It's 2 7/12
Hope this helped!
Answer would be D
, you need to divide the total distance by the spacing to find total markers
Answer:
19.0, 19.5, 19.054, 19.0541
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Yeh definitely its b
Answer:
![\displaystyle x=\left \{\frac{2\pi}{3}+2\pi k,\frac{4\pi}{3}+2\pi k, \frac{8\pi}{3}+2\pi k, \frac{10\pi}{3}+2\pi k\right \}k\in \mathbb{Z}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cleft%20%5C%7B%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%5Cfrac%7B4%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%20%5Cfrac%7B8%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%20%5Cfrac%7B10%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%5Cright%20%5C%7Dk%5Cin%20%5Cmathbb%7BZ%7D)
Step-by-step explanation:
Hi there!
We want to solve for
in:
![4\sin^2(\frac{x}{2})=3](https://tex.z-dn.net/?f=4%5Csin%5E2%28%5Cfrac%7Bx%7D%7B2%7D%29%3D3)
Since
is in the argument of
, let's first isolate
by dividing both sides by 4:
![\displaystyle \sin^2\left(\frac{x}{2}\right)=\frac{3}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%5E2%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%3D%5Cfrac%7B3%7D%7B4%7D)
Next, recall that
is just shorthand notation for
. Therefore, take the square root of both sides:
![\displaystyle \sqrt{\sin^2\left(\frac{x}{2}\right)}=\sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%7B%5Csin%5E2%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%7D%3D%5Csqrt%7B%5Cfrac%7B3%7D%7B4%7D%7D%2C%5C%5C%5Csin%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B3%7D%7B4%7D%7D)
Simplify using
:
![\displaystyle \sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \frac{\sqrt{3}}{\sqrt{4}}=\pm \frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B3%7D%7B4%7D%7D%2C%5C%5C%5Csin%5Cleft%28%5Cfrac%7Bx%7D%7B2%7D%5Cright%29%3D%5Cpm%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B4%7D%7D%3D%5Cpm%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
Let
.
<h3><u>Case 1 (positive root):</u></h3>
![\displaystyle \sin(\phi)=\frac{\sqrt{3}}{2},\\\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%28%5Cphi%29%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2C%5C%5C%5Cphi%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%20k%5Cin%20%5Cmathbb%7BZ%7D%2C%20%5C%5C%5C%5C%5Cphi%20%3D%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%20k%5Cin%20%5Cmathbb%7BZ%7D)
Therefore, we have:
![\displaystyle \frac{x}{2}=\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\frac{x}{2}=\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z},\\\\\begin{cases}x=\boxed{\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{4\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bx%7D%7B2%7D%3D%5Cphi%20%3D%20%5Cfrac%7B%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%20k%5Cin%20%5Cmathbb%7BZ%7D%2C%20%5C%5C%5C%5C%5Cfrac%7Bx%7D%7B2%7D%3D%5Cphi%20%3D%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%20k%5Cin%20%5Cmathbb%7BZ%7D%2C%5C%5C%5C%5C%5Cbegin%7Bcases%7Dx%3D%5Cboxed%7B%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%20k%5Cin%20%5Cmathbb%7BZ%7D%7D%2C%5C%5Cx%3D%5Cboxed%7B%5Cfrac%7B4%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%20%2C%20k%20%5Cin%20%5Cmathbb%7BZ%7D%7D%5Cend%7Bcases%7D)
<h3><u>Case 2 (negative root):</u></h3>
![\displaystyle \sin(\phi)=-\frac{\sqrt{3}}{2},\\\phi = \frac{4\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{5\pi}{3}+2\pi k, k\in \mathbb{Z},\\\begin{cases}x=\boxed{\frac{8\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{10\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%28%5Cphi%29%3D-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D%2C%5C%5C%5Cphi%20%3D%20%5Cfrac%7B4%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%20k%5Cin%20%5Cmathbb%7BZ%7D%2C%20%5C%5C%5C%5C%5Cphi%20%3D%5Cfrac%7B5%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%20k%5Cin%20%5Cmathbb%7BZ%7D%2C%5C%5C%5Cbegin%7Bcases%7Dx%3D%5Cboxed%7B%5Cfrac%7B8%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%2C%20k%5Cin%20%5Cmathbb%7BZ%7D%7D%2C%5C%5Cx%3D%5Cboxed%7B%5Cfrac%7B10%5Cpi%7D%7B3%7D%2B2%5Cpi%20k%20%2C%20k%20%5Cin%20%5Cmathbb%7BZ%7D%7D%5Cend%7Bcases%7D)