<em>V = 120 in^3</em>
<u><em>Here is why:</em></u>
The volume formula for a pyramid is:
![V=\frac{1}{3}Bh](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7DBh)
The B stands for the area of the base, which in this case is a right triangle. We will find the area of the right triangle first, then plug it into the equation.
The area formula for a triangle is:
![A=\frac{1}{2}bh](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7Dbh)
Plug in the numbers.
![A=\frac{1}{2}*9*10](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%2A9%2A10)
A = 45
Now we have found the area of B, we can plug it into the volume formula for the pyramid.
![V=\frac{1}{3}*45*8](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%2A45%2A8)
V = 120 in^3
Answer:
![x_2 \approx -1.769](https://tex.z-dn.net/?f=x_2%20%5Capprox%20-1.769)
Step-by-step explanation:
Let ![f(x)=x^3+x+7](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E3%2Bx%2B7)
So ![f'(x)=3x^2+1](https://tex.z-dn.net/?f=f%27%28x%29%3D3x%5E2%2B1)
![x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}](https://tex.z-dn.net/?f=x_%7Bn%2B1%7D%3Dx_n-%5Cfrac%7Bf%28x_n%29%7D%7Bf%27%28x_n%29%7D)
Let ![x_1=-2](https://tex.z-dn.net/?f=x_1%3D-2)
We are going to find ![x_2](https://tex.z-dn.net/?f=x_2)
So we are evaluating ![-2-\frac{f(-2)}{f'(-2)}](https://tex.z-dn.net/?f=-2-%5Cfrac%7Bf%28-2%29%7D%7Bf%27%28-2%29%7D)
First step find f(-2)
Second step find f'(-2)
Third step plug in those values and apply PEMDAS!
![f(-2)=(-2)^3+(-2)+7=-8-2+7=-10+7=-3](https://tex.z-dn.net/?f=f%28-2%29%3D%28-2%29%5E3%2B%28-2%29%2B7%3D-8-2%2B7%3D-10%2B7%3D-3)
![f'(-2)=3(-2)^2+1=3(4)+1=12+1=13](https://tex.z-dn.net/?f=f%27%28-2%29%3D3%28-2%29%5E2%2B1%3D3%284%29%2B1%3D12%2B1%3D13)
So
![x_2=-2-\frac{-3}{13} \\\\ x_2=\frac{-26+3}{13} \\\\ x_2=\frac{-23}{13} \\\\ x_2 \approx -1.769](https://tex.z-dn.net/?f=x_2%3D-2-%5Cfrac%7B-3%7D%7B13%7D%20%5C%5C%5C%5C%20x_2%3D%5Cfrac%7B-26%2B3%7D%7B13%7D%20%5C%5C%5C%5C%20x_2%3D%5Cfrac%7B-23%7D%7B13%7D%20%5C%5C%5C%5C%20x_2%20%5Capprox%20-1.769)
Answer:
The total number of balls in the pyramid will be 55.
Step-by-step explanation:
Cannonballs are stacked In a pyramid shape with a base of 5 cannonballs on a side.
Therefore, at the base, the number of balls is 5².
In the layer above the base layer, there are 4 balls on each side.
So, in the layer above the base layer, the number of balls is 4².
Similarly, in the next levels, the number of balls will be 3², 2² and 1.
Therefore, the total number of balls in the pyramid will be (5² + 4² + 3² + 2² + 1) = 55. (Answer)
I don’t know spanish sorry