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3 years ago

Decrease £16870 by 3% , give your answer rounded 2 decimal places

1 answer:

5 0

To decrease it by 3% we need to fine 97% of it and 97% is the same as 0.97

16870 times 0.97=16363.9

16870 decreased by 3% is 16363.9

I hope I've helped!

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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

Olga had more than 6 aces in what percent of tennis matches

Tanya [424]

Answer:

50%

Step-by-step explanation:

TRUST

5 0

3 years ago

*27. Jane has -$30 in her bank account, her electric company charges her her monthly bill of

Lorico [155]

Answer:

-$173

Step-by-step explanation:

$-30-128=-158 \\ \\ -158-15=-173$

8 0

2 years ago

Absolute value equations please help!!!!

Leona [35]

Answer:

#3×|x-9|=0

|x-9|=0

X-9=0

X=9

# |2x-9|-4=2

|2x-9|=2+4

|2x-9|=6

2x-9=6

2x=9=-6

X=15/2

X=3/2

1 to x power =3/2 or

2 to x power =15/2

Step-by-step explanation:

Hope I helped u

4 0

3 years ago

If 2x − 3 = 7, evaluate 3x + 4.

timofeeve [1]

X equals 5 so 3x+4= 19 ..................

6 0

3 years ago

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