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3 years ago

Help will be appreciated I need help with math

Mathematics

1 answer:

k0ka [10]3 years ago

3 0

3. (-12,4)
4. (0,-14)
5. (14,0)
6. (0,0)

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Find the radius of convergence, r, of the series. ? n2xn 7 · 14 · 21 · ? · (7n) n = 1

defon

I'm guessing the series is supposed to be

$\displaystyle\sum_{n=1}^\infty\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}$

By the ratio test, the series converges if the following limit is less than 1.

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7\cdot14\cdot21\cdot\cdots\cdot(7n)\cdot(7(n+1))}}{\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}}\right|$

The first $n$ terms in the numerator's denominator cancel with the denominator's denominator:

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7(n+1)}}{n^2x^n}\right|$

$|x^n|$ also cancels out and the remaining factor of $|x|$ can be pulled out of the limit (as it doesn't depend on $n$ ).

$\displaystyle|x|\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2}{7(n+1)}}{n^2}\right|=|x|\lim_{n\to\infty}\frac{|n+1|}{7n^2}=0$

which means the series converges everywhere (independently of $x$ ), and so the radius of convergence is infinite.

3 0

3 years ago

I need help plss!! I don’t understand

MA_775_DIABLO [31]

Since it says what the area of the circle is, you need to work the problem backwards from finding the area. So it would be 100 ÷ 3.14 = 31.84 that is the radius. Next you need to find the diameter, so 31.84 × 2 = 63.68. Now you multiply 63.68 × 3.14 = 199.95, round that to 200, divide 200 ÷ 2 = 100 ÷ 2 = 50 miles

Answer= 50 miles

4 0

3 years ago

Solve:

Alex Ar [27]

Answer:

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

Simplify cos^2 A/1+sin A

Stels [109]

Answer:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)$

Step-by-step explanation:

We want to simplify:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}$

Recall the Pythagorean Identity:

$\sin^2(A)+\cos^2(A)=1$

So:

$\cos^2(A)=1-\sin^2(A)$

Substitute:

$\displaystyle =\frac{1-\sin^2(A)}{1+\sin(A)}$

Factor. We can use the difference of two squares pattern:

$\displaystyle =\frac{\left(1-\sin(A))(1+\sin(A))}{1+\sin(A)}$

Cancel. Hence:

$\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)$

7 0

2 years ago

A meal at a restaurant costs $49.28. If the customers leave $8.23 for a tip, determine the tip rate to the nearest whole percent

Ede4ka [16]

The cost for the total meal, I think, is $58. If you add 49.28 and 8.23, you get 57.51. I rounded to the nearest one and I got 58, so thats the answer I got. Hope this helps!

5 0

3 years ago

Read 2 more answers