Understanding 1/cos(x) with x=pi/4: Simplifying to Root 2

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k guys if you have 1/cos (x)
and x= pi/4

then the answer is root 2

but I'm actually having trouble writing it out

so...

1/ cos (pi/4) = 1/(root2 / 2)

so how come answer isn't 2/root2?
 
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2/sqrt(2)=sqrt(2). Can you see why?
 
yea.. i see it.. brain fart been studying all day :(
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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