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3 years ago

Find the Y intercept of a line that passes through 3, -5 and has a slope of -1

1 answer:

6 0

$\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-5})~\hspace{10em} slope = m\implies -1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-5)=-1(x-3)\implies y+5=-x+3$

$\bf y=-x\underset{\uparrow }{-2}\leftarrow \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~\hfill \stackrel{y-intercept}{(0,-2)}$

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Derrick and Sam need 10 pounds of colored gravel for the bottom of their new fish tank. Derrick has 2 pounds of purple gravel an

Sunny_sXe [5.5K]

Answer:

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8 0

3 years ago

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.

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3 years ago

Solve the equation 3(x+2)=5(x-2)

Sladkaya [172]

Answer:

3( x + 2 ). = 5( x - 2)

3x + 6 = 5x - 10

-2x = - 16 

minus,minus cancel

x = 16/2 

x = 8 

8 0

3 years ago

Read 2 more answers

What is the answer to 2/3-4x+7/2=-9x+5/6

zzz [600]

Answer:

-2/3

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4 0

4 years ago

Read 2 more answers

The number of boys varies directly as the number of girls and inversely as the number of teachers. When there are 24 boys and 16

lidiya [134]

SO from what I did was...

Since 24 x 3 = 72 , I did the same to 16.

16 x 3 = 48

But because instead of their being 3 teachers there is 1... What I did is just was to divide 48 / 2 which gave me the answer of 24...

So what I think the answer is...

There are 72 boys, 24 girls, and 1 teacher...

Unless I am just dumb and it would be 48 girls, but I think I did it right.

I hope I was able to help out.

3 0

3 years ago