I suspect you mean
1/8 sin(4<em>t </em>) = 1/2 (cos³(<em>t</em> ) sin(<em>t</em> ) - sin³(<em>t</em> ) cos(<em>t</em> ))
On the right side, pull out a factor of cos(<em>t</em> ) sin(<em>t</em> ):
1/2 (cos³(<em>t</em> ) sin(<em>t</em> ) - sin³(<em>t</em> ) cos(<em>t</em> )) = 1/2 cos(<em>t</em> ) sin(<em>t</em> ) (cos²(<em>t</em> ) - sin²(<em>t</em> ))
Recall the double angle identities for sin and cos :
sin(2<em>t</em> ) = 2 sin(<em>t</em> ) cos(<em>t</em> )
cos(2<em>t</em> ) = cos²(<em>t</em> ) - sin²(<em>t</em> )
Then
… = 1/4 (2 cos(<em>t</em> ) sin(<em>t</em> )) (cos²(<em>t</em> ) - sin²(<em>t</em> ))
… = 1/4 sin(2<em>t</em> ) cos(2<em>t</em> )
… = 1/8 (2 sin(2<em>t</em> ) cos(2<em>t</em> ))
… = 1/8 sin(4<em>t</em> )
the second is the correct one...
Answer:
20
Step-by-step explanation:
1/3 = .3
6/.3 = 20
Answer:
P(2)=0.256
Step-by-step explanation:
We know that Nancy has noticed that 20 trucks pass by her apartment daily (24 hours). We conclude that for 1 hours, pass 20/24=5/6 trucks.
We calculate how many trucks pass for 3 hours:
3 · 5/6= 15/6=2.5=λ
We use a Poisson distribution:
P(k)=\frac{λ^k · e^{-λ}}{k!}
For 2 trucks we have that is k=2. We know that is λ=2.5
We caclulate the probability
P(2)=\frac{2.5² · e^{-2.5}}{2!}
P(2)=0.256
Answer:
Step-by-step explanation:
First we square the parenthesis. Apply FOIL method to multiply
distribute -2 inside the parenthesis
Now combine like terms