13)
there are 2π radians in 1 revolution, and there are 60 seconds in 1 minute, so keeping that in mind, then,
![\bf \cfrac{4\underline{\pi} }{5~\underline{s}}\cdot \cfrac{rev}{2\underline{\pi} }\cdot \cfrac{60~\underline{s}}{min}\implies \cfrac{4\cdot 60~rev}{5\cdot 2~min}\implies \cfrac{240~rev}{10~min}\implies 24\frac{rev}{min}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B4%5Cunderline%7B%5Cpi%7D%20%7D%7B5~%5Cunderline%7Bs%7D%7D%5Ccdot%20%5Ccfrac%7Brev%7D%7B2%5Cunderline%7B%5Cpi%7D%20%7D%5Ccdot%20%5Ccfrac%7B60~%5Cunderline%7Bs%7D%7D%7Bmin%7D%5Cimplies%20%5Ccfrac%7B4%5Ccdot%2060~rev%7D%7B5%5Ccdot%202~min%7D%5Cimplies%20%5Ccfrac%7B240~rev%7D%7B10~min%7D%5Cimplies%2024%5Cfrac%7Brev%7D%7Bmin%7D)
14)
![\bf \textit{linear velocity}\\\\ v=rw\quad \begin{cases} r=radius\\ w=angular~speed\\ ----------\\ v=32\frac{m}{sec}\\ w=100\frac{rev}{min} \end{cases}\\\\ -------------------------------\\\\ \textit{let's convert \underline{w} to }\frac{radians}{sec}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Blinear%20velocity%7D%5C%5C%5C%5C%0Av%3Drw%5Cquad%20%0A%5Cbegin%7Bcases%7D%0Ar%3Dradius%5C%5C%0Aw%3Dangular~speed%5C%5C%0A----------%5C%5C%0Av%3D32%5Cfrac%7Bm%7D%7Bsec%7D%5C%5C%0Aw%3D100%5Cfrac%7Brev%7D%7Bmin%7D%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%5Ctextit%7Blet%27s%20convert%20%5Cunderline%7Bw%7D%20to%20%7D%5Cfrac%7Bradians%7D%7Bsec%7D)
![\bf \cfrac{100~\underline{rev}}{\underline{min}}\cdot \cfrac{2\pi }{\underline{rev}}\cdot \cfrac{\underline{min}}{60~sec}\implies \cfrac{100\cdot 2\pi }{60~sec}\implies \cfrac{10\pi }{3~sec}\implies \cfrac{10\pi }{3}\frac{radians}{sec}\\\\ -------------------------------\\\\ v=rw\implies \cfrac{v}{w}=r\implies \cfrac{\frac{30~m}{sec}}{\frac{10\pi }{3~sec}}\implies r=\cfrac{30~m}{\underline{sec}}\cdot \cfrac{3~\underline{sec}}{10\pi } \\\\\\ r=\cfrac{90}{10\pi }m](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B100~%5Cunderline%7Brev%7D%7D%7B%5Cunderline%7Bmin%7D%7D%5Ccdot%20%5Ccfrac%7B2%5Cpi%20%7D%7B%5Cunderline%7Brev%7D%7D%5Ccdot%20%5Ccfrac%7B%5Cunderline%7Bmin%7D%7D%7B60~sec%7D%5Cimplies%20%5Ccfrac%7B100%5Ccdot%202%5Cpi%20%7D%7B60~sec%7D%5Cimplies%20%5Ccfrac%7B10%5Cpi%20%7D%7B3~sec%7D%5Cimplies%20%5Ccfrac%7B10%5Cpi%20%7D%7B3%7D%5Cfrac%7Bradians%7D%7Bsec%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0Av%3Drw%5Cimplies%20%5Ccfrac%7Bv%7D%7Bw%7D%3Dr%5Cimplies%20%5Ccfrac%7B%5Cfrac%7B30~m%7D%7Bsec%7D%7D%7B%5Cfrac%7B10%5Cpi%20%7D%7B3~sec%7D%7D%5Cimplies%20r%3D%5Ccfrac%7B30~m%7D%7B%5Cunderline%7Bsec%7D%7D%5Ccdot%20%5Ccfrac%7B3~%5Cunderline%7Bsec%7D%7D%7B10%5Cpi%20%7D%0A%5C%5C%5C%5C%5C%5C%0Ar%3D%5Ccfrac%7B90%7D%7B10%5Cpi%20%7Dm)
15)
what is the radians per seconds "w" in revolutions per minute? just another conversion like in 13)
Answer:
1 or 5
Step-by-step explanation:
Given the function h(x)=(2x−2)(x−5)
The zeros of h(x) are the values of x for which h(x)=0
h(x)=(2x−2)(x−5)=0
Note that if a.b=0, either a=0 or b=0.
Appying the above,
If (2x−2)(x−5)=0
Then:
2x−2=0 or x-5=0
2x=2 or x=5
x=1 0r 5
The zeroes of h(x) as defined are 1 or 5.
Answer:
28.1%
Step-by-step explanation:
Population increased by (561000-438000)=123000
rate of increase
= (123000/438000)*100
=28.08
=28.1
Answer:
B. Subtract the bottom equation from the top equation.
Step-by-step explanation:
When looking at the two equations:
8x + 8y = 2
8x + 5y = 1
We can easily get rid of the x variable by subtracting the two equations from each other since the terms are equivalent. This would allow us to solve for the y value, which we could plug into the an equation to solve for the x value.
Answer:
15 ounces
Step-by-step explanation:
6/40 = 0.15
0.15 x 100 = 15
15 ounces