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3 years ago

Hi can anybody tell me the answer

Mathematics

2 answers:

MArishka [77]3 years ago

6 0

<u>Answer</u>:

8x^5y^7

<u>Step by step explanation</u>

$4 {x}^{2} {y}^{3} \times 2 {x}^{3} {y}^{4} \\ 4 \times 2 \times {x}^{2} \times {x}^{3} \times {y}^{3} \times y ^{4} \\ 8 \times {x}^{2 + 3} \times {y}^{3 + 4} \\ =8 {x}^{5} {y}^{7}$

AlexFokin [52]3 years ago

5 0

Answer:

$\huge \purple { \boxed{ 8 {x}^{5} {y}^{7} }}$

Step-by-step explanation:

$4 {x}^{2} {y}^{3} \times 2 {x}^{3} {y}^{4} \\ = 2 \times 4 \times {x}^{2} \times {x}^{3} \times {y}^{3} \times {y}^{4} \\ = 8 \times {x}^{2 + 3} \times {y}^{3 + 4} \\ \huge \red { \boxed{= 8 {x}^{5} {y}^{7} }}$

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How many 7-digit numbers can be

padilas [110]

Answer: 5040 7-digit numbers

Step-by-step explanation:

Permutations:

1: 1 ==> 1 permutation ==> 1 ==> 1!

12: 12, 21 ==> 2 permutations ==> 1*2 ==> 2!

123: 123, 132, 213, 231, 312, 321 ==> 6 permutations ==> 1*2*3 ==> 3!

7-digits: 7!=

1*2*3*4*5*6*7=5040 7-digit numbers

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2 years ago

Guys,whats 1 2/3 times 4?

Lemur [1.5K]

6 and 2/3 that is the answer

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3 years ago

Read 2 more answers

(1) (10 points) Find the characteristic polynomial of A (2) (5 points) Find all eigenvalues of A. You are allowed to use your ca

Yuri [45]

Answer:

Step-by-step explanation:

Since this question is lacking the matrix A, we will solve the question with the matrix

$\left[\begin{matrix}4 & -2 \\ 1 & 1 \end{matrix}\right]$

so we can illustrate how to solve the problem step by step.

a) The characteristic polynomial is defined by the equation $det(A-\lambdaI)=0$ where I is the identity matrix of appropiate size and lambda is a variable to be solved. In our case,

$\left|\left[\begin{matrix}4-\lamda & -2 \\ 1 & 1-\lambda \end{matrix}\right]\right|= 0 = (4-\lambda)(1-\lambda)+2 = \lambda^2-5\lambda+4+2 = \lambda^2-5\lambda+6$

So the characteristic polynomial is $\lambda^2-5\lambda+6=0$ .

b) The eigenvalues of the matrix are the roots of the characteristic polynomial. Note that

$\lambda^2-5\lambda+6=(\lambda-3)(\lambda-2) =0$

So $\lambda=3, \lambda=2$

c) To find the bases of each eigenspace, we replace the value of lambda and solve the homogeneus system(equalized to zero) of the resultant matrix. We will illustrate the process with one eigen value and the other one is left as an exercise.

If $\lambda=3$ we get the following matrix

$\left[\begin{matrix}1 & -2 \\ 1 & -2 \end{matrix}\right]$ .

Since both rows are equal, we have the equation

$x-2y=0$ . Thus x=2y. In this case, we get to choose y freely, so let's take y=1. Then x=2. So, the eigenvector that is a base for the eigenspace associated to the eigenvalue 3 is the vector (2,1)

For the case $\lambda=2$ , using the same process, we get the vector (1,1).

d) By definition, to diagonalize a matrix A is to find a diagonal matrix D and a matrix P such that $A=PDP^{-1}$ . We can construct matrix D and P by choosing the eigenvalues as the diagonal of matrix D. So, if we pick the eigen value 3 in the first column of D, we must put the correspondent eigenvector (2,1) in the first column of P. In this case, the matrices that we get are

$P=\left[\begin{matrix}2&1 \\ 1 & 1 \end{matrix}\right], D=\left[\begin{matrix}3&0 \\ 0 & 2 \end{matrix}\right]$

This matrices are not unique, since they depend on the order in which we arrange the eigenvalues in the matrix D. Another pair or matrices that diagonalize A is

$P=\left[\begin{matrix}1&2 \\ 1 & 1 \end{matrix}\right], D=\left[\begin{matrix}2&0 \\ 0 & 3 \end{matrix}\right]$

which is obtained by interchanging the eigenvalues on the diagonal and their respective eigenvectors

4 0

3 years ago

Can anyone help me with Qs 9-14 pls

lions [1.4K]

Answer:

Step-by-step explanation:

angle 2 and angle 3 are linear pair

angle 1 and angle 7 are alternate exterior angle

angle 4 + angle 7=a80 degree

124 + angle 7=180

angle 7=180-124

angle 7=56 degree

angle 1 is supplementary to angle 2 ,angle 4, angle 6, angle 8 .In supplementary angle sum of two angle is always 180 degree.

angle 4 and angle 5 are supplementary angles because their sum is equal to 180 degree.

angle 4 + angle 5(being co interior angle)

3x+17+x+23=180

4x+40=180

4x=19=180-40

x=140/4

x=35

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3 years ago

The graph is a two-dimensional representation of the

Mila [183]

Answer: D. 12 ft

Step-by-step explanation:

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2 years ago