Which inequality represents the sentence below?

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

2 years ago

Find the slope and reduce.<br> P=(-2, -1) Q=(6,5)<br> Slope = [ ? ]

m_a_m_a [10]

Answer:

Slope=3/4

Step-by-step explanation:

1) Label all values with x1 y1, x2 y2

Then, plug jn each value into this equation:y2-y1/x2-x1

Remember that negative values will become positive when dealjng with a subtraction sign.

5-(-1)=5+1.

---------------= 6/8

6-(-2)=6+2

After getting 6/8, simplify by the gcf (2) to get 3/4

Answer:3/4

3 0

3 years ago

Original price; 30.50; Markdown 30%

Stels [109]

Answer:

After the markdown, the cost will be $21.35

Step-by-step explanation:

This is shown by multiplying the original price, 30.50 by 30%, or 0.30 to get 9.15. Next you subject your product from the original price to get the marked down value at 21.35.

8 0

3 years ago

Which statement explains why one of these triangles is a right triangle? HELP ME!!

lesantik [10]

Answer:

Triangle B

Step-by-step explanation: Look at the square figure on one of the corners. That means that your triangle is a right triangle, which means, its measurement on that corner is 90 degrees

7 0

3 years ago

Read 2 more answers

Arianna earns a weekly salary of $400 plus a 6.5% commission on sales at a gift shop. How much would she make in a workweek if s

lilavasa [31]

Answer:

712

Step-by-step explanation:

400+6.5%of 4800

312+400=712

6 0

2 years ago