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3 years ago

Find the common ratio of the following geometric sequence 5/12, 1/4 , 3/20,9/100,27/500

1 answer:

7 0

All you have to is divide two consecutive terms to calculate the common ratio

1/4 divided by 5/12 = 1/4 * 12/5 = 12/20 = 3/5

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What is the y-interceptof the graph below?*

Talja [164]

Answer:

J- 2

Step-by-step explanation:

its where the line goes through the plot on the vertical axis

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2 years ago

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Which ratio is equivalent to 7:3?

aliina [53]

Answer:

The answer is B.

Step-by-step explanation:

7x4 is 28 which means you have to multiply 3x4. That gives you 12. 28:12 is the proper ratio. (Hope this helped!)

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2 years ago

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If ƒ(x) = 2x, then ƒ -1(x) =<br><br> -2x<br> ½x<br> x - 2

kap26 [50]

Answer: second option

Step-by-step explanation:

To find the inverse function of the given function f(x):

$f(x)=2x$

You need to:

Substitute $f(x)=y$ into the function:

$y=2x$

Now, you need to solve for "x", to do this, you must divide both sides of the function by 2:

$\frac{y}{2}=\frac{2x}{2}\\\\\frac{y}{2}=x$

Now, replace "x" with "y" and replace "y" with "x":

$\frac{x}{2}=y$

Therefore, substituting $y=f^{-1}(x)$ you get:

$f^{-1}(x)=\frac{x}{2}$ or $f^{-1}(x)=\frac{1}{2}x$

7 0

2 years ago

(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

2 years ago

How to Evaluate 5/9 x 8

GuDViN [60]

Answer:

4 4/9

Step-by-step explanation:

First, you have to set it up: 5/9 times 8/1

We made it 8/1 since it has to be a fraction in the multipying ocess and the one does not change the value.

Next, Multiply.

5/9x8/1=40/9 as an inproper fraction

As a proper fraction, it is written as 4 4/9

3 0

2 years ago