A train leaves Philadelphia at 3 PM. The second train leaves the same city in the same direction at 9 PM. What is the speed of t
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Answer:
Step-by-step explanation:
Given: See Attachment
Required
Determine the length of the legs
To do this, we apply Pythagoras theorem.
In this case:
Open Bracket
Collect Like Terms
Solving using quadratic formula:
So:
or
Since, x can't be negative, then:
One of the leg is:
Any locker with a number that is a multiple of 8, 12, and 75 will contain all three animals.
The least common multiple of these three numbers is
and so any multiples of 600 between 1 and 3500 will contain all three animals. These are 600, 1200, 1800, 2400, and 3000.
Why is the LCM 600? You can determine that using the prime factorizations of the three given numbers:
The LCM can be obtained by multiplying as many prime numbers together as are needed to contain the prime factorizations of the three numbers. This is obtained with
(at least three 2s to get the 8; at least one 3 and two of the previous 2s to get 12; and at least two 5s along with the previous 3 to get 75)
The least common multiple of these three numbers is
and so any multiples of 600 between 1 and 3500 will contain all three animals. These are 600, 1200, 1800, 2400, and 3000.
Why is the LCM 600? You can determine that using the prime factorizations of the three given numbers:
The LCM can be obtained by multiplying as many prime numbers together as are needed to contain the prime factorizations of the three numbers. This is obtained with
(at least three 2s to get the 8; at least one 3 and two of the previous 2s to get 12; and at least two 5s along with the previous 3 to get 75)