Verified Answer :

  • Substitute \(x = 30\) into the expression \(x^3 - 1750\).
  • Calculate the exponent: \(30^3 = 27000\).
  • Subtract the constant: \(27000 - 1750 = 25250\).
  • Final result: \(\boxed{25250}\).

Explanation

  1. Problem Analysis

To solve the problem, we start by analyzing the given expression and the value assigned to the variable. We are given the expression \(x^3 - 1750\) and instructed to evaluate it for \(x = 30\). This involves substituting the value \(30\) for \(x\) and following the order of operations to find the numerical result.

  1. Substitution and Exponentiation

The first step is to substitute \(x = 30\) into the expression \(x^3 - 1750\). This gives us:
\[ (30)^3 - 1750 \]
Next, we calculate the cube of \(30\). Since \(30^3 = 30 \times 30 \times 30\), we can compute this as:
\[ 30 \times 30 = 900 \]
\[ 900 \times 30 = 27000 \]
So, \(30^3 = 27000\).

  1. Final Calculation

Now that we have the value of \(30^3\), we substitute it back into our expression:
\[ 27000 - 1750 \]
Performing the subtraction:
\[ 27000 - 1750 = 25250 \]
Thus, the value of the expression \(x^3 - 1750\) when \(x = 30\) is \(25250\).

Examples

Evaluating algebraic expressions is a fundamental skill used in many real-life applications, such as calculating the volume of a storage container or determining the total cost of a project. For instance, if you were designing a cube-shaped box with a side length of \(30\) cm and needed to subtract the volume of an internal component of \(1750 \text{ cm}^3\), you would use this exact method to find the remaining volume of the box. Mastering these steps helps in solving various optimization and design problems.

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