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3 years ago

14

Find the domain and range of the function graphed below.

1 answer:

earnstyle [38]3 years ago

4 0

Answer:

Domain -1 ≤x<2

Range 0 < y ≤4

Step-by-step explanation:

Domain is the input values

X goes from -1 to 2 ( 2 not included)

Domain -1 ≤x<2

Range is the output values

y goes from 0 ( not included) to 4

Range 0 < y ≤4

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Which of the following represents the ratio of the long leg to the short leg in the right triangle shown below

madreJ [45]

D) 2:1 because long leg will be bigger, and small leg will be smaller, e.g. Long Leg(2): Small Leg(1)

6 0

4 years ago

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Consider the matrix A. A = 1 0 1 1 0 0 0 0 0 Find the characteristic polynomial for the matrix A. (Write your answer in terms of

dusya [7]

Answer with Step-by-step explanation:

We are given that a matrix

$A=\left[\begin{array}{ccc}1&0&1\\1&0&0\\0&0&0\end{array}\right]$

a.We have to find characteristic polynomial in terms of A

We know that characteristic equation of given matrix $\mid{A-\lambda I}\mid=0$

Where I is identity matrix of the order of given matrix

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

Substitute the values then, we get

$\begin{vmatrix}1-\lambda&0&1\\1&-\lambda&0\\0&0&-\lambda\end{vmatrix}=0$

$(1-\lambda)(\lamda^2)-0+0=0$

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

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

Hence, characteristic polynomial = $\lambda^3-\lambda^2=0$

b.We have to find the eigen value for given matrix

$\lambda^2(1-\lambda)=0$

Then , we get $\lambda=0,0,1-\lambda=0$

$\lambda=1$

Hence, real eigen values of for the matrix are 0,0 and 1.

c.Eigen space corresponding to eigen value 1 is the null space of matrix $A-I$

$E_1=N(A-I)$

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

Apply $R_1\rightarrow R_1+R_3$

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

Now,(A-I)x=0[/tex]

Substitute the values then we get

$\left[\begin{array}{ccc}0&0&1\\1&-1&0\\0&0&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]=0$

Then , we get $x_3=0$

And $x_1-x_2=0$

$x_1=x_2$

Null space N(A-I) consist of vectors

x= $\left[\begin{array}{ccc}x_1\\x_1\\0\end{array}\right]$

For any scalar $x_1$

$x=x_1\left[\begin{array}{ccc}1\\1\\0\end{array}\right]$

$E_1=N(A-I)=Span(\left[\begin{array}{ccc}1\\1\\0\end{array}\right]$

Hence, the basis of eigen vector corresponding to eigen value 1 is given by

$\left[\begin{array}{ccc}1\\1\\0\end{array}\right]$

Eigen space corresponding to 0 eigen value

$N(A-0I)=\left[\begin{array}{ccc}1&0&1\\1&0&0\\0&0&0\end{array}\right]$

$(A-0I)x=0$

$\left[\begin{array}{ccc}1&0&1\\1&0&0\\0&0&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]=0$

$\left[\begin{array}{ccc}x_1+x_3\\x_1\\0\end{array}\right]=0$

Then, $x_1+x_3=0$

$x_1=0$

Substitute $x_1=0$

Then, we get $x_3=0$

Therefore, the null space consist of vectors

$x=x_2=x_2\left[\begin{array}{ccc}0\\1\\0\end{array}\right]$

Therefore, the basis of eigen space corresponding to eigen value 0 is given by

$\left[\begin{array}{ccc}0\\1\\0\end{array}\right]$

5 0

3 years ago

Help me please! Thank you.

Alex_Xolod [135]

f'(x) = 9+1/x

f'(9) = 9+1/9 = 82/9

6 0

4 years ago

Given: sin theta=2/3 and is in the second quadrant; evaluate the following expression. sin 2 theta

Dmitry [639]

Answer:The answer to your question is 3. 0

Step-by-step explanation:

Process

1.- Find the cos a

Opposite side = 5

Hypotenuse = 13

Adjacent side = ?

Adjacent side² = 13² - 5²

= 169 - 25

= 144

Adjacent side = 12

cos a = 12/13

2.- Find the sin b

sin b = 5/13

3.- Use the formula below to find sin(a + b)

sin (a + b) = sina cosb + sin b cos a

- Substitution

sin (a + b) = (5/13)((-12/13) + (5/13)/12/13)

- Simplification

sin (a + b) = -60/169 + 60/13

- Result

sin(a + b) = 0

Step-by-step explanation:

4 0

3 years ago

#7 Cecilia made a fruit basket for her grandmother. There were 3 bananas and 6 oranges in the basket. What is the ratio of the n

castortr0y [4]

The answer is A.

explanation:

the obvious ratio is 3:6, because there are 3 bananas and 6 oranges. if you simplify 3:6 it’s 1:2.

hope i helped :)

4 0

4 years ago

Read 2 more answers