9514 1404 393
Answer:
1/3; geometric
Step-by-step explanation:
Apparently, your sequence is ...
81, 27, 9, 3, 1, ...
The differences between these numbers vary, but the ratio of each to the one before is a constant:
27/81 = 9/27 = 3/9 = 1/3
The sequence is geometric with a common ratio of 1/3. The next number in the sequence is (1)(1/3) = 1/3.
The inverse of the matrix ![\left[\begin{array}{cc}11&-5\\3&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D11%26-5%5C%5C3%26-1%5Cend%7Barray%7D%5Cright%5D)
is the matrix ![\left[\begin{array}{cc}\frac{-1}{4} &\frac{5}{4} \\\\\frac{-3}{4} &\frac{11}{4} \end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Cfrac%7B-1%7D%7B4%7D%20%26%5Cfrac%7B5%7D%7B4%7D%20%5C%5C%5C%5C%5Cfrac%7B-3%7D%7B4%7D%20%26%5Cfrac%7B11%7D%7B4%7D%20%5Cend%7Barray%7D%5Cright%5D)
.
The inverse of a matrix A is calculated by the formula:
A' = (1/|A|)(Adj A),
where A' represents the inverse of matrix A,
|A| represents the determinant value of matrix A, and
Adj A represents the Adjoin matrix of matrix A.
So, to calculate the inverse of the matrix , we will first calculate its Adj.
Adj = ![\left[\begin{array}{cc}-1&-3\\5&11\end{array}\right] ^{T}](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%26-3%5C%5C5%2611%5Cend%7Barray%7D%5Cright%5D%20%5E%7BT%7D)
= ![\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%265%5C%5C-3%2611%5Cend%7Barray%7D%5Cright%5D)
.
Now, we calculate |A| = 11*(-1) - (-5)*3 = -11 + 15 = 4.
Therefore A' = (1/|A|)(Adj A),
or, A' = ![(1/4)*\left[\begin{array}{cc}-1&5\\-3&11\end{array}\right]](https://tex.z-dn.net/?f=%281%2F4%29%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%265%5C%5C-3%2611%5Cend%7Barray%7D%5Cright%5D)
,
or, A' = .
Therefore, the inverse of the matrix is the matrix .
Learn more about the inverse of a matrix at
brainly.com/question/16862241
#SPJ10
Start with the equation of a circle whose center is at (h,k) and whose radius is r:
(x-h)^2 + (y-k)^2 = r^2
Substituting the given coordinates of the center:
(x-5)^2 + (y-[-5])^2 = r^2, or (x-5)^2 + (y+5)^2 = r^2
Substituding the given coordinates of a point (6,-2) on the circle:
(6-5)^2 + (-2+5)^2 = r^2
Simplifying:
1^2 + 3^2 = r^2, or 1 + 9 = r^2, or 10= r^2. Then r = sqrt(10).
Answer:
Step-by-step :
Your answer
Your answer
9.75
Mark it as Brainlist answer. Follow me.
Mark it as Brainlist answer. Follow me.
Answer:
a. m/6
b. k-9 (don't get confused with k less than nine)
c. 2x
d. 2x+4
e. n/7
f. (a+b)/4
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