an open box is to be made from a rectangular piece of tin 12 inches long and 10 inches wide by cutting pieces of x-inches square from each corner and bending up the sides.find the domain of the function
?
Find out what is the minimum and maximum size of the cut out in consideration of the size (12"x10") of the tin piece.
The domain of the function consists of all the possible values of x.
If it is not clear, draw a rectangle to represent the tin sheet, and draw the four squares at each corner.
To find the domain of the function, we need to determine the possible values for x in the given scenario.
Let's consider the rectangular piece of tin with dimensions 12 inches by 10 inches. When we cut x-inches squares from each corner and fold up the sides, the resulting open box will have a length, width, and height.
The length of the open box will be (12 - 2x) inches, as we remove x inches from each of the two long sides.
The width of the open box will be (10 - 2x) inches, as we remove x inches from each of the two short sides.
The height (h) of the open box will be x inches since we use the cut-out squares as the vertical sides.
However, for the tin to be able to fold properly into an open box, the cut-out squares cannot be larger than half the dimensions of the tin. In other words, the maximum value of x is half of the smaller dimension.
Let's find the smaller dimension first:
Smaller dimension = min(12, 10) = 10 inches
Therefore, the maximum value of x would be half of the smaller dimension:
Maximum x = 10/2 = 5 inches
So, the domain for the function is the set of values less than or equal to 5:
Domain: x ≤ 5, where x represents the size of the squares cut from each corner.