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]3 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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Evaluate 3x+4(y+3) when x is 5 less than the quotient of y and 3, and y=18.

romanna [79]

It is given that x is 5 less than the quotient of y and 3.

And given value of y is 18 .

So quotient of y and 3 is

$\frac{18}{3} = 6$

And 5 less than 6 =1

So we have y=18 and x=1

Given expression is

$3x+4(y+3)$

At x=1 and y=18, we will get

$3(1)+4(18+3) =3 + 4(21)$

$= 3+84=87$

4 0

3 years ago

Given two vectors A=2i+3j+4k,B=i-2j+3k find the magnitude and direction of sum (physics question)

Law Incorporation [45]

Answer:

$Magnitude =\sqrt{59} \\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}}$

Step-by-step explanation:

A=2i+3j+4k

B=i-2j+3k

Sum of the vectors:

A + B = 2i+3j+4k + i-2j+3k = 3i + j + 7k

$Magnitude =\sqrt{3^2 + 1^2+ 7^2} \\\\Magnitude =\sqrt{9+1+49} \\\\Magnitude =\sqrt{59}$

Direction of the sum of the vectors:

$\widehat{A + B} =\frac{\overrightarrow{A + B}}{Magnitude\: of \:\overrightarrow{A + B}} \\\\\widehat{A + B} =\frac{3i + j + 7k}{\sqrt {59}} \\\\\widehat{A + B} =\frac{3}{\sqrt {59}} i +\frac{1}{\sqrt {59}} j+\frac{7}{\sqrt {59}} k\\\\Direction \: of \: \overrightarrow{A + B} = \frac{3}{\sqrt {59}} , \:\frac{1}{\sqrt {59}} , \:\frac{7}{\sqrt {59}} \\\\$