Find A ∩ B if A = {2, 5, 8, 11, 14} and B = {1, 3, 5, 7}.

Mathematics

2 answers:

Gwar [14]2 years ago

8 0

Answer:

Step-by-step explanation:

$A=\{2,\ 5,\ 8,\ 11,\ 14\}\\\\B=\{1,\ 3,\ 5,\ 7\}\\\\A\ \cap\ B-\text{the intersection of two sets A and B,}\\\text{ is the set that contains all elements of A that also belong to B.}\\\\\text{Therefore:}\ A\ \cap\ B=\{5\}$

LekaFEV [45]2 years ago

7 0

Answer:

Option 2 - $A\cap B=\{5\}$

Step-by-step explanation:

Given : A = {2, 5, 8, 11, 14} and B = {1, 3, 5, 7}.

To find : $A\cap B$ ?

Solution :

The intersection of two sets A and B is the set containing all elements of A that also belong to B and nothing else.

A = {2, 5, 8, 11, 14}

B = {1, 3, 5, 7}

The common elements are 5.

So, $A\cap B=\{5\}$

Therefore, Option 2 is correct.

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Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base.

Tanya [424]

Answer:

The larger cross section is 24 meters away from the apex.

Step-by-step explanation:

The cross section of a right hexagonal pyramid is a hexagon; therefore, let us first get some things clear about a hexagon.

The length of the side of the hexagon is equal to the radius of the circle that inscribes it.

The area is

$A=\frac{3\sqrt{3} }{2} r^2$

Where $r$ is the radius of the inscribing circle (or the length of side of the hexagon).

Now we are given the areas of the two cross sections of the right hexagonal pyramid: $A_1=216\:ft^2\: \:\:\:A_2=486\:ft^2$

From these areas we find the radius of the hexagons:

$r_1=\sqrt{\frac{2A_1}{3\sqrt{3} } } =\sqrt{\frac{2*216}{3\sqrt{3} } }=\boxed{9.12ft}$

$r_2=\sqrt{\frac{2A_2}{3\sqrt{3} } } =\sqrt{\frac{2*486}{3\sqrt{3} } }=\boxed{13.68ft}$

Now when we look at the right hexagonal pyramid from the sides ( as shown in the figure attached ), we see that $r_1$ $r_2$ form similar triangles with length $H$