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2 years ago

Plz help I need by tonight

Mathematics

1 answer:

Romashka-Z-Leto [24]2 years ago

6 0

He can use three bookshelves. there will be 3 math books on each of the three shelves and 2 reading books on each of the shelves. 3 is the greatest common factor of 9 and 6.

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What is the value of x that makes PQ←→||RS←→?

Inessa05 [86]

Answer:

x = 55

Step-by-step explanation:

For PQ and RS to be parallel then

∠ACQ = ∠RDB ( Alternate exterior angles ), thus

3x - 65 = 2x - 10 ( subtract 2x from both sides )

x - 65 = - 10 ( add 65 to both sides )

x = 55

3 0

2 years ago

Lim (n/3n-1)^(n-1) n → ∞

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, e :

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

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

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

From the relation 9m = n - 9, we see that m also approaches infinity as n 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

2 years ago

Parellel lines it says 75 degrees and on another line it says 11x-2 what's the answer?

likoan [24]

Answer:

x = 7

Step-by-step explanation:

Parallel lines so their the same

11x - 2 = 75

add 2 to both sides

11x = 77

divide both signs with 11

x = 7

8 0

2 years ago

Read 2 more answers

In a classroom 12 students are wearing glasses, while 6 are not. What percent of the students are wearing glasses? Explainnn

ASHA 777 [7]

Answer:

66,666666666666666666666666666666666667% :))

Step-by-step explanation:

total number of students in 1 class: 12 + 6 = 18 students

percentage of student wearing glasses are:

$\frac{12}{18} \times 100 = 66.666666667\%$

Done :))

4 0

2 years ago

Arlecino [84]

Answer:

-2,4

Step-by-step explanation:

4 0

2 years ago