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1 year ago

Consider the sets A = {4,6,8} and B = {4,5,6} Find Ax B (b) Find the power set AB)

Mathematics

1 answer:

katrin [286]1 year ago

7 0

a) A × B is the Cartesian product of A and B, given by the set

A × B = {(a, b) | a ∈ A and b ∈ B}

Then for A = {4, 6, 8} and {4, 5, 6}, we have the product

A × B = {(4, 4), (4, 5), (4, 6), (6, 4), (6, 5), (6, 6), (8, 4), (8, 5), (8, 6)}

b) The power set of a set X is the set containing all subsets of X. I'm not sure what you're asking to find the power set of, though. Hopefully it's not of A × B, since that would contain 2⁹ = 512 elements...

Instead I'll assume you mean a simpler set, such as A ∩ B. The intersection of A and B is

A ∩ B = {4, 6, 8} ∩ {4, 5, 6} = {4, 6}

and has only 2 elements, so its power set has 2² = 4 elements (much more manageable!) and is the set

Pow(A ∩ B) = {{}, {4}, {6}, {4, 6}}

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Otrada [13]

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2 years ago

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he value of y varies directly with the value of x. When y = 32.5, x = 5. What is the value of y when x = 10? A) 1.5 B) 2.2 C) 37

xz_007 [3.2K]

Answer:

D) 65

Step-by-step explanation:

The formula for direct variation is

y = kx

where k is the constant of variation.

If we know y=32.5 and x=5, we can substitute in to calculate k

32.5 = k * 5

Divide each side by 5

32.5/5 = k

6.5 = k

So the equation is

y = 6.5k

Given x =10

y = 6.5*10

y = 65

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3 years ago

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HELP PLZ.....I NEED THIS....One wheel of a bicycle has 24-inch diameter. About how many feet will the bicycle travel when the wh

Ne4ueva [31]

First, find the circumference of the wheel using $C=2 \pi r$

You know that your diameter is 24. To find the radius, divide the diameter by 2, which is 12.

Input 12 as r and simplify. -> $C=2 \pi (12)$
$C=24 \pi$

estimate your Pi as 3.14
$C=24(3.14)$

and multiply. C=75.36

Now you know the distance of one full revolution in inches. To find 200 revolutions, multiply that answer by 200.

75.36 * 200 = 15,072 inches

But because this is in inches, you have to find the answer in feet, so just divide that answer by 12.

15,072 / 12 = 1,256 ft

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2 years ago

6. This solid is a composite of a cube and square pyramid. The base of the solid is the base of the cube. Find the surface area

Sergio039 [100]

Answer:

960 ft^2

Step-by-step explanation:

There are 9 surfaces forming the solid.

5 of them are congruent squares and 4 of them are congruent triangles.

area of square = (side)^2

area of triangle = (base)(height)/2

total surface area = 5 * area of square + 4 * area of triangle

A = 5 * (12 ft)^2 + 4 * (12 ft * 10 ft)/2

A = 5 * 144 ft^2 + 4 * 60 ft^2

A = 720 ft^2 + 240 ft^2

A = 960 ft^2

3 0

2 years ago

2x + 3y = -6<br> -2x + 3y = 6<br><br> How do I graph it

Elanso [62]

Answer:

$(-3, 0)$

Step-by-step explanation:

$\: \: \: 2x + 3y = - 6 \\ -2x + 3y = \: \: \: 6 \\ \frac{ + \: \: \: \: \: \: - \: \: \: \: \: \: = - }{ }{} \\ \: \: \: 4x \: \: \: \: \: \: \: \: \: \: \: \: = - 12 \\ \\ x = \frac{ - 12}{4} \\ \\ x = - 3$

now,

$-2( - 3) + 3y = 6 \\ 6 + 3y = 6 \\ 3y = 6 - 6 \\ 3y = 0 \\ y = \frac{0}{ 3} \\ y = 0$

thus, (-3, 0)

3 0

2 years ago

Consider the sets A = {4,6,8} and B = {4,5,6} Find Ax B (b) Find the power set AB)​

Consider the sets A = {4,6,8} and B = {4,5,6} Find Ax B (b) Find the power set AB)