Solution: Step 1: Compute the square of 5, which gives 52 = 25. The expression becomes fracpi cdot 252. Step 2: Rearrange the terms to place the constant before pi. The expression now reads frac25pi2. Step 3: Present the final result in its various representations: - Exact Form: frac25pi2 - Decimal Form: Approximately 39.26990816 ldots Knowledge Notes: The problem involves evaluating a mathematical expression that includes the constant pi (pi), exponentiation, and division. Here are the relevant knowledge points: 1. Exponentiation: This is the operation of raising one number (the base) to the power of another (the exponent). In this case, 52 means 5 multiplied by itself, which equals 25. 2. Multiplication with pi: pi is an irrational number approximately equal to 3.14159. It is often used in formulas related to circles and spheres. In this problem, pi is being multiplied by 25. 3. Division: The division operation is represented by the symbol /. Here, the product of 25 and pi is being divided by 2. 4. Order of Operations: In mathematics, the order of operations dictates the sequence in which a complex expression should be evaluated. According to this convention, exponentiation is performed before multiplication and division. 5. Representation of Numbers: The final result of a mathematical expression can be represented in different forms. The exact form maintains the mathematical symbols and constants, while the decimal form converts the expression into a decimal number, which may be an approximation if it involves irrational numbers like pi. 6. Use of LaTeX in Formatting: LaTeX is a typesetting system that is widely used for the communication and publication of scientific documents. It is used here to format mathematical expressions and symbols for clarity and precision.

Evaluate (pi*5^2)/2

The problem presents an arithmetic expression that needs to be evaluated. It involves the mathematical constant pi (approximately 3.14159), the exponentiation of the number 5 to the power of 2, and the division of the resulting product by 2. The task is to perform the calculations according to the order of operations: squaring the number 5, multiplying that result by pi, and finally dividing the product of these operations by 2.

$\frac{π \cdot 5^{2}}{2}$

Answer

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Solution:

Step 1:

Compute the square of $5$ , which gives $5^{2} = 25$ . The expression becomes $\frac{π \cdot 25}{2}$ .

Step 2:

Rearrange the terms to place the constant before $π$ . The expression now reads $\frac{25 π}{2}$ .

Step 3:

Present the final result in its various representations:

Exact Form: $\frac{25 π}{2}$
Decimal Form: Approximately $39.26990816 \dots$

Knowledge Notes:

The problem involves evaluating a mathematical expression that includes the constant $π$ (pi), exponentiation, and division. Here are the relevant knowledge points:

Exponentiation: This is the operation of raising one number (the base) to the power of another (the exponent). In this case, $5^{2}$ means $5$ multiplied by itself, which equals $25$ .
Multiplication with $π$ : $π$ is an irrational number approximately equal to $3.14159$ . It is often used in formulas related to circles and spheres. In this problem, $π$ is being multiplied by $25$ .
Division: The division operation is represented by the symbol $/$ . Here, the product of $25$ and $π$ is being divided by $2$ .
Order of Operations: In mathematics, the order of operations dictates the sequence in which a complex expression should be evaluated. According to this convention, exponentiation is performed before multiplication and division.
Representation of Numbers: The final result of a mathematical expression can be represented in different forms. The exact form maintains the mathematical symbols and constants, while the decimal form converts the expression into a decimal number, which may be an approximation if it involves irrational numbers like $π$ .
Use of LaTeX in Formatting: LaTeX is a typesetting system that is widely used for the communication and publication of scientific documents. It is used here to format mathematical expressions and symbols for clarity and precision.