What is the value of $6\lceil 4-9.4\rceil $?
Answer (1)
Calculate the value inside the ceiling function: 4 − 9.4 = − 5.4 .
Apply the ceiling function: ⌈ − 5.4 ⌉ = − 5 .
Multiply by 6: 6 × ( − 5 ) = − 30 .
The final answer is − 30 .
Explanation
Understanding the Problem We are asked to evaluate the expression 6 ⌈ 4 − 9.4 ⌉ . The ceiling function ⌈ x ⌉ returns the smallest integer greater than or equal to x .
Calculating the Value Inside the Ceiling Function First, we need to calculate the value inside the ceiling function: 4 − 9.4 = − 5.4 .
Applying the Ceiling Function Next, we apply the ceiling function to − 5.4 . The smallest integer greater than or equal to − 5.4 is − 5 . Therefore, ⌈ − 5.4 ⌉ = − 5 .
Multiplying by 6 Finally, we multiply the result by 6: 6 × ( − 5 ) = − 30 .
Final Answer Therefore, the value of 6 ⌈ 4 − 9.4 ⌉ is − 30 .
Examples
Understanding ceiling functions is useful in many real-life situations. For example, if you need to ship several items that weigh 1.2 kg each, and the shipping company charges per whole kg, you would use the ceiling function to determine the cost. If you have 5 items, the total weight is 6 kg. The shipping cost would be calculated based on \lceil 6 \rceil = 6 kg.
