What is the Correct Solution to 92x^3y divided by -28xy^3 in Algebra?

AI Thread Summary
The problem involves simplifying the expression 92x^3y divided by -28xy^3. The correct simplification yields 23x^2 divided by -7y^2. A common point of confusion is the handling of the negative sign, which can be placed in front of the numerator. The discussion emphasizes that -1/2 is equivalent to 1/-2, reinforcing the importance of consistent sign placement. Understanding these simplification rules is crucial for accurate algebraic manipulation.
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Homework Statement



92x^3y divided by -28xy^3

Homework Equations





The Attempt at a Solution



I got 23x^2 divided by -7y^2

book inverted the negative. What did I do wrong?
 
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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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