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4 years ago

Compare 1/5 and 0.201

1 answer:

8 0

$We\ convert\ \frac{1}{5 }\ into\ decimal\\\\
\frac{1}{5}=\frac{20}{100}=0,2\\\\\
Now\ compare\ \frac{1}{5}=0,2\ and\ 0,201:\\\\
0,201>\frac{1}{5}$

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A solid right pyramid has a square base. The length of the base edge is4 cm and the height of the pyramid is 3 cm period what is

Illusion [34]

Answer:

The volume of this pyramid is 16 cm³.

Step-by-step explanation:

The volume $V$ of a solid pyramid can be given as:

$\displaystyle V = \frac{1}{3} \cdot b \cdot h$ ,

where

$b$ is the area of the base of the pyramid, and
$h$ is the height of the pyramid.

Here's how to solve this problem with calculus without using the previous formula.

Imaging cutting the square-base pyramid in half, horizontally. Each horizontal cross-section will be a square. The lengths of these squares' sides range from 0 cm to 3 cm. This length will be also be proportional to the vertical distance from the vertice of the pyramid.

Refer to the sketch attached. Let the vertical distance from the vertice be $x$ cm.

At the vertice of this pyramid, $x = 0$ and the length of a side of the square is also $0$ .
At the base of this pyramid, $x = 3$ and the length of a side of the square is $4$ cm.

As a result, the length of a side of the square will be

$\displaystyle \frac{x}{3}\times 4 = \frac{4}{3}x$ .

The area of the square will be

$\displaystyle \left(\frac{4}{3}x\right)^{2} = \frac{16}{9}x^{2}$ .

Integrate the area of the horizontal cross-section with respect to $x$

from the top of the pyramid, where $x = 0$ ,
to the base, where $x = 3$ .

$\displaystyle \begin{aligned}\int_{0}^{3}{\frac{16}{9}x^{2}\cdot dx} &= \frac{16}{9}\int_{0}^{3}{x^{2}\cdot dx}\\ &= \frac{16}{9}\cdot \left(\frac{1}{3}\int_{0}^{3}{3x^{2}\cdot dx}\right) & \text{Set up the integrand for power rule}\\ &= \left.\frac{16}{9}\times \frac{1}{3}\cdot x^{3}\right|^{3}_{0}\\ &= \frac{16}{27}\times 3^{3} \\ &= 16\end{aligned}$ .

In other words, the volume of this pyramid is 16 cubic centimeters.

5 0

3 years ago

Is this right I need help with this

Margarita [4]

Y axis is counting by 2's
it started at 2 and went up to 6
Y = 4

X axis is counting by 2'2
starts at one goes to 3
X = 2

Slope is 4/2 because rise over run
4/2 = 2
Slope is simplified to 2.

5 0

3 years ago

A triangle has two sides of lengths 7 and 12. What value could the length of

Norma-Jean [14]

Answer:

A. 7

Step-by-step explanation:

Since the triangle sides are not defined, therefore let the base side have the 12 unit and one of the slant side be 7 unit.

Therefore height of the triangle, h can gotten from the Pythagoras theorem as thus:

7² = (12/2)² + h²

49 = 36 + h²

h² = 49 - 36 = 13

h = √13

knowing the height of the triangle, we can apply same rule to the other unknown slant side, x as thus:

x² = (12/2)² + h²

x² = 36 + 13 = 49

x = √49

x = 7

4 0

3 years ago

1) Give 5 examples of a difference of two perfect squares

Katyanochek1 [597]

ᴀɴsᴡᴇʀ:

1.Example, x²-25 can be factored as (x+5)(x-5).

2.This method is based on the pattern (a+b)(a-b)=a²-b², which can be verified by expanding the parentheses in (a+b)(a-b).

3.When an expression can be viewed as the difference of two perfect squares, i.e. a²-b², then we can factor it as (a+b)(a-b). For example, x²-25 can be factored as (x+5)(x-5).

ʜᴏᴘᴇ ɪᴛ ʜᴇʟᴘs!

☞︎︎︎ᴄᴀʀʀʏ ᴏɴ ʟᴇᴀʀɴɪɴɢ☜︎︎︎

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3 years ago

Winston bought an encyclopedia priced at $42. Shipping and handling cost anadditional 30% of the price. What was the total cost

Sergio039 [100]

Answer:

42.3

Sorry I haven't been answering your questions I'm just behind on homework.

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3 years ago