Answer:
![90\pi\text{ ft/s}\approx282.74\text{ ft/s}](https://tex.z-dn.net/?f=90%5Cpi%5Ctext%7B%20ft%2Fs%7D%5Capprox282.74%5Ctext%7B%20ft%2Fs%7D)
Step-by-step explanation:
Refer to physics equation
, where
is angular velocity.
Angular velocity's SI unit is rad/s. Convert rev/min to rad/s:
![\displaystyle 5\text{ rev/min}=5\cdot \frac{1}{60}\cdot 2\pi\approx 0.524\text{ rad/s}](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Ctext%7B%20rev%2Fmin%7D%3D5%5Ccdot%20%5Cfrac%7B1%7D%7B60%7D%5Ccdot%202%5Cpi%5Capprox%200.524%5Ctext%7B%20rad%2Fs%7D)
Now substitute
and
into
:
![\displaystyle v=\frac{1\pi}{6}\cdot 9=\frac{3}{2}\pi\text{ ft/s}=\boxed{90\pi\text{ ft/s}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20v%3D%5Cfrac%7B1%5Cpi%7D%7B6%7D%5Ccdot%209%3D%5Cfrac%7B3%7D%7B2%7D%5Cpi%5Ctext%7B%20ft%2Fs%7D%3D%5Cboxed%7B90%5Cpi%5Ctext%7B%20ft%2Fs%7D%7D)
Answer:
1.) 5(4)-3(5)+8
20-15+8
5+8
13
The other ones make no sense. Can you take a picture of the problems
Answer: 31,020
Step-by-step explanation:
Answer: (28/37) - (48/37)*i
Step-by-step explanation:
We want to solve the quotient:
![\frac{6 - 7*i}{6 + i}](https://tex.z-dn.net/?f=%5Cfrac%7B6%20-%207%2Ai%7D%7B6%20%2B%20i%7D)
To solve it, we need to multiply the whole quotient by the complex conjugate of the denominator.
Remember that for a complex number:
a + b*i
the complex conjugate is:
a - b*i
Then if the denominatoris:
6 + i
the complex conjugate is:
6 - i
Then to solve the quotient we have:
![\frac{6 - 7*i}{6 + i} *\frac{6 - i}{6 - i} = \frac{(6 -7*i)*(6 - i)}{(6 + i)*(6 - i)} = \frac{6*6 -7*6*i - 6*i + (-7*i)*(-i)}{6*6 +6*i - 6*i -i^2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%20-%207%2Ai%7D%7B6%20%2B%20i%7D%20%2A%5Cfrac%7B6%20-%20i%7D%7B6%20-%20i%7D%20%3D%20%20%5Cfrac%7B%286%20%20-7%2Ai%29%2A%286%20-%20i%29%7D%7B%286%20%2B%20i%29%2A%286%20-%20i%29%7D%20%3D%20%5Cfrac%7B6%2A6%20-7%2A6%2Ai%20-%206%2Ai%20%2B%20%28-7%2Ai%29%2A%28-i%29%7D%7B6%2A6%20%2B6%2Ai%20-%206%2Ai%20-i%5E2%7D)
This is equal to:
![\frac{6*6 -7*6*i - 6*i + (-7*i)*(-i)}{6*6 +6*i - 6*i -i^2} = \frac{36 - 42*i - 6*I - 7}{36 + 1} = \frac{29 - 48*i}{37}](https://tex.z-dn.net/?f=%5Cfrac%7B6%2A6%20-7%2A6%2Ai%20-%206%2Ai%20%2B%20%28-7%2Ai%29%2A%28-i%29%7D%7B6%2A6%20%2B6%2Ai%20-%206%2Ai%20-i%5E2%7D%20%3D%20%5Cfrac%7B36%20-%2042%2Ai%20-%206%2AI%20-%207%7D%7B36%20%2B%201%7D%20%20%3D%20%5Cfrac%7B29%20-%2048%2Ai%7D%7B37%7D)
Then the initial quotient is equal to:
(28/37) - (48/37)*i