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If a cylindrical tank holds 1,000 gallons of water, which can be drained from the bottom of the tank in an hour, then Torricelli's Law gives the volume of water remaining in the tank after t minutes as V(t) + 1,000 1 - biossa Find the rate at which the water is flowing out of the tank (the instantaneous rate of change of V with respect to 1) as a function of t.

Answer 1

Q.1 2 Vlt) = 1000 t 60 Ost=60 using chain rule of differentiation, let g(t)= 1- t 60 g’lt) -1 60 v(t) = 1000(941)] Differentiating, V"(t) = 1000 [2(g(t)]gʻt) v'lt) - 2000 glt).gʻlt) Putting value of glt) & g'(t) in above expression, v'(t) = 2000 || 2000[1-] (-20) v'lt) = -100 Pli- ) 3 60 vilt) = + - 100 gallon brin

Q.2. y = Differentiating with respect to x, = 23- Pre above equation dy = 3n²-2(1) de dy 3x²_2 die AF (2,4), dyl 312)2-2 - = 3(4)-2 dre li-2 m 1 10 dre la=2 g with m isa dy slope of tangent line drawn to at (2,4) Equation of of tangent line pass drawn at (2,941) slope (y - y1) = m (x - x1) where (...y,) = (2,4) and (y-4)= 10(x - 2) y = 10x - 20+4 y = 10x - 16 me 10. .: ci None of these Answer