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3 years ago

Tell whether the sequence is arithmetic. If it is, what is the common difference? (1 point)

Mathematics

1 answer:

larisa [96]3 years ago

7 0

Since an arithmetic sequence is a sequence of numbers and the difference of any two successive members of the sequence is a constant

So this question is arithmetic because it keep minus by 7

from 19 - 7 = 12

12 - 7 = 5

5 - 7 = -2

so common difference is -7

or you can check with arithmetic formular as

$a_{n}$ = $a_{1}$ + (n−1)d

I will just put in the 4th term which is -2 and n will equal to 4

and $a_{1}$ is the 1st term which is 19

-2 = 19 + (4−1)d

-2 - 19 = 3d

d = $\frac{-21}{3}$

d = -7

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PLSS HELP IVE BEEN ASKING FOR SO LONG :(

yan [13]

Answer: 7

Step-by-step explanation:

\frac{-14}{-2}

Both 14 and 2 are divisible by 2, so we can divide both of these numbers by 2.

\frac{-7}{-1}

Both numbers are negative, so we can divide both of these numbers by -1.

\frac{7}{1}

This gives us 7.

7 0

2 years ago

Read 2 more answers

Find the local maximum and minimum values and saddle point(s) of the function.

iogann1982 [59]

$f(x,y)=9e^y(y^2-x^2)$
$\nabla f=\left\langle-18xe^y,9ye^y(2+y)\right\rangle$

Critical points occur where the gradient is zero. This is guaranteed whenever $x=0$ and either $y=0$ or $y=-2$ .

The Hessian matrix for this function looks like

$H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}-18e^y&-18xe^y\\-18xe^y&9e^y(2-x^2+4y+y^2)\end{bmatrix}$

and has determinant

$|H(x,y)|=-162e^{2y}(2+x^2+4y+y^2)$

Maxima occur whenever the determinant is positive and $f_{xx}$ . Minima occur whenever both the determinant and $f_{xx}$ are positive. Saddle points occur whenever the determinant is negative.

At $(0,0)$ , you have a saddle point since the determinant reduces to -324, so $(0,0,0)$ is the saddle point.

At $(0,-2)$ , the determinant is $\dfrac{324}{e^4}>0$ and $f_{xx}(0,-2)=-\dfrac{18}{e^2}$ , so $\left(0,-2,\dfrac{36}{e^2}\right)$ is a local maximum.

No other critical points remain, so you're done.

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