Answer:
V=349525.333*pi
Step-by-step explanation:
Volume of a sphere: V=(4/3)*pi*r^3 where r=radius.
r=64
V=(4/3)*pi*(64)^3=(4/3)(262144)pi=349525.333*pi
The answer is true to all of them.
There are 20! number of ways for everyone to do this so that at the end of the move, each seat is taken by exactly one person.
People are seated in a 2 by 10 rectangle grid. All 20 persons stand up from their seats and relocate to an orthogonally neighboring one upon the blowing of a whistle.
Now, we have to find the number of possible ways in which each seat is taken up by exactly one person after the move.
As the number of people is 20 and 20 seats are to filled exactly once.
So, the number of ways = 20!
Learn more about number here:
brainly.com/question/1991469
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We want to find the values of a, b, c, and d such that the given matrix product is equal to a 2x2 identity matrix. We will solve a system of equations to find:
<h3>
Presenting the equation:</h3>
Basically, we want to solve:
![\left[\begin{array}{cc}-1&2\\a&1\end{array}\right]*\left[\begin{array}{cc}b&c\\1&d\end{array}\right] = \left[\begin{array}{cc}1&0\\0&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%262%5C%5Ca%261%5Cend%7Barray%7D%5Cright%5D%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Db%26c%5C%5C1%26d%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D)
The matrix product will be:
![\left[\begin{array}{cc}-b + 2&-c + 2d\\a*b + 1&a*c + d\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-b%20%2B%202%26-c%20%2B%202d%5C%5Ca%2Ab%20%2B%201%26a%2Ac%20%2B%20d%5Cend%7Barray%7D%5Cright%5D)
Then we must have:
-b + 2 = 1
This means that:
b = 2 - 1 = 1
We also need to have:
a*b + 1 = 0
we know the value of b, so we just have:
a*1 + b = 0
Now the two remaining equations are:
-c + 2d = 0
a*c + d = 1
Replacing the value of a we get:
-c + 2d = 0
-c + d = 1
Isolating c in the first equation we get:
c = 2d
Replacing that in the other equation we get:
-(2d) + d = 1
-d = 1
Then:
c = 2d = 2*(-1) = -2
So the values are:
If you want to learn more about systems of equations, you can read:
brainly.com/question/13729904
Answer:
Step 1: Simplify both sides of the equation.
8−2(3−x)=4x+6
8+(−2)(3)+(−2)(−x)=4x+6(Distribute)
8+−6+2x=4x+6
(2x)+(8+−6)=4x+6(Combine Like Terms)
2x+2=4x+6
2x+2=4x+6
Step 2: Subtract 4x from both sides.
2x+2−4x=4x+6−4x
−2x+2=6
Step 3: Subtract 2 from both sides.
−2x+2−2=6−2
−2x=4
Step 4: Divide both sides by -2.
−2x
−2
=
4
−2
Step-by-step explanation:
