All categories

2 years ago

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second.

Mathematics

1 answer:

scoray [572]2 years ago

3 0

Answer:

It makes 360 / 60 = 6 revolutions per second. 6 revolutions is 12π radians.

You might be interested in

Identify the segment bisector of XY

zhuklara [117]

The midpoint (W) of XY is also on segment PQ, so PQ is the bisector of XY.

Hope it helps you :)

3 0

2 years ago

Which graph represents this system? 3x+2y=-6 y=-3/2x+2

Eva8 [605]

Answer: look at the picture

Step-by-step explanation: hope this help:)

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

What is the value of x to the nearest tenth?

Ipatiy [6.2K]

Answer:

Step-by-step explanation:

4 0

2 years ago

4x/5 - 3x/7 = 4x/7 + 5x/7 can anyone please help with explanation...

kirill115 [55]

Answer: x=0

Step-by-step explanation:

Multiply both sides of the equation by 35, the least common multiple of 5,7.

7×4x−5×3x=5×4x+5×5x

Multiply 7 and 4 to get 28.

28x−5×3x=5×4x+5×5x

Multiply −5 and 3 to get −15.

28x−15x=5×4x+5×5x

Combine 28x and −15x to get 13x.

13x=20x+25x

Combine 20x and 25x to get 45x.

13x=45x

Subtract 45x from both sides

13x−45x=0

Combine 13x and −45x to get −32x

−32x=0

Product of two numbers is equal to 0 if at least one of them is 0. Since −32 is not equal to 0, x must be equal to 0.

X=0

7 0

2 years ago