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3 years ago

40 points! Find the distance UV between the points U(2,−2) and V(−5,−3). Round your answer to the nearest tenth, if necessary.

Mathematics

2 answers:

puteri [66]3 years ago

8 0

Answer:

7.1

Step-by-step explanation:

Using the distance formula

d = sqrt ( (x2-x1)^2 + ( y2-y1)^2)

sqrt ( (-5-2)^2 + ( -3- -2)^2)

sqrt( ( -7)^2 + ( -3 +2)^2)

sqrt( ( 49 + 1)

sqrt( 50)

7.071067812

To the nearest tenth

7.1

Ivanshal [37]3 years ago

3 0

Answer:

7.1 units

Step-by-step explanation:

We can use the distance formula to find the distance between these two points.

The distance formula is:

$\sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$ .

x1 is 2, x2 is -5, y1 is -2, and y2 is -3, so we can plug these values into the equation.

$\sqrt {\left( {2 - (-5) } \right)^2 + \left( {-2 - (-3) } \right)^2 }\\\\\sqrt {7^2 + 1^2}\\\\\sqrt{49+1}\\\\\sqrt{50}\approx7.1$

Hope this helped!

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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 $s^3$ .