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3 years ago

8

A statue has the hieght of 510 feet Jesse's model used a scale in which 1 in equals 100 feet. What is the height in inches of Je

sse's model?

2 answers:

Aleksandr-060686 [28]3 years ago

4 0

Answer:

5.1 inches. I`m sure

Step-by-step explanation:

Grace [21]3 years ago

4 0

Answer:

5.1 is answer.

Step-by-step explanation:

You divide 510 to 100 to get 5.1.

Hope this Helps. :)

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Lim (n/3n-1)^(n-1)<br> n<br> →<br> ∞

n200080 [17]

Looks like the given limit is

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1}$

With some simple algebra, we can rewrite

$\dfrac n{3n-1} = \dfrac13 \cdot \dfrac n{n-9} = \dfrac13 \cdot \dfrac{(n-9)+9}{n-9} = \dfrac13 \cdot \left(1 + \dfrac9{n-9}\right)$

then distribute the limit over the product,

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \lim_{n\to\infty}\left(\dfrac13\right)^{n-1} \cdot \lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}$

The first limit is 0, since 1/3ⁿ is a positive, decreasing sequence. But before claiming the overall limit is also 0, we need to show that the second limit is also finite.

For the second limit, recall the definition of the constant, <em>e</em> :

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

To make our limit resemble this one more closely, make a substitution; replace 9/(<em>n</em> - 9) with 1/<em>m</em>, so that

$\dfrac{9}{n-9} = \dfrac1m \implies 9m = n-9 \implies 9m+8 = n-1$

From the relation 9<em>m</em> = <em>n</em> - 9, we see that <em>m</em> also approaches infinity as <em>n</em> approaches infinity. So, the second limit is rewritten as

$\displaystyle\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8}$

Now we apply some more properties of multiplication and limits:

$\displaystyle \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m+8} = \lim_{m\to\infty}\left(1+\dfrac1m\right)^{9m} \cdot \lim_{m\to\infty}\left(1+\dfrac1m\right)^8 \\\\ = \lim_{m\to\infty}\left(\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)^m\right)^9 \cdot \left(\lim_{m\to\infty}\left(1+\dfrac1m\right)\right)^8 \\\\ = e^9 \cdot 1^8 = e^9$

So, the overall limit is indeed 0:

$\displaystyle \lim_{n\to\infty} \left(\frac n{3n-1}\right)^{n-1} = \underbrace{\lim_{n\to\infty}\left(\dfrac13\right)^{n-1}}_0 \cdot \underbrace{\lim_{n\to\infty}\left(1+\dfrac9{n-9}\right)^{n-1}}_{e^9} = \boxed{0}$

7 0

3 years ago

Jan’s family has 3/4 of a cake left. How many members of her family can get 1/4 of what is left?

VikaD [51]

Answer:

3

Step-by-step explanation:

3/4 divided by 1/4 equals 3

6 0

3 years ago

Read 2 more answers

W over 3< 1 or 3w+5>11

s344n2d4d5 [400]

Step-by-step explanation:

$\dfrac{w}{3}6\qquad\text{divide both sides by 3}\\\\\dfrac{3w}{3}>\dfrac{6}{3}\\\\w>2\\\\$

$\text{If is}\ \bold{OR},\ \text{then}:\\\\w2\Rightarrow w\in\mathbb{R}\ /\text{any real number/}\\\\\text{If there is a mistake, and it should be}\ \bold{AND},\ \text{then}:\\\\w2\Rightarrow 2$

4 0

3 years ago

Hunter had 3⁄8 of a pizza. He gave 2⁄3 of the pizza to his friend Taylor. What fraction of the whole pizza did Taylor get?

Nikitich [7]

Answer:

1/4

Step-by-step explanation:

3/8 * 2/3 = 6/24 = 1/4

AAAAAAAA .... whole pizza

AAA ... Hunter had

AA ... tylor get

4 0

3 years ago

A bolt has 6 1/2 turns per inch. How many turns would be in 2 1/2 inches of threads?

Reika [66]

There would be 41 1/4 turns in 2 1/2 inches of threads.

Given, number of turns a bolt has = 16 1/2 turns per inch.

per inch bolt turns = 16 1/2 =33/2

how many turns would be there in 2 1/2 inches of threads = ?

Threads Per Inch, or TPI, is a measure of how many threads are found in one inch along a fastener's length. American fasteners are the only ones that employ TPI. Typically, the thread count is higher for smaller fasteners since they have finer threads. Just as the name implies, the Threads Per Inch (TPI) refers to the number of threads that run the length of a screw for one inch. The TPI of a screw can be easily calculated by simply counting the threads and dividing the total length.

so, 5/2 inches bolt turns =33/2 x 5/2

=165/4

hence 41 1/4 turns

Therefore, 2 1/2 inches of threads have 41 1/2 turns.

Learn more about Conversions here:

brainly.com/question/16851332

#SPJ1

4 0

1 year ago