issues with the algebra in a problem

I have figured out how to solve this problem but I'm not getting the correct answer.

A 1000 L tank loses water so that, after t days, the remaining volume is

v(t) = 1000[1-(t/10)]^2 for 0<t<10.

How rapidly is the water being lost when the tank is half full?

I got the derivative fine. -200(1-(t/10))

I know to solve v(t) = 500 then take the value of t and input it into v'(t)

when solving v(t) = 500 I end up with the answer 10-5sqrt(2) or -5(sqrt(2) - 2)

but to get the correct answer to the question it needs to be 5sqrt2

the correct answer is 100sqrt(2) litres/day

thank you for your help!

Re: issues with the algebra in a problem

Re: issues with the algebra in a problem

ah okay, thank you! I thought the derivative inside the parenthesis was (-1/10) making for

1000(2)[1-(t/10)](-1/10) -> 2000[1-(1 - (t/10)](-1/10) -> -200[1 - (t/10)]

Re: issues with the algebra in a problem

Oops, you are right, I misread it >_< disregard my last response...

Re: issues with the algebra in a problem

haha no worries. if you could, would you show me how you would work through v'(t) for t = 10-5sqrt2 because I am not getting the correct answer of 100sqrt2

Thank you!

Re: issues with the algebra in a problem

Well let's see...

And of course the negative value represents the fact that the water level is decreasing...

Re: issues with the algebra in a problem

ah I see where I messed up!

Thank you!!