sinx-✓(1-3sin2x)=0
-✓(1-3sin2x)=-sinx
apply squared both sides
(-✓(1-3sin2x)^2=(-sinx)^2
1-3sin2x=sin2x
collect like terms
-3sin2x-sin2x+1=0
-4sin2x+1=0
-4sin2x=-1
devide both sides by -4
sin2x=-1/-4
sin2x=0.25
sinx*sinx =0.25
[sinx]^2 = 0.25
apply square root both sides
<h2>✓(sinx)2 = ✓0.25</h2>
<h2>sinx=0.5</h2><h2> </h2><h2>x=sin^-(0.5)</h2>
<h2>x=30°</h2>
<h3>check quadrant where sin is positive, sin is +ve in second quandrant</h3>
180-x= Theta(X)
180-30=X
X=150°
therefore, all angles for sinx -✓(1-3sin2x)=0 are (X= 30° and 150°)
Answer: B
Step-by-step explanation:
Part A:
Given that <span>A
presidential candidate plans to begin her campaign by visiting the
capitals in 4 of 50 states.
The number of ways of selecting the route of 4 specific capitals is given by
![^{50}P_4= \frac{50!}{(50-4)!} = \frac{50!}{46!} =50\times49\times48\times47=5,527,200](https://tex.z-dn.net/?f=%20%5E%7B50%7DP_4%3D%20%5Cfrac%7B50%21%7D%7B%2850-4%29%21%7D%20%3D%20%20%5Cfrac%7B50%21%7D%7B46%21%7D%20%3D50%5Ctimes49%5Ctimes48%5Ctimes47%3D5%2C527%2C200)
Therefore, the probability that she selects
the route of four specific capitals is
![\frac{1}{5,527,200}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%2C527%2C200%7D%20)
Part B:
</span>
<span>The number of ways of selecting the route of 4 specific capitals is 5,527,200.
Since </span><span>the number of ways of selecting the route of 4 specific capitals is too large it is not practical to list all of
the different possible routes in order to select the one that is best.
Therefore, "</span><span>No, it is not practical to list all of the different possible
routes because the number of possible permutations is very
large."</span>
Both child would receive 1/2