Answer:
h = 19.7 ft.
Step-by-step explanation:
Use the Pythagoras Theorem

Now we take square root on both sides,

so the value of h equals 19.7 ft.
Answer:
-20
Step-by-step explanation:
-20
You find the eigenvalues of a matrix A by following these steps:
- Compute the matrix
, where I is the identity matrix (1s on the diagonal, 0s elsewhere) - Compute the determinant of A'
- Set the determinant of A' equal to zero and solve for lambda.
So, in this case, we have
![A = \left[\begin{array}{cc}1&-2\\-2&0\end{array}\right] \implies A'=\left[\begin{array}{cc}1&-2\\-2&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right]=\left[\begin{array}{cc}1-\lambda&-2\\-2&-\lambda\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D%20%5Cimplies%20A%27%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C-2%260%5Cend%7Barray%7D%5Cright%5D-%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Clambda%260%5C%5C0%26%5Clambda%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1-%5Clambda%26-2%5C%5C-2%26-%5Clambda%5Cend%7Barray%7D%5Cright%5D)
The determinant of this matrix is

Finally, we have

So, the two eigenvalues are


Let's solve your problem:
The answer would be 280%.
We know the following information:
2pm - 15 toilet paper rolls
5pm - 57 toilet paper rolls
We have to find the <u>percent rate of change.</u>
Here is how we will do this problem:
<h3><u>
First, Set up a ratio:</u></h3>
Change in the quantity [15 - 57]
-------------------------------------
Original quantity [15]
57 - 15 = 42
<h3><u>
Next, we will divide. the ratio.</u></h3>
Given quantity - 42
Number of packs sold at 2pm - 15
Fraction - 42/15
<h3><u>
Convert the fraction to a decimal.</u></h3>
Fraction - 42/15
Decimal - 2.8
<h3>
<u>Make the decimal to a percent.</u></h3>
Decimal - 2.8
Percent - 28%
<u>Add a zero to the 28.</u>
<h2><u>
Our answer is 280%</u></h2>
<h3>
</h3>
Answer:
x = 2
Step-by-step explanation:
