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3 years ago

PLS HELP ME AND SHOW WORK.

Mathematics

1 answer:

Alex17521 [72]3 years ago

3 0

Answer:

$4 = (x + 7 {)}^{2} + (y - 3 {)}^{2}$

Step-by-step explanation:

equation of a circle

${r}^{2} = (x - {h} )^{2} + (y - {k)}^{2}$

we know the center is (-7, 3)

the radius is 2

we replace (h,k) with the center coordinates

and input the radius

${2}^{2} = (x -( - 7)) ^{2} + (y - 3)^{2}$

simplify to this:

$4 = (x + 7 {)}^{2} + (y - 3 {)}^{2}$

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Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.

Aleks [24]

Answer:

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

Step-by-step explanation:

The actual Series is::

$\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$

The method we are going to use is comparison method:

According to comparison method, we have:

$\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n$

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

$=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}$

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}$

Now:

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}$

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

$\sum_{n=1}^{inf}\frac{1}{n^p}$

if p>1 then series converges. In oue case we have:

$\sum_{n=1}^{inf}b_n=\frac{1}{n^4}$

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

5 0

3 years ago

What is the correct answer?

natima [27]

Answer:

The first one:

Equation n+(n+1) +(n+2)=36

3n+3=36

the numbers are 11, 12,13

Step-by-step explanation:

So if you plug ll for n you get 36

So if you plug 12 in for in u get 39

Then in you plug 13 in for n u get 41

I hoped that helped

4 0

2 years ago

Read 2 more answers

What are all the exact solutions of -3tan^2(x)+1=0? Give your answer in radians.

goldenfox [79]

$\displaystyle\\
 -3\tan^2x + 1 = 0\\\\
 -3\tan^2x = -1\\\\
\tan^2x = \frac{-1}{-3} \\\\
\tan^2x = \frac{1}{3} ~~~~~ \Big|~\sqrt{~~~} \\\\
\sqrt{\tan^2x} = \sqrt{\frac{1}{3}} \\\\
\tan x = \Big| \frac{1}{ \sqrt{3} } \Big|\\\\
\tan x = \Big| \frac{\sqrt{3}}{ 3 } \Big|\\\\
\tan x = \frac{\sqrt{3}}{ 3 }~~~\Longrightarrow~~x_1= \frac{\pi}{6} + k\pi,~~k \in N \\\\ 
\tan x = -\frac{\sqrt{3}}{ 3 }~~~\Longrightarrow~~x_2= \pi-\frac{\pi}{6} + k\pi = \frac{5\pi}{6} + k\pi,~~k \in N \\\\ 
$

4 0

3 years ago

Read 2 more answers

What is the answer to 71m= Cm

Veseljchak [2.6K]

180 cm. it is that answer because ...

K H D U D C M

71 m times 100 is 180

8 0

3 years ago

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which option shows 18÷15 as a fraction or a mixed number? A. 2315 B. 1518 C. 11815 D. 1315

Marysya12 [62]

Answer:

It's B.) 1518

using fraction calculator**

As a positive improper fraction (numerator > denominator):

18/15 = 6/5

As a mixed number

(a whole number and a proper fraction, of the same sign):

18/15 = 1 1/5

As a decimal number:

18/15 = 1.2

As a percentage:

18/15 = 120%

Step-by-step explanation:

4 0

3 years ago