of daily decision-making.

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91影视

Determine whether \(ab\). $$ a=(3.2)^{2}, b=10 $$

Short Answer

Step by step solution

Calculate the Value of 'a'

Compare Values of 'a' and 'b'

Key Concepts

Comparison of Values

Squaring Numbers

Problem-Solving Steps

One App. One Place for Learning.

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