Final answer:
The expression ⌈√⅔⌉ + ⌈÷⌉ + ⌈(÷)^2⌉ evaluates to 11 after individually finding the ceiling values for each term and adding them together.
Step-by-step explanation:
To evaluate the expression ⌈√⅔⌉ + ⌈÷⌉ + ⌈(÷)^2⌉, we first need to understand the ceiling function. The ceiling function, denoted by the ceiling brackets ⌈ ⌉, rounds a number up to the nearest integer. Now, let's evaluate each term individually:
1. ⌈√⅔⌉: The square root of ⅔ is √(9/4) = √(2.25) = 1.5. The ceiling of 1.5 is 2.
2. ⌈÷⌉: The value of 9/4 is 2.25. The ceiling of 2.25 is 3.
3. ⌈(÷)^2⌉: First, we square 9/4 getting (9/4)^2 = 81/16, which is 5.0625. The ceiling of 5.0625 is 6.
Adding these values together gives us 2 + 3 + 6 = 11. Therefore, the evaluated expression is 11.