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4 years ago

Are the set of all square numbers under 50 and the set of all triangular numbers that are less than 50 disjoint?

Mathematics

1 answer:

Alina [70]4 years ago

7 0

Answer:

No, the two sets are not disjoint.

Step-by-step explanation:

Set of triangular numbers to 50: 1, 3, 6, 10, 15, 21, 28, 36, 45

Set of square numbers to 50: 1, 4, 9, 16, 25, 36, 49

They have 1 and 36 in common, so they are not disjoint, or in other words, they have some of the same numbers.

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3 years ago

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barxatty [35]

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3 years ago

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Why is 1 neither prime nor a composite number?

Nadya [2.5K]

Answer:

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2 years ago

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BaLLatris [955]

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3 years ago

Find the least common multiple of 8x³y6z, 6x5z², and 10yzº.

kvv77 [185]

Answer:

The Least Common Multiple (LCM) of $8x^3y6z,6x5z^2, \text{ and } 10yz^0 \text{ is } 240 x^3yz^2$

Step-by-step explanation:

Definition of LCM

The LCM of a, b , c is the smallest multiplier that is divisible by a, b and c

Here the three terms are :

$8x^3y6z$

$6x5z^2$

$10yz^0=10y$ since $z^0 = 1$

Factoring using prime factorization we get $8x^3y6z = 2.2.2.x^3.y.2.3.z$ ³

= $2^4\cdot \:3\cdot \:x^3\cdot \:y\cdot \:z$ (1)

Factoring $6x5z^2$ we get

$2\cdot \:3\cdot \:5\cdot \:x\cdot \:z^2$ (2)

Factoring $10yz^0$ we get

$2 \;\cdot\; 5y$ ( $z^0 = 1)$ (3)

The LCM is the multiple of each of the highest power in each factor

$2^4\;.\;3\;.\;5\;.x^2\;.\;y\;.z^2 = 240 x^3yz^2$

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2 years ago