Which of the following points are solutions to the equation

Mathematics

2 answers:

Artyom0805 [142]2 years ago

5 0

(3,14). & (0,-4)& (-2,-16)

vodomira [7]2 years ago

4 0

(0,-4) (3,14) (-2,-16)

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GIVING BRAINLIEST!!!!!!! A rectangular prism has a length of 4 1/4 in., a width of 3 in., and a height of 1 1/4 in. Which expres

den301095 [7]

Answer:

15.9

Step-by-step explanation:

4 1/4 x 3 x 1 1/4 = 15.93

15.93 rounded is 15.9

Hope this helps!

5 0

3 years ago

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.