Answer:
Input Output
-3 -9
2 6
1 3
0 0
5 15
-1 -3
7 21
3 9
10 30
-4 16
1/2 1.5
Step-by-step explanation: Just multiply everything by 3 I think, please tell me if I am wrong
Compute the derivative dy/dx using the power, product, and chain rules. Given
x³ + y³ = 11xy
differentiate both sides with respect to x to get
3x² + 3y² dy/dx = 11y + 11x dy/dx
Solve for dy/dx :
(3y² - 11x) dy/dx = 11y - 3x²
dy/dx = (11y - 3x²)/(3y² - 11x)
The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when
11y - 3x² = 0
or
y = 3/11 x²
(provided that 3y² - 11x ≠ 0)
Substitute y into into the original equation:
x³ + (3/11 x²)³ = 11x (3/11 x²)
x³ + (3/11)³ x⁶ = 3x³
(3/11)³ x⁶ - 2x³ = 0
x³ ((3/11)³ x³ - 2) = 0
One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with
(3/11)³ x³ - 2 = 0
(3/11 x)³ - 2 = 0
(3/11 x)³ = 2
3/11 x = ³√2
x = (11•³√2)/3
Solving for y gives
y = 3/11 x²
y = 3/11 ((11•³√2)/3)²
y = (11•³√4)/3
So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).
56x56=3136 you would divide that by 500 and get 6.272
Answer:
The value of AB is
and it's not possible to multiply BA.
Step-by-step explanation:
Consider the provided matrices.
, ![B=\left[\begin{array}{ccc}3\\5\end{array}\right]](https://tex.z-dn.net/?f=B%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
Two matrices can be multiplied if and only if first matrix has an order m × n and second matrix has an order n × v.
Multiply AB
Matrix A has order 2 × 2 and matrix B has order 2 × 1. So according to rule we can multiply both the matrix as shown:
![AB=\left[\begin{array}{ccc}2&3\\2&1\end{array}\right] \left[\begin{array}{ccc}3\\5\end{array}\right]](https://tex.z-dn.net/?f=AB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%263%5C%5C2%261%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
![AB=\left[\begin{array}{ccc}2\times 3+3\times 5\\2\times 3+1\times 5\end{array}\right]](https://tex.z-dn.net/?f=AB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%5Ctimes%203%2B3%5Ctimes%205%5C%5C2%5Ctimes%203%2B1%5Ctimes%205%5Cend%7Barray%7D%5Cright%5D)
![AB=\left[\begin{array}{ccc}6+15\\6+5\end{array}\right]](https://tex.z-dn.net/?f=AB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%2B15%5C%5C6%2B5%5Cend%7Barray%7D%5Cright%5D)
![AB=\left[\begin{array}{ccc}21\\11\end{array}\right]](https://tex.z-dn.net/?f=AB%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D21%5C%5C11%5Cend%7Barray%7D%5Cright%5D)
Hence, the value of AB is ![\left[\begin{array}{ccc}21\\11\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D21%5C%5C11%5Cend%7Barray%7D%5Cright%5D)
Now calculate the value of BA as shown:
Multiply BA
Matrix B has order 2 × 1 and matrix A has order 2 × 2. So according to rule we cannot multiply both the matrix.
We can multiply two matrix if first matrix has an order m × n and second matrix has an order n × v.
That means number of column of first matrix should be equal to the number of rows of second matrix.
Hence, it's not possible to multiply BA.
Answer:
V ≈ 2144.70 
Step-by-step explanation:
Radius is going to be used instead of the diameter. Half of 16 is 8, and so that will be the value that shall be used.

V ≈ 2144.66 
V ≈ 2144.70 