Mathematics: A20 foot ladder is lean against a building. the foot of the ladder is 6 feet from the building. find theangle the ladder makes with the building.

A20 foot ladder is lean against a building. the

Laydax1587

18.06.2022

Given:

The set is

$A=\{x:x^2=25\text{ and }6x=125\}$

To find:

Whether the given set is empty or not.

Solution:

A set is called empty set if it has no elements.

We have,

$A=\{x:x^2=25\text{ and }6x=125\}$

We need to find the solutions of x^2=25 and 6x=125 . The common solutions of these two equations are the elements of given set.

x^2=25

$x=\pm \sqrt{25}$

$x=\pm 5$

x=5,-5 ...(i)

And,

6x=125

$x=\dfrac{125}{6}$

$x\approx 20.83$ ...(ii)

From (i) and (ii) it is clear that, there is no common value of x which satisfy both equations x^2=25 and 6x=125 .

Since there is no element in set A, therefore, the given get A is an empty set.

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