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4 years ago

What is the domain and range of the relation shown in

Mathematics

1 answer:

Leya [2.2K]4 years ago

6 0

Answer:

Domain : {10, 15, 19, 32}

Range: {-1, 5, 9}

Step-by-step explanation:

As the table of the relation is given as follows:

X Y

10 5

15 9

19 -1

32 5

From this table, we can define the relation by combining the ordered pairs from the table. Each and every order pair consists of x-coordinate and corresponding y-coordinate of any corresponding point.

So, the relation from the table can be made as follows:

relation : {(10, 5), (15, 9), (19, -1), (32, 5)}

Domain of a relation consists of all the x-coordinates (first elements) of order pairs.

Range of a relation consists of all the y-coordinates (second elements) of ordered pairs.

So, domain and range of relation will be as follows:

Domain : {10, 15, 19, 32}

Range: {-1, 5, 9}

Note: If there is any duplicate element in any x or y-coordinate of any ordered pair, it will be written only once when we determine domain and range. Here, in this example, 5 is duplicate, so, it will be mentioned only one time when we determine the range of this relation.

Keywords: domain, relation, range

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Answer:

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Step-by-step explanation:

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3 years ago

The volume of a cube is related to the area of a face by the formula V = A^3/2What is the volume of a cube whose face has an are

Sveta_85 [38]

Answer:

$\huge\boxed{1000 \ \text{cm}^3}$

Step-by-step explanation:

There are two ways we can solve this equation.

<h2>A) Using the formula provided</h2>

The formula provided states that the volume of a cube based on the area of one of it's faces will be $a^{\frac{3}{2}}$ , a the area of one face. Since we know the area of one face, we can substitute that inside the equation.

$100^{\frac{3}{2}}$

It's important to note that when we have a number to a fraction power, it's the same as taking the denominator root of the base to the numerator power.

So - $100^{\frac{3}{2}}$ becomes $\sqrt{100^3}$

$100^3=1000000$

$\sqrt{1000000}=1000$

Therefore, the volume of this cube will be $1000 \ \text{cm}^3$

<h2>B) Using prior knowledge about cubes</h2>

We can additionally use prior knowledge to find the volume of this cube.

We know that the area of a square will be $s^2$ , where s is the length of a side. We also know the formula to find the volume of a cube from it's side length is $s^3$ .