First, let me show you some notation.
To show a matrix is an inverse of another matrix, we write
-1 is not an exponent. It just shows that a matrix is an inverse of another matrix.
For a 2x2 matrix, we can get the inverse by first making b and c negatives and swap the positions of a and d.
Then multiply each entry in the matrix by 1 divided by the determinant.
![\left[\begin{array}{ccc}a&b\\c&d\end{array}\right]^{-1} = \frac{1}{ad - bc}\left[\begin{array}{ccc}d&{-b}\\{-c}&a\end{array}\right] = \\ \\ \\ \left[\begin{array}{ccc}d(\frac{1}{ad-bc})&{-b}(\frac{1}{ad-bc}) \\ {-c}(\frac{1}{ad-bc}) &a(\frac{1}{ad-bc}) \end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D%5E%7B-1%7D%20%3D%20%0A%20%20%5Cfrac%7B1%7D%7Bad%20-%20bc%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%26%7B-b%7D%5C%5C%7B-c%7D%26a%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5C%5C%20%20%5C%5C%20%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dd%28%5Cfrac%7B1%7D%7Bad-bc%7D%29%26%7B-b%7D%28%5Cfrac%7B1%7D%7Bad-bc%7D%29%20%5C%5C%20%7B-c%7D%28%5Cfrac%7B1%7D%7Bad-bc%7D%29%20%26a%28%5Cfrac%7B1%7D%7Bad-bc%7D%29%20%5Cend%7Barray%7D%5Cright%5D)
I hope this helped!
9514 1404 393
Answer:
a) 4
b) 3
Step-by-step explanation:
a. The total number of real and complex zeros is equal to the degree of the polynomial. That total is (1 negative real) + (3 positive real/complex) = 4 total zeros. The degree of the polynomial is 4.
The even degree is confirmed by the answer to part b, and by the end-behavior shown in the table, which has a tendency to -∞ for |x|→∞.
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b. The intermediate value theorem tells you there will be zeros in the intervals (0, 1), (1, 2), and (2, 3) according to the values in the table. (The function changes sign in those intervals.) Thus there are 3 positive real zeros.
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<em>Additional comment</em>
Stanley cannot tell anything about Descartes' rule of signs by analyzing the table of function values. To use that rule, he must have terms of the polynomial. If he has those terms, he already knows the degree of the polynomial.
Answer:
<h2>x = 10.3</h2>
Step-by-step explanation:
Use sine.
We have:
<em>look at the table in the picture</em>
Substitute:
<em>multiply both sides by 16</em>
10 children cuz those seven sons are siblings so they would have the same sisters
