Math 126 word problem grr lol?
A tank holds 175 gallons of water, which drains from a leak at the bottom, causing the tank to empty in 46 minutes. Toricelli's Law gives the volume of water remaining in the tank after t minutes as follows.
V(t)=175(1-t/46)^2
(a) Find V ^-1.
(b) (b) Find V ^-1(13). Round your answer to the tenths place.
Thank you whoever can help :-)
Answers & Comments
Verified answer
v = 175(1 - t/46)^2
Switch v and t then solve for v, which will be V^-1
t = 175(1 - v/46)^2
t/175 = (1 - v/46)^2
√(t/175) = 1 - v/46
√(t/175) - 1 = -v/46
-46 (√(t/175) - 1) = v = V^-1 (t)
so -46 (√(13/175) - 1) = V^-1(13) which my TI-84 says is 33.5 rounded.
Check: V(33.5) should be around 13; 175( 1 - 33.5/46)^2 = 12.922... so it looks okay.
But check it over to see what you think.