To find the volume of a cylinder , you will use the formula
V = Bh, where B is the area of the circular base.
Pi x r^2 x h
pi x 6^2 x 12
V = 432
The volume of the cylinder is 432pi cm³.
Answer:
-b=11
Step-by-step explanation:
Nothing else is equal to a number except its self
Answer:
12
Step-by-step explanation:
if you multiply everything by 5, then you can get rid of the fraction and the equation would now look like this:
x - 40 = 20
and now you can answer this simply
x - 40 = 20
+40 +40
x = 60
and since you multiplied 5 beforehand, now you have to divide by 5 to get the real answer
60 ÷ 5 = 12
therefore, x = 12
Complete Question
The complete question is shown on the first uploaded image
Answer:
First Question
Option A is correct
Second Question
Option C is correct
Third Question
![D = A^{-1} * B^{-1} * C^{-1}](https://tex.z-dn.net/?f=D%20%3D%20%20A%5E%7B-1%7D%20%20%2A%20%20B%5E%7B-1%7D%20%2A%20%20C%5E%7B-1%7D)
Fourth Question
So substituting for D in (ABC) D = I
![(ABC) * A^{-1} * B^{-1} * C^{-1} = I](https://tex.z-dn.net/?f=%28ABC%29%20%2A%20%20A%5E%7B-1%7D%20%20%2A%20%20B%5E%7B-1%7D%20%2A%20%20C%5E%7B-1%7D%20%3D%20%20I)
![I = I](https://tex.z-dn.net/?f=I%20%3D%20%20I)
This proof that ABC is invertible
Step-by-step explanation:
From the question we are told that
A , B and C are invertible which means that
exist
Now
From the question
(ABC) D = I
Where I is an identity matrix
Now when we multiply both sides by
we have
![A^{-1} A BCD = A^{-1} * I](https://tex.z-dn.net/?f=A%5E%7B-1%7D%20%20A%20BCD%20%3D%20%20A%5E%7B-1%7D%20%2A%20I)
![IBCD = A^{-1}](https://tex.z-dn.net/?f=IBCD%20%3D%20%20A%5E%7B-1%7D)
Now when we multiply both sides by
we have
![B^{-1 } *I BCD = A^{-1} * B^{-1}](https://tex.z-dn.net/?f=B%5E%7B-1%20%7D%20%2AI%20BCD%20%3D%20%20A%5E%7B-1%7D%20%20%2A%20%20B%5E%7B-1%7D)
![I CD = A^{-1} * B^{-1}](https://tex.z-dn.net/?f=I%20CD%20%3D%20%20A%5E%7B-1%7D%20%20%2A%20%20B%5E%7B-1%7D)
Now when we multiply both sides by
we have
![C^{-1} * I CD = A^{-1} * B^{-1} * C^{-1}](https://tex.z-dn.net/?f=C%5E%7B-1%7D%20%2A%20I%20CD%20%3D%20%20A%5E%7B-1%7D%20%20%2A%20%20B%5E%7B-1%7D%20%2A%20%20C%5E%7B-1%7D)
![I D = A^{-1} * B^{-1} * C^{-1}](https://tex.z-dn.net/?f=I%20D%20%3D%20%20A%5E%7B-1%7D%20%20%2A%20%20B%5E%7B-1%7D%20%2A%20%20C%5E%7B-1%7D)
![D = A^{-1} * B^{-1} * C^{-1}](https://tex.z-dn.net/?f=D%20%3D%20%20A%5E%7B-1%7D%20%20%2A%20%20B%5E%7B-1%7D%20%2A%20%20C%5E%7B-1%7D)
So substituting for D in the above equation
![(ABC) * A^{-1} * B^{-1} * C^{-1} = I](https://tex.z-dn.net/?f=%28ABC%29%20%2A%20%20A%5E%7B-1%7D%20%20%2A%20%20B%5E%7B-1%7D%20%2A%20%20C%5E%7B-1%7D%20%3D%20%20I)
![I = I](https://tex.z-dn.net/?f=I%20%3D%20%20I)
This proof that ABC is invertible
The second i think you did good