1yard =3ft so 》 6ft/4×3ft=6/12=1/2
Answer:
d. 15
Step-by-step explanation:
Putting the values in the shift 2 function
X1 + X2 ≥ 15
where x1= 13, and x2=2
13+12≥ 15
15≥ 15
At least 15 workers must be assigned to the shift 2.
The LP model questions require that the constraints are satisfied.
The constraint for the shift 2 is that the number of workers must be equal or greater than 15
This can be solved using other constraint functions e.g
Putting X4= 0 in
X1 + X4 ≥ 12
gives
X1 ≥ 12
Now Putting the value X1 ≥ 12 in shift 2 constraint
X1 + X2 ≥ 15
12+ 2≥ 15
14 ≥ 15
this does not satisfy the condition so this is wrong.
Now from
X2 + X3 ≥ 16
Putting X3= 14
X2 + 14 ≥ 16
gives
X2 ≥ 2
Putting these in the shift 2
X1 + X2 ≥ 15
13+2 ≥ 15
15 ≥ 15
Which gives the same result as above.
![9\cos(2t)=6\implies\cos(2t)=\dfrac23](https://tex.z-dn.net/?f=9%5Ccos%282t%29%3D6%5Cimplies%5Ccos%282t%29%3D%5Cdfrac23)
Using the fact that cos is 2π-periodic, we have
![\cos(2t)=\dfrac23\implies2t=\cos^{-1}\left(\dfrac23\right)+2n\pi](https://tex.z-dn.net/?f=%5Ccos%282t%29%3D%5Cdfrac23%5Cimplies2t%3D%5Ccos%5E%7B-1%7D%5Cleft%28%5Cdfrac23%5Cright%29%2B2n%5Cpi)
That is,
for any
and integer
.
![\implies t=\dfrac12\cos^{-1}\left(\dfrac23\right)+n\pi](https://tex.z-dn.net/?f=%5Cimplies%20t%3D%5Cdfrac12%5Ccos%5E%7B-1%7D%5Cleft%28%5Cdfrac23%5Cright%29%2Bn%5Cpi)
We get 2 solutions in the interval [0, 2π] for
and
,
![t=\dfrac12\cos^{-1}\left(\dfrac23\right)\text{ and }t=\dfrac12\cos^{-1}\left(\dfrac23\right)+\pi](https://tex.z-dn.net/?f=t%3D%5Cdfrac12%5Ccos%5E%7B-1%7D%5Cleft%28%5Cdfrac23%5Cright%29%5Ctext%7B%20and%20%7Dt%3D%5Cdfrac12%5Ccos%5E%7B-1%7D%5Cleft%28%5Cdfrac23%5Cright%29%2B%5Cpi)
Answer:
7
Step-by-step explanation:
Since 9 and 11 do not factor 35, they are not the answer.
5 is a factor of 35, but not the largest. So, the answer is 7.
Answer:
x=3
Step-by-step explanation: