Volume a sphere: [4/3]π(r^3)
Space between the spheres = Volume of the larger sphere - Volume of the smaller sphere
= [4/3]π (R^3) - [4/3π](r^3) = [4/3]π(R^3 - r^3) = [4/3]π {(5cm)^3 - (4cm)^3} =
= 255.5 cm^3
Answer: 255.5 cm^3
Answer:
![(x -3 )^2 = 10](https://tex.z-dn.net/?f=%28x%20-3%20%29%5E2%20%3D%2010)
Step-by-step explanation:
Given
![x^2 - 6x - 1 = 0](https://tex.z-dn.net/?f=x%5E2%20-%206x%20-%201%20%3D%200)
Required: Express as a perfect square
![x^2 - 6x - 1 = 0](https://tex.z-dn.net/?f=x%5E2%20-%206x%20-%201%20%3D%200)
Add 10 to both sides
![x^2 - 6x - 1 +10= 0+10](https://tex.z-dn.net/?f=x%5E2%20-%206x%20-%201%20%2B10%3D%200%2B10)
![x^2 - 6x +9= 10](https://tex.z-dn.net/?f=x%5E2%20-%206x%20%2B9%3D%2010)
Expand
![x^2 - 3x - 3x+9= 10](https://tex.z-dn.net/?f=x%5E2%20-%203x%20%20-%203x%2B9%3D%2010)
Factorize:
![x(x - 3) - 3(x - 3)= 10](https://tex.z-dn.net/?f=x%28x%20-%203%29%20-%203%28x%20%20-%203%29%3D%2010)
Factorize:
![(x -3 )(x - 3) = 10](https://tex.z-dn.net/?f=%28x%20-3%20%29%28x%20-%203%29%20%3D%2010)
![(x -3 )^2 = 10](https://tex.z-dn.net/?f=%28x%20-3%20%29%5E2%20%3D%2010)
Answer:
671/1296
The probability of rolling at least one six is therefore 1 − 625/1296 = 671/1296 ≈ . 517.
Step-by-step explanation:
For this case we must find
![(f + g) (x).](https://tex.z-dn.net/?f=%28f%20%2B%20g%29%20%28x%29.)
By definition we have to:
![(f + g) (x) = f (x) + g (x)](https://tex.z-dn.net/?f=%28f%20%2B%20g%29%20%28x%29%20%3D%20f%20%28x%29%20%2B%20g%20%28x%29)
We have the following functions:
![f (x) = 5x ^ 3-2\\g (x) = 2x + 1](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%205x%20%5E%203-2%5C%5Cg%20%28x%29%20%3D%202x%20%2B%201)
Now, applying the given definition, we have:
![(f + g) (x) = 5x ^ 3-2 + 2x + 1\\(f + g) (x) = 5x ^ 3 + 2x-1](https://tex.z-dn.net/?f=%28f%20%2B%20g%29%20%28x%29%20%3D%205x%20%5E%203-2%20%2B%202x%20%2B%201%5C%5C%28f%20%2B%20g%29%20%28x%29%20%3D%205x%20%5E%203%20%2B%202x-1)
Answer:
![(f + g) (x) = 5x ^ 3 + 2x-1](https://tex.z-dn.net/?f=%28f%20%2B%20g%29%20%28x%29%20%3D%205x%20%5E%203%20%2B%202x-1)