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A hypothetical square shrinks at a rate of 2 m²/min. At what rate are the diagonals of the square changing when the diagonals are 7 m each?

Answer 1

Isaiah Allen

The diagonal is given by

#d = sqrt(s^2 + s^2) = sqrt(2s^2) #, or #s = sqrt(d^2/2) = d/sqrt(2)#.

Since the area of a square is given by #A = s^2#, we have:

#A = (d/sqrt(2))^2 = d^2/2#

Differentiating:

#(dA)/dt= (4d(dd)/(dt))/4#

#(dA)/dt = d(dd)/(dt)#

We know that the area changes with respect to time at #2" m^2"# per minute and we want to find at which rate the diagonals are changing when #d = 7" meters"#.

#-2 = 7(dd)/(dt)#

#-2/7 = (dd)/(dt)#

So, the diagonals shrink at a rate of #-2/7# metres per minute.

Hopefully this helps!

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Answer 2

Emma Aldridge

The rate at which the diagonals of the square are changing is ( \frac{7}{2} \sqrt{2} ) m/min.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.