If all three coloured lights blink together at 8:49 pm, they will blink together at 8:50 pm
<u>Solution:</u>
Given that the red light blinks at intervals of 4 seconds, the green at 5 seconds and the white at 6 seconds.
If all three colored lights blink together at 8:49 pm,
We have to find when will they blink together again?
First let us know, at what intervals they all together blink.
For that we have to find the lcm of 4, 5, 6.
L.C.M (4, 5, 6) = 2 x L.C.M(2, 5, 3)
As 2,3,5 are primes, we can’t take common further, so multiply all
= 2 x 2 x 5 x 3
= 4 x 15 = 60
So, after every 60 seconds = 1 minute they will blink.
Then, after 8 : 49 pm, they will blink at 8 : 49 + 1 = 8 : 50 pm.
Hence, they all blink at 8 : 50 pm.
![\bf \stackrel{f(x)}{0}=-4cos\left(x-\frac{\pi }{2} \right)\implies 0=cos\left(x-\frac{\pi }{2} \right) \\\\\\ cos^{-1}(0)=cos^{-1}\left[ cos\left(x-\frac{\pi }{2} \right) \right]\implies cos^{-1}(0)=x-\cfrac{\pi }{2} \\\\\\ x-\cfrac{\pi }{2}= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bf%28x%29%7D%7B0%7D%3D-4cos%5Cleft%28x-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20%20%5Cright%29%5Cimplies%200%3Dcos%5Cleft%28x-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20%20%5Cright%29%0A%5C%5C%5C%5C%5C%5C%0Acos%5E%7B-1%7D%280%29%3Dcos%5E%7B-1%7D%5Cleft%5B%20cos%5Cleft%28x-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%20%20%5Cright%29%20%5Cright%5D%5Cimplies%20cos%5E%7B-1%7D%280%29%3Dx-%5Ccfrac%7B%5Cpi%20%7D%7B2%7D%0A%5C%5C%5C%5C%5C%5C%0Ax-%5Ccfrac%7B%5Cpi%20%7D%7B2%7D%3D%0A%5Cbegin%7Bcases%7D%0A%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5C%5C%5C%5C%0A%5Cfrac%7B3%5Cpi%20%7D%7B2%7D%0A%5Cend%7Bcases%7D)
