What is the value of $6\lceil 4-9.4\rceil $?
Answer (2)
To calculate 6 ⌈ 4 − 9.4 ⌉ , we first find 4 − 9.4 = − 5.4 , then apply the ceiling function to get ⌈ − 5.4 ⌉ = − 5 . Finally, we multiply by 6 to get the answer of − 30 .
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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 . So, ⌈ − 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 scenarios. For example, if you need to ship several items that weigh 1.2 kg each, and the shipping company charges per whole kilogram, you would use the ceiling function to determine the cost. If you have 5 items, the total weight is 5 × 1.2 = 6 kg. However, the shipping company will charge you for ⌈ 6 ⌉ = 6 kg. Another example is when calculating the number of whole steps needed to climb a staircase. If each step is 0.15 meters high and you need to climb 2 meters, you would need ⌈ 0.15 2 ⌉ = ⌈ 13.33 ⌉ = 14 steps.
