Answer
(1/6)⁴ = 1/1296
Step-by-step explanation:
robabilty of getting a 5 in a throw of dice is 1/6 . So, the required probability of getting 4 5’s in rolling a dice 4 times is (1/6)4
Prove that:
![cos(2\alpha )-cos(8\alpha )=sin(5\alpha )sin(3\alpha )](https://tex.z-dn.net/?f=cos%282%5Calpha%20%29-cos%288%5Calpha%20%29%3Dsin%285%5Calpha%20%29sin%283%5Calpha%20%29)
Remember that:
![cos(A+B)=cos(A)cos(B)-sin(A)sin(B)\\cos(A-B)=cos(A)cos(B)+sin(A)sin(B)\\\\\\cos(A+B)-cos(A-B)=-2sin(A)sin(B)](https://tex.z-dn.net/?f=cos%28A%2BB%29%3Dcos%28A%29cos%28B%29-sin%28A%29sin%28B%29%5C%5Ccos%28A-B%29%3Dcos%28A%29cos%28B%29%2Bsin%28A%29sin%28B%29%5C%5C%5C%5C%5C%5Ccos%28A%2BB%29-cos%28A-B%29%3D-2sin%28A%29sin%28B%29)
We wish to remove this add (A+B).
![\left \{ {{A+B=p} \atop {A-B=q}} \right. \\\\2A=p+q](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7BA%2BB%3Dp%7D%20%5Catop%20%7BA-B%3Dq%7D%7D%20%5Cright.%20%5C%5C%5C%5C2A%3Dp%2Bq)
![A=\frac{p+q}{2} \\\\B=\frac{p-q}{2}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7Bp%2Bq%7D%7B2%7D%20%5C%5C%5C%5CB%3D%5Cfrac%7Bp-q%7D%7B2%7D)
Then we de identity:
![cos(p)-cos(q)=-2sin(\frac{p+q}{2}) sin(\frac{p-q}{2})](https://tex.z-dn.net/?f=cos%28p%29-cos%28q%29%3D-2sin%28%5Cfrac%7Bp%2Bq%7D%7B2%7D%29%20sin%28%5Cfrac%7Bp-q%7D%7B2%7D%29)
Let p=2α and q=8α
![cos(2\alpha )-cos(8\alpha )=-2sin(\frac{2\alpha +8\alpha }{2})sin(\frac{2\alpha -8\alpha }{2}) \\\\cos(2\alpha )-cos(8\alpha )=-2sin(5\alpha )sin(-3\alpha )\\\\*sin(-\alpha )=-sin(\alpha )\\\\cos(2\alpha )-cos(8\alpha )=2sin(5\alpha )sin(3\alpha )](https://tex.z-dn.net/?f=cos%282%5Calpha%20%29-cos%288%5Calpha%20%29%3D-2sin%28%5Cfrac%7B2%5Calpha%20%2B8%5Calpha%20%7D%7B2%7D%29sin%28%5Cfrac%7B2%5Calpha%20-8%5Calpha%20%7D%7B2%7D%29%20%20%5C%5C%5C%5Ccos%282%5Calpha%20%29-cos%288%5Calpha%20%29%3D-2sin%285%5Calpha%20%29sin%28-3%5Calpha%20%29%5C%5C%5C%5C%2Asin%28-%5Calpha%20%29%3D-sin%28%5Calpha%20%29%5C%5C%5C%5Ccos%282%5Calpha%20%29-cos%288%5Calpha%20%29%3D2sin%285%5Calpha%20%29sin%283%5Calpha%20%29)
Answer: -24 e -23
Step-by-step explanation: Denoting the numbers by x and x + 1, and writing the equation and solving we get:
x + x + 1 = -47
2x + 1 = -47
2x = -47 - 1
2x = -48
x = - 48/2
x = -24
Therefore, the numbers are -24 and -23.
The y-intercept is found solving for Y when X = 0.
The correct answer is evaluate at x=0
But maybe after finding the y-intercept, we could still do the Hokey Pokey? lol
Answer:
8
Step-by-step explanation:
1/2*4*4*1=8