33s^5t^4u^8 ÷ 11st^3u^8
1 answer:
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First check for the critical points of <em>f</em> by checking where the first-order derivatives vanish.
Notice how the point (1, 2) lies on the line <em>y</em> = 2<em>x</em> ; at this point, we get a value of <em>f</em>(1, 2) = -5 (MIN).
Next, check the points where the boundary lines intersect, which occurs at the points (0, 0), (0, 2), and (1, 2). We already checked the last one. We find <em>f</em>(0, 0) = 1 (MAX) and <em>f</em>(0, 2) = -3.
Now check on the boundary lines themselves. If <em>x</em> = 0, then
which has a maximum value of -3 when <em>y</em> = 2 (so we get the same critical point as before).
If <em>y</em> = 2, then
with a maximum of -5 when <em>x</em> = 1.
If <em>y</em> = 2<em>x</em>, then
with the same maximum of -5 when <em>x</em> = 1.
<u>Answer:</u>
A) 720 ways
B) 15 ways
C) 6 ways
<u>Step-by-step explanation:</u>
A) To find the number of ways Alicia can arranger her 6 paintings, we will find factorial of 6 by multiplying all of the positive integers equal to or less than that number i.e. 6 to get:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Alicia can arrange her paintings in 720 ways.
B) We use the following formula (when order is not important) to find the number of permutations of n objects taken r at a time:
Therefore, Alicia can choose any 4 of her paintings in 15 ways.
C) Number of ways Alicia can arrange 3 out of 6 paintings = 3! = 3*2*1 = 6 ways