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dontcareanyonemo
08.01.2021 •
Mathematics
A rainwater was 2/3 full of water. After 60 liters of water were used from the barrel, it was 5/12 full. How much water does the barrel hold when full?
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Ответ:
240 liters
Work Shown:
x = capacity of barrel in liters
This value of x is some positive real number. It represents the most amount of water the barrel can hold.
The problem states that the barrel is 2/3 full to start with. This means, we start off with (2/3)x liters of water. Then we subtract off 60 of them to get to 5/12 full, meaning we have (5/12)x liters left.
We can form this equation
(2/3)x - 60 = (5/12)x
Multiply both sides by 12 to clear out the fractions
(2/3)x - 60 = (5/12)x
12*( (2/3)x - 60 ) = 12*(5/12)x
12*(2/3)x - 12*60 = 12*(5/12)x
8x - 720 = 5x
From here we solve for x
8x - 5x = 720
3x = 720
x = 720/3
x = 240
The barrel's full capacity is 240 liters
Check:
2/3 of 240 = (2/3)*240 = 160
The barrel starts off with 160 liters of water inside.
We then use 60 of them to be left with 160-60 = 100 liters
Note how 100/240 = (5*20)/(12*20) = 5/12, showing that 100 liters out of 240 total reduces to the fraction 5/12. In other words, when we say "5/12 full" we mean 100 liters full. This helps confirm we have the right answer.
Ответ:
Step-by-step explanation:
1] the minimum number of arcs in any strongly connected digraph with n vertices is 'n' . the graph look like a cycle
the graph is in the attached file
in a directed cycle we have strongly connected graph since we can reach any vertax from any vertax, it has minimum arc which is 'n'
since if we use less than n vertax then the given graph has atmost one tree which is not strongly connected graph.
2] the maximum distance between two vertax is 5 which from veratx 1 to vertax 6 distance is 5
1----->2------->3--------->4------->5-------->6
if we use cycle of n node then the maximum distance between two vertax is n-1