To evaluate the expression \( B^3 = 24 \cdot (-1.5)^3 - 1 = 24 \cdot 2.25 \), let's break it down step by step.
Calculate \((-1.5)^3\): \[ (-1.5)^3 = -1.5 \cdot -1.5 \cdot -1.5 = -3.375 \]
Rewrite the expression: Now substituting \((-1.5)^3\) into the equation: \[ B^3 = 24 \cdot (-3.375) - 1 \]
Calculate \(24 \cdot (-3.375)\): \[ 24 \cdot (-3.375) = -81 \]
Substitute back: Now substituting this value back into the equation: \[ B^3 = -81 - 1 = -82 \]
Thus, \[ B^3 = -82 \]
If you need to find \(B\), take the cube root of \(-82\): \[ B = \sqrt[3]{-82} \]
At this stage, if a numerical approximation is required, you can use a calculator: \[ B \approx -4.326 \]
So finalize the answers as:
- \(B^3 = -82\)
- \(B \approx -4.326\)