A box of colored crayons contains 9 distinct colors. In how many ways can 2 colors be chosen, assuming that the order of the col
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Answer:
Step-by-step explanation:
Have in mind the definition of the term , and now work on what the term
is based on the previous definition:
In the next step do NOT combine the numerical values, but try to identify the term (
) in the expression (notice the use of square brackets to group the relevant terms):
So now we have the term "" defined in a recursive manner based on the previous term "
"
Find the intersection point between the 2 restraint equations:
Substitute back in to find y-value:
P is maximized at point (12,6)
Substitute back in to find y-value:
P is maximized at point (12,6)
Let be the dimensions of the rectangle. We know the equations for both area and perimeter:
So, we have the following system:
From the second equation, we can deduce
Plug this in the first equation to get
Refactor as
And solve with the usual quadratic formula to get
Both solutions are feasible, because they're both positive.
If we chose the positive solution, we have
If we choose the negative solution, we have
So, we're just swapping the role of and
. The two dimensions of the rectangle are
and