Answer:
<u><em>The length of AD is 32 feet</em></u>
Step-by-step explanation:
<u>Proportional distances
</u>
When distances are proportions of others, we can express all of them as relative fractions until we reach some known distance and solve for the desired length
Let's call x the length of AD. Given C is the midpoint of AD, then
![\displaystyle AC=CD=\frac{x}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AC%3DCD%3D%5Cfrac%7Bx%7D%7B2%7D)
Given B is the midpoint of AC, then
![\displaystyle AB=BC=\frac{AC}{2}=\frac{x}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AB%3DBC%3D%5Cfrac%7BAC%7D%7B2%7D%3D%5Cfrac%7Bx%7D%7B4%7D)
If we know BC=8 feet
![\displaystyle \frac{x}{4}=8\ feet](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bx%7D%7B4%7D%3D8%5C%20feet)
![\displaystyle x=32\ feet](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D32%5C%20feet)
The length of AD is 32 feet
25+80=105
180-105=75=a
y=90 because it’s a right triangle so
25+90=115
180-115=65=x
y=90
x=65
a=75
Answer:
See proof below.
Step-by-step explanation:
True
For this case we need to use the following theorem "If
are eigenvectors of an nxn matrix A and the associated eigenvalues
are distinct, then
are linearly independent". Now we can proof the statement like this:
Proof
Let A a nxn matrix and we can assume that A has n distinct real eingenvalues let's say ![\lambda_1, \lambda_2, ....,\lambda_n](https://tex.z-dn.net/?f=%20%5Clambda_1%2C%20%5Clambda_2%2C%20....%2C%5Clambda_n)
From definition of eigenvector for each one
needs to have associated an eigenvector
for ![1 \leq i \leq n](https://tex.z-dn.net/?f=%201%20%5Cleq%20i%20%5Cleq%20n)
And using the theorem from before , the n eigenvectors
are linearly independent since the
are distinct so then we ensure that A is diagonalizable.
Answer:
2a. 1/4
2b. 2/8
2c. yes, 1/4 = 2/8 because
2 / 8 = 2 ÷ 2 / 8 ÷ 2 = 1 / 4.
2d. the total number of parts doubled in the denominator, the number of parts represented in the numerator doubled as well.
The operations of division and multiplication are made proportionally to the numerator and denominator.