Answer:
- 50 ft by 75 ft
- 3750 square feet
Step-by-step explanation:
Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...
y = (300 -2x)/3
And the enclosed area is ...
A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)
This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.
The maximum area is enclosed when the dimensions are ...
50 ft by 75 ft
That maximum area is 3750 square feet.
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<em>Comment on the solution</em>
The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).
Answer:
Observe that the first and the second player have equal probability to get any of number. Using the principle of that symmetry, we have that
<u>Event X = 1 </u>means that the first player has got greater number than the second player, but not than the third player. So, choose any three numbers out of five of them and say that the minimal number out of these three goes to the second player, mean number to the first one and the largest to the third one. Permute remaining two numbers on remaining two people. Hence
<u>Event X = 2</u> means that the first player has got greater number than the second and the third player, but not than the fourth player. So, choose any four numbers out of five of them and say that the minimal number and the next minimal out of these four go to the second and the third player (and permute them), third number to the first one and the largest to the fourth player. Give remaining number to the last person. Hence
<u>Event X = 3</u> means that the first player has got greater number than the second, the third, and the forth player, but not than the fifth player. So, permute these five numbers as follows: give the highest to the last person, the second highest to the first, and permute remaining numbers on the remaining people. Hence
<u>Event X = 4</u> means basically the first player has won all the battles i.e, he has got the greatest number. Hence
Answer:
The answer to your question is: ∠K = 138°
Step-by-step explanation:
m∠N = 42°
m∠K = ?
The sum of all the internal angles in a quadrangle equals 360°
then
∠N + ∠L + ∠M + ∠K = 360°
∠N = ∠ L and ∠M = ∠K
So, 2 ∠N + 2 ∠K = 360
Substitution
2 (42) + 2 ∠K = 360
84 + 2 ∠K = 360
2 ∠K = 360 - 84
2 ∠K = 276
∠K = 276 / 2
∠K = 138°
Answer:
You will get 13 groups.
Step-by-step explanation:
324 / 24 = 13.5 So there are 13 groups with 5 left over. Hope this helps.
Answer:
Awww love you man!
(And me lol)
Step-by-step explanation: