What is the constant term of x+10+3x

Find all of the eigenvalues λ of the matrix A. (Hint: Use the method of Example 4.5 of finding the solutions to the equation 0 =

Svetradugi [14.3K]

Answer:

$\lambda=8,\ \lambda=-5$

Step-by-step explanation:

<u>Eigenvalues of a Matrix</u>

Given a matrix A, the eigenvalues of A, called $\lambda$ are scalars who comply with the relation:

$det(A-\lambda I)=0$

Where I is the identity matrix

$I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right]$

The matrix is given as

$A=\left[\begin{array}{cc}3&5\\8&0\end{array}\right]$

Set up the equation to solve

$det\left(\left[\begin{array}{cc}3&5\\8&0\end{array}\right]-\left[\begin{array}{cc}\lambda&0\\0&\lambda \end{array}\right]\right)=0$

Expanding the determinant

$det\left(\left[\begin{array}{cc}3-\lambda&5\\8&-\lambda\end{array}\right]\right)=0$

$(3-\lambda)(-\lambda)-40=0$

Operating Rearranging

$\lambda^2-3\lambda-40=0$

Factoring

$(\lambda-8)(\lambda+5)=0$

Solving, we have the eigenvalues

$\boxed{\lambda=8,\ \lambda=-5}$

8 0

3 years ago

When Sam’s little brother was born, he was 18 inches tall. Each year, he grows an average of 3 inches. Sam’s brother continues t

andrew-mc [135]

Answer:

45

Step-by-step explanation:

year 1 : 18 in

every year after that he grows 3 in so 3 in so 3x9=27

then 27+18=45

8 0

2 years ago

What does 17/10x 10/17 equal

Rasek [7]

$\frac{17}{10}\times\frac{10}{17}=\frac{17\times10}{10\times17}=\frac{170}{170}=1$

5 0

1 year ago

Trapezoids and kites

lisov135 [29]

QUESTION 3

The sum of the interior angles of a kite is $360\degree$ .

$\Rightarrow 36\degree +70\degree+m$ .

$\Rightarrow 106\degree+m$ .

$\Rightarrow m$ .

But the two remaining opposite angles of the kite are congruent.

$\Rightarrow m$

$\Rightarrow m$ .

$\Rightarrow 2m$ .

$\Rightarrow m$ .

QUESTION 4

RH is the hypotenuse of the right triangle formed by the triangle with side lengths, RH,12, and 20.

Using the Pythagoras Theorem, we obtain;

$|RH|^2=12^2+20^2$

$|RH|^2=144+400$

$|RH|^2=544$

$|RH|=\sqrt{544}$

$|RH|=4\sqrt{34}$

QUESTION 5

The given figure is an isosceles trapezium.

The base angles of an isosceles trapezium are equal.

Therefore $m$

QUESTION 6

The measure of angle Y and Z are supplementary angles.

The two angles form a pair of co-interior angles of the trapezium.

This implies that;

$m$

$\Rightarrow m$

QUESTION 7

The sum of the interior angles of a kite is $360\degree$ .

$\Rightarrow 48\degree +110\degree+m$ .

$\Rightarrow 158\degree+m$ .

$\Rightarrow m$ .

But the two remaining opposite angles are congruent.

$\Rightarrow m$

$\Rightarrow m$ .

$\Rightarrow 2m$ .

$\Rightarrow m$ .

QUESTION 8

The diagonals of the kite meet at right angles.

The length of BC can also be found using Pythagoras Theorem;

$|BC|^2=4^2+7^2$

$\Rightarrow |BC|^2=16+49$

$\Rightarrow |BC|^2=65$

$\Rightarrow |BC|=\sqrt{65}$

QUESTION 9.

The sum of the interior angles of a trapezium is $360\degree$ .

$\Rightarrow m$ .

But the measure of angle M and K are congruent.

$\Rightarrow m$ .

6 0

3 years ago

Which of the following situations calls for a hypothesis test about a population mean?

tigry1 [53]

Answer:

Step-by-step explanation:

Hypothesis test about a population mean is done to evaluate two exclusive statements about a population in order to determine which is best supported by the sample data.

From the situations given, the correct options are

b. A recent study estimated that 20% of all college students in the United States smoke. The head of Health Services at Goodheart University suspects that the proportion of smokers may be lower there. This would require taking a sample and determining the probability of success.

c. A certain prescription allergy medicine is suppose to contain an average of 245 parts per million (ppm) of active ingredient. The manufacturer wants to check whether the mean concentration in a large shipment of pills is 245 ppm or not.

d. A report on the College Board website stated that in 2003 males scored generally higher than females on the SAT exam. An educational researcher wants to check whether this is true in her school district.

3 0

3 years ago