What is the solution to the system of equations 2x + 3y = 40 and y = x + 10? oy - y

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

Solve the following equations using any method. Show your work and check your

Gemiola [76]

a) The solution for the equation 2x + 16 = 5x + 4 is x=4.

b) The solution for the equation 3x − 5 = 2x + 14 is x=19.

c) The solution for the equation 5x − 5 = x + 15 is x=5.

Step-by-step explanation:

a) The given equation is 2x + 16 = 5x + 4

From the above equation, it can be found that the equation consists of x terms and constant terms.
Therefore, bring all the x terms on one side and the constant terms on other side of the equation.
This gives the simplified form of the equation to solve for x value.

⇒ 16-4 = 5x-2x

⇒ 12 = 3x

⇒ x = 12/3

⇒ x = 4

The solution for the given equation is x=4.

To check, substitute x=4 in the equation :

2(4) + 16 = 5(4) + 4

8+16 = 20+4

24 = 24

Therefore, the solution x=4 satisfies the equation 2x + 16 = 5x + 4

Similarly,

b) The given equation is 3x − 5 = 2x + 14

⇒ 3x-2x = 14+5

⇒ x = 19

The solution for the given equation is x=19.

To check, substitute x=19 in the equation :

3(19) - 5 = 2(19) + 14

57-16 = 38+14

52 = 52

Therefore, the solution x=19 satisfies the equation 3x − 5 = 2x + 14

Similarly,

c) The given equation is 5x − 5 = x + 15

⇒ 5x-x = 15+5

⇒ 4x = 20

⇒ x = 20/4

⇒ x = 5

The solution for the given equation is x=5.

To check, substitute x=5 in the equation :

5(5) - 5 = 5 + 15

25-5 = 20

20 = 20

Therefore, the solution x=5 satisfies the equation 5x − 5 = x + 15

5 0

2 years ago

Compare the probability of winning

kykrilka [37]

Answer:

B. would be the best choice

7 0

3 years ago

Read 2 more answers

Read through the solution below. Then, answer

serg [7]

Answer:

the answer is e=mc^2 I think

6 0

2 years ago

-4(x+5)=-4x-30 solution

luda_lava [24]

Answer:

no solution

Step-by-step explanation:

-4(x+5)=-4x-30

-4x-20=-4x+30

no solution

x cancel

7 0

2 years ago

What is the solution to the system of equations 2x + 3y = 40 and y = x +10?oy - y - 12​

What is the solution to the system of equations 2x + 3y = 40 and y = x +10?oy - y - 12