Find the domain and range of the function graphed below. Write your answers in interval notation.

Mathematics

1 answer:

attashe74 [19]2 years ago

7 0

Answer:

Domain: $[-3, 1)$
Range: $[-5, 4]$

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

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Three brothers have ages that are consecutive odd integers. The difference between the age of the oldest and twice the age of th

Genrish500 [490]

N, N+2, and N + 4 are the ages

(N + 4) - (2N) = (N + 2) -24

4 - N = N - 22

2N = 26

N = 13

The brothers are 13, 15, and 17 years old.

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3 years ago

Determine which of the indicated column vectors are eigenvectors of the given matrix

gladu [14]

]Eigenvectors are found by the equation $(A-\lambda I) \vec{v} = 0$$ implying that $\det(A-\lambda I) = 0$ . We then can write:

$A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ]$

And:

$\det(A-\lambda I) = (4-\lambda)(1-\lambda) - 10 = 0$

Gives us the characteristic polynomial:

$\lambda^2 - 5 \lambda -6 = 0 \implies \lambda_1 = -1, \lambda_2 = 6$

So, solving for each eigenvector subspace:

$\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]$

Gives us the system of equations:

$4x + 2y = -x \newline 5x + y = - y$

Producing the subspace along the line $y = -\frac{5}{2} x$

We can see then that 3 is the answer.

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3 years ago

Write the first five terms of the sequence defined by the explicit formula

denis-greek [22]

<u>Answer:</u>

The correct answer option is: 19, 13, 3, -11, -29.

<u>Step-by-step explanation:</u>

We are given the following explicit formula for an arithmetic sequence:

$a_n=21-2n^2$