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3 years ago

5

Suppose you put one of your x-tiles and two unit tiles with another pile of three x-tiles and five unit tiles. What is in this n

ew pile? Write it as a sum

1 answer:

Lorico [155]3 years ago

7 0

4 x-tiles 7 unit tiles

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If A is the area of a square measured in square inches and s is the square's side length measured in inches, then the square's s

motikmotik

Answer:

a)

g(3.5), g(26.92)

or

g(3.5)=3.5^2, g(26.92)=26.92^2

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3 years ago

Consider the series ∑n=1[infinity]2nn!nn. Evaluate the the following limit. If it is infinite, type "infinity" or "inf". If it d

Vikki [24]

I guess the series is

$\displaystyle\sum_{n=1}^\infty\frac{2^nn!}{n^n}$

We have

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

Recall that

$e=\displaystyle\lim_{n\to\infty}\left(1+\frac1n\right)^n$

In our limit, we have

$\dfrac n{n+1}=\dfrac{n+1-1}{n+1}=1-\dfrac1{n+1}$

$\left(\dfrac n{n+1}\right)^n=\dfrac{\left(1-\frac1{n+1}\right)^{n+1}}{1-\frac1{n+1}}$

$\implies\displaystyle2\lim_{n\to\infty}\left(\frac n{n+1}\right)^n=2\frac{\lim\limits_{n\to\infty}\left(1-\frac1{n+1}\right)^{n+1}}{\lim\limits_{n\to\infty}\left(1-\frac1{n+1}\right)}=\frac{2e}1=2e$

which is greater than 1, which means the series is divergent by the ratio test.

On the chance that you meant to write

$\displaystyle\sum_{n=1}^\infty\frac{2^n}{n!n^n}$

we have

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{2^{n+1}}{(n+1)!(n+1)^{n+1}}}{\frac{2^n}{n!n^n}}\right|=2\lim_{n\to\infty}\frac1{(n+1)^2}\left(\frac n{n+1}\right)^2$

$=\displaystyle2\left(\lim_{n\to\infty}\frac1{(n+1)^2}\right)\left(\lim_{n\to\infty}\left(\frac n{n+1}\right)^n\right)=2\cdot0\cdot e=0$

which is less than 1, so this series is absolutely convergent.

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3 years ago

Standard form of two hundred ten million sixty four thousand fifty

cluponka [151]

210,064,000,050 is standard form

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2 years ago

Please Help practice #3

algol [13]

Answer:

(2x+5)(4x+3)

Step-by-step explanation:

Given the expression 8x^2 + 26x + 15

Factorize

8x^2 + 26x + 15

= 8x^2 + 6x + 20x + 15

= 2x(4x+3) + 5 (4x+3)

= (2x+5)(4x+3)

Hence the factored form of the expression is (2x+5)(4x+3)

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3 years ago

Johnny works after school and earns $8 per hour. He needs at least $2000 to purchase a car so he does not need to take the bus.

Inga [223]

2hours

Step-by-step explanation:

2 hours

4 0

2 years ago