Write the slope intercept form equation of the line given in graph
1 answer:
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]Eigenvectors are found by the equation 
implying that 
. We then can write:
![A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ]](https://tex.z-dn.net/?f=%20A-%5Clambda%20I%20%3D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%204-%5Clambda%20%26%202%20%5C%5C%205%20%26%201-%5Clambda%20%5Cend%7Barray%7D%5Cright%20%5D%20)
And:
Gives us the characteristic polynomial:
So, solving for each eigenvector subspace:
![\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]](https://tex.z-dn.net/?f=%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%204%20%26%202%20%5C%5C%205%20%26%201%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20x%20%5C%5C%20y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%3D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20-x%20%5C%5C%20-y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20)
Gives us the system of equations:
Producing the subspace along the line
We can see then that 3 is the answer.
And:
Gives us the characteristic polynomial:
So, solving for each eigenvector subspace:
Gives us the system of equations:
Producing the subspace along the line
We can see then that 3 is the answer.
Answer:
45 square inches
Step-by-step explanation:
Akira receives the prize at the science fair for having the most informative project her trophy is in the shape of a square pyramid and is covered in shiny gold foil how much gold foil did it take to cover the trophy including the bottom
Total surface = surface area of the base square + area of 4 triangles
Calculate the surface area of the base square
surface area of the square = s^2
where s= side length
s=3 in
The surface area of the base =s^2
=3^2
= 9 square inches
The surface area of the side triangles
The area of the triangle = (1/2)* side length* slant height
Side length=3 in
Slant height=6 in
substituting the values,
The area of the triangle =1/2*3*6
= 18/2
= 9 square inches
There are 4 triangles
The area of 4 triangles = 4 x 9
= 36 square inches
Therefore,
Total surface = surface area of the base square + area of 4 triangles
= 9 + 36
= 45 square inches
