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3 years ago

PLEASE HELP ME 40 PTS!!!!!!

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

8 0

Answer:

The sequence converges to infinity.

Step-by-step explanation:

$a_n = \frac{n^3 - n}{n^2 + 5n}\\\\ \lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{n^3 - n}{n^2 + 5n}$

$= \lim_{n \to \infty} \frac{n(n^2 - 1)}{n(n + 5)} \\\\= \lim_{n \to \infty} \frac{(n^2 - 1)}{(n + 5)}\\\\= \lim_{n \to \infty} \frac{n(n - \frac{1}{n})}{n(1 + \frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n - \frac{1}{n})}{(1 + \frac{5}{n})}$

$denominator = \lim_{n \to \infty} 1 + \frac{5}{n} = 1 + \lim_{n \to \infty} \frac{5}{n} = 1+0 = 1$

$numerator = \lim_{n \to \infty} n - \frac{1}{n} = \infty$

Therefore,

$\lim_{n \to \infty} a_n = \frac{ \infty}{1} = \infty$

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please help John's age increased by 11 is 5 less than 5 times his age. How old is he? If x represents John's age, which of the f

Keith_Richards [23]

So x is John's age.
We can solve this problem by working backwards.
Since it's 5 times his age, we first do 5x.
And then since it's five less, we move on to 5x - 5
And then we add the John's age is increased by 11: 5x - 5 = x + 11
I hope this helped :)
(It should be the second one you listed)

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3 years ago

The Volume of a sphare is 28/3 times the surface area calculate The surface area and the Volume of the sphere, correct to the ne

Aloiza [94]

Given:

Volume of a sphere is $\dfrac{28}{3}$ times the surface area.

To find:

The surface area and the volume of the sphere.

Solution:

Volume of a sphere:

$V=\dfrac{4}{3}\pi r^3$ ...(i)

Surface area of a sphere:

$A=4\pi r^2$ ...(ii)

Where, r is the radius of the sphere.

Volume of a sphere is $\dfrac{28}{3}$ times the surface area.

$V=\dfrac{28}{3}\times A$

$\dfrac{4}{3}\pi r^3=\dfrac{28}{3}\times 4\pi r^2$

Multiply both sides by 3.

$4\pi r^3=112\pi r^2$

$\dfrac{\pi r^3}{\pi r^2}=\dfrac{112}{4}$

$r=28$

Using (i), the volume of the sphere is:

$V=\dfrac{4}{3}\times \dfrac{22}{7}\times (28)^3$

$V\approx 91989$

Using (ii), the surface area of the sphere is:

$A=4\times \dfrac{22}{7}\times (28)^2$

$A=9856$

Therefore, the surface area of the sphere is 9856 sq. units and the volume of the sphere is 91989 cubic units.

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Julli [10]

Answer:

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Step-by-step explanation:

The Central Limit Theorem helps us find the standard error of the mean:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .