Answer: one value is lesser than the other
Step-by-step explanation: when you see that word your number going to be smaller then your other number.
Take the deritiivive
![ln(2)cos(x)2^{sin(x)}-ln(2)sin(x)2^{cos(x)}](https://tex.z-dn.net/?f=ln%282%29cos%28x%292%5E%7Bsin%28x%29%7D-ln%282%29sin%28x%292%5E%7Bcos%28x%29%7D)
it is zero at pi/4 and it repeats at every pi
minimum at where slope goesfrom negative to positive
so at 5pi/4 and 13pi/4 so at every 2pi interval
evaluate origial at 5pi/4
![2^{sin(5pi/4)}+2^{cos(5pi/4)}](https://tex.z-dn.net/?f=2%5E%7Bsin%285pi%2F4%29%7D%2B2%5E%7Bcos%285pi%2F4%29%7D)
=
![(2^ \frac{- \sqrt{2} }{2} )+(2^ \frac{- \sqrt{2} }{2} )](https://tex.z-dn.net/?f=%282%5E%20%5Cfrac%7B-%20%5Csqrt%7B2%7D%20%7D%7B2%7D%20%29%2B%282%5E%20%5Cfrac%7B-%20%5Csqrt%7B2%7D%20%7D%7B2%7D%20%29)
=
![2(2^ \frac{- \sqrt{2} }{2} )](https://tex.z-dn.net/?f=2%282%5E%20%5Cfrac%7B-%20%5Csqrt%7B2%7D%20%7D%7B2%7D%20%29)
or aprox 1.22509
Answer:
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Step-by-step explanation:
The generating function of a sequence is the power series whose coefficients are the elements of the sequence. For the sequence
![1,1,1,2,3,4,5,6,...](https://tex.z-dn.net/?f=1%2C1%2C1%2C2%2C3%2C4%2C5%2C6%2C...)
the generating function would be
![P(x)=1+x+x^2+2x^3+3x^4+4x^5+5x^6+...\\](https://tex.z-dn.net/?f=P%28x%29%3D1%2Bx%2Bx%5E2%2B2x%5E3%2B3x%5E4%2B4x%5E5%2B5x%5E6%2B...%5C%5C)
we can multiply P(x) by x to get
Note that
![P(x)-xP(x)=1+(2x^3-x^3)+(3x^4-2x^4)+(4x^5-3x^5)+(5x^6-4x^6)+...\\ \\=1+x^3+x^4+x^5+x^6+...=1+x^3(1+x+x^2+x^3+x^4+...)](https://tex.z-dn.net/?f=P%28x%29-xP%28x%29%3D1%2B%282x%5E3-x%5E3%29%2B%283x%5E4-2x%5E4%29%2B%284x%5E5-3x%5E5%29%2B%285x%5E6-4x%5E6%29%2B...%5C%5C%20%20%20%5C%5C%3D1%2Bx%5E3%2Bx%5E4%2Bx%5E5%2Bx%5E6%2B...%3D1%2Bx%5E3%281%2Bx%2Bx%5E2%2Bx%5E3%2Bx%5E4%2B...%29)
which for
can be rewritten as
![(1-x)P(x)=1+\dfrac{x^3}{(1-x)} \quad \Rightarrow \\\\P(x)=\dfrac{1}{(1-x)}+\dfrac{x^3}{(1-x)^2}](https://tex.z-dn.net/?f=%281-x%29P%28x%29%3D1%2B%5Cdfrac%7Bx%5E3%7D%7B%281-x%29%7D%20%5Cquad%20%5CRightarrow%20%5C%5C%5C%5CP%28x%29%3D%5Cdfrac%7B1%7D%7B%281-x%29%7D%2B%5Cdfrac%7Bx%5E3%7D%7B%281-x%29%5E2%7D)
you would need to divide 90 by 3 because that is how many there are in each row.
you will get 30
then you need to multiply 30 by 2 becanse that is how many are in the rows on the left.
you will get 60,
so there are 60 seats on the left.
90 degrees converted to radians is pi/2 or π/2 radians.