Answer:
4096
Step-by-step explanation:
Answer:
12 minutes I think question kinda confusing
Check where the first-order partial derivatives vanish to find any critical points within the given region:

The Hessian for this function is

with
, so unfortunately the second partial derivative test fails. However, if we take
we see that
for different values of
; if we take
we see
takes on both positive and negative values. This indicates (0, 0) is neither the site of an extremum nor a saddle point.
Now check for points along the boundary. We can parameterize the boundary by

with
. This turns
into a univariate function
:



At these critical points, we get






We only care about 3 of these results.



So to recap, we found that
attains
- a maximum value of 4096 at the points (0, 8) and (0, -8), and
- a minimum value of -1024 at the point (-8, 0).
Answer:
The expression
has two variables x and y.
Step-by-step explanation:
<u>What is a variable?</u>
A variable is a letter, for instance
or
, that represents an unknown number.
Given the expression

The given expression has three terms which are x, 4y, and -9.
Here:
- The term 'x' is the unknown variable x.
- The term '4y' has a coefficient (the number next to a variable y) of 4.
- The term '-6' is a constant.
As we already know that a variable is a letter, for instance x or y, that represents an unknown number. In other words, the values of x, or y are unknown to us.
Thus, the expression
has two variables x and y.
There are two cases to consider.
A) The removed square is in an odd-numbered column (and row). In this case, the board is divided by that column and row into parts with an even number of columns, which can always be tiled by dominos, and the column the square is in, which has an even number of remaining squares that can also be tiled by dominos.
B) The removed square is in an even-numbered column (and row). In this case, the top row to the left of that column (including that column) can be tiled by dominos, as can the bottom row to the right of that column (including that column). The remaining untiled sections of the board have even numbers of rows, so can be tiled by dominos.
_____
Perhaps the shorter answer is that in an odd-sized board, the corner squares are the ones that there is one of in excess. Cutting out one that is of that color leaves an even number of squares, and equal numbers of each color. Such a board seems like it <em>ought</em> to be able to be tiled by dominos, but the above shows there is actually an algorithm for doing so.