To determine the capacities of the first ten vessels that can be filled completely by the X jar with an exact number of fillings, we can follow these steps:
Step 1: Identify the capacity of the X jar. We are given that the capacity of the X jar is 101 liters.
Step 2: A vessel that can be filled completely by the X jar with an exact number of fillings must have a capacity that is a multiple of the X jar's capacity. Therefore, we need to find the first ten multiples of 101 liters.
Step 3: Find the first multiple, which is just 101 liters itself. This means the smallest vessel we're considering has a capacity of 101 liters and can be filled exactly once with the X jar.
Step 4: To find subsequent multiples, we multiply 101 liters by 2, 3, 4, and so on, up to the tenth multiple. Each result gives us the capacity of a vessel that can be filled by an exact number of fillings from the X jar.
Step 5: Continue this process until we have the capacities for the first ten vessels.
Following through these steps, we get:
1st vessel: [tex]\( 101 \times 1 = 101 \)[/tex] liters
2nd vessel: [tex]\( 101 \times 2 = 202 \)[/tex] liters
3rd vessel: [tex]\( 101 \times 3 = 303 \)[/tex] liters
4th vessel: [tex]\( 101 \times 4 = 404 \)[/tex] liters
5th vessel: [tex]\( 101 \times 5 = 505 \)[/tex] liters
6th vessel: [tex]\( 101 \times 6 = 606 \)[/tex] liters
7th vessel: [tex]\( 101 \times 7 = 707 \)[/tex] liters
8th vessel: [tex]\( 101 \times 8 = 808 \)[/tex] liters
9th vessel: [tex]\( 101 \times 9 = 909 \)[/tex] liters
10th vessel: [tex]\( 101 \times 10 = 1010 \)[/tex] liters
These are the capacities of the first ten vessels that can be filled completely with the X jar using an exact number of fillings.
