Find m AB and CD intersect at point E

First you have to convert 3 2/5 into a decimal (3.04) than you have to add that number by itself (3.04 + 3.04) which equals 6.08 Second you Convert 5 1/4 into a decimal (5.25) Than again you add that number by itself (5.25 + 5.25) which equals 10.5 you would than take 6.08 and 10.5 and add those together to get 16.58

4 0

3 years ago

Show your solution read the instructions

Annette [7]

Answer:

1) $5r + 2 < s$

2) $12t + 6s < 960$

3) $p - q > 30$

Step-by-step explanation:

1) Length of a ruler = r

Height of Shiela = s

According to the question ,

5 times the length of a ruler increased by 2 .

⇒ $5r + 2$

Also , 5r + 2 is less than height of Shiela.

Hence , the linear inequality is ⇒ $5r + 2 < s$

2) Let the cost of each t-shirt be 't' & cost of each short be 's'.

⇒ Cost of dozen of t-shirts = 12t and Cost of half a dozen shorts = 6s

According to the question ,

12t & 6s is not greater than Php 960.

Hence the linear inequality is ⇒ $12t + 6s < 960$

3) Let the number of Php 100-peso tickets be 'p' and let the number of Php 50-peso tickets be 'q'.

According to the question ,

Difference of p & q is not less than 30

Hence the linear inequality is ⇒ $p - q > 30$

8 0

3 years ago

Suppose that v is an eigenvector of matrix A with eigenvalue λA, and it is also an eigenvector of matrix B with eigenvalue λB. (

galben [10]

Answer:

(a) Yes, $λ_{A}+λ_{B}$

(b) Yes, $λ_{A}λ_{B}$

Step-by-step explanation:

First, lets understand what are eigenvectors and eigenvalues?

Note: I am using the notation $λ_{A}$ to denote Lambda(A) sign.

$v$ is an eigenvector of matrix A with eigenvalue $λ_{A}$

$v$ is also eigenvector of matrix B with eigenvalue $λ_{B}$

So we can write this in equation form as

$Av=λ_{A}v$

So what does this equation say?

When you multiply any vector by A they do change their direction. any vector that is in the same direction as of $Av$ , then this $v$ is called the eigenvector of $A$ . $Av$ is $λ_{A}$ times the original $v$ . The number $λ_{A}$ is the eigenvalue of A.

$λ_{A}$ this number is very important and tells us what is happening when we multiply $Av$ . Is it shrinking or expanding or reversed or something else?

It tells us everything we need to know!

Bonus:

By the way you can find out the eigenvalue of $Av$ by using the following equation:

$det(A-λI)=0$

where I is identity matrix of the size of same as A.

Now lets come to the solution!

(a) Show that $v$ is an eigenvector of $A + B$ and find its associated eigenvalue.

The eigenvalues of $A$ and $B$ are $λ_{A}$ and $λ_{B}$ , then

$(A+B)(v)=Av+Bv=(λ_{A})v + (λ_{B})v=(λ_{A}+λ_{B})(v)$

so, $(A+B)(v)=(λ_{A}+λ_{B})(v)$

which means that $v$ is also an eigenvector of $A+B$ and the associated eigenvalues are $λ_{A}+λ_{B}$

(b) Show that $v$ is an eigenvector of $AB$ and find its associated eigenvalue.

The eigenvalues of $A$ and $B$ are $λ_{A}$ and $λ_{B}$ , then

$(AB)(v)=A(Bv)=A(λ_{B})=λ_{B}(Av)=λ_{B}λ_{A}(v)=λ_{A}λ_{B}(v)$

so,

$(AB)(v)=λ_{A}λ_{B}(v)$

which means that $v$ is also an eigenvector of $AB$ and the associated eigenvalues are $λ_{A}λ_{B}$

5 0

3 years ago