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3 years ago

5

The circle has a radius of 5 cm. Find the circumference. Give your answer to the nearest tenth. Use pi on your calculator. DO NO

T WRITE THE UNITS IN YOUR ANSWER

2 answers:

poizon [28]3 years ago

8 0

Answer:

Step-by-step explanation:

Circumference is pi × diameter

Diameter is 2x radius

10π is the circumference

10π= 31.4cm

Leviafan [203]3 years ago

3 0

Answer:

31.4

Step-by-step explanation:

Diameter = 2 * radius = 2 * 5 = 10

Circumference = pi * diameter = 3.14 * 10 = 31.4

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Explain how to estimate the quotient using compatible<br>numbers.plz help fast

Nadya [2.5K]

<h2><u>PLEASE MARK BRAINLIEST!</u></h2>

Answer:

To estimate the quotient, make the fractions "like" fractions. To do this, you need to make the fractions have the same denominator, and turn them into improper fractions.

Step-by-step explanation:

$27\frac{2}{3} = 27 \frac{20}{30}$

$3\frac{9}{10} = 3\frac{27}{30}$

Now the denominators are the same --> they are "like" fractions.

$27\frac{20}{30} + 3\frac{27}{30} = ?$

$27\frac{20}{30} + 3\frac{27}{30} = (27 + 3) + (\frac{20}{30} + \frac{27}{30})$

$27\frac{20}{30} + 3\frac{27}{30} = (30) + (\frac{47}{30})$

$27\frac{20}{30} + 3\frac{27}{30} = (30) + (1 \frac{17}{30})$

$27\frac{20}{30} + 3\frac{27}{30} = 31 \frac{17}{30}$

Your answer is $31\frac{17}{30}$ .

I hope this helps!

3 0

3 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

3 years ago

A= 1/2bh pls help I don’t remember how to do this

marta [7]

I think it’s the triangle

8 0

3 years ago

Read 2 more answers

For what value of h is 24=h/10-6

faltersainse [42]

Answer:

h=3

Step-by-step explanation:

h/10 -6 =24

+6 to each side

h/10=30

divide each side by 10

h=3

5 0

3 years ago

I NEED REAL HELP IF NOT REAL GET BANNED

kari74 [83]

Answer:

Every minute, the hour hand moves 1/2 of a degree, and the minute hand moves 6 degrees. So in 48 minutes, the hour hand moves 24 degrees and the minute hand moves 288 degrees. 288-180-24=84. So, 84 degrees.

6 0

3 years ago