Ice is forming on a pond at a rate given by dydt=kt√, dydt=kt, where yy is the thickness of the ice in centimeters at time tt measured in hours since the ice started forming, and kk is a positive constant. find yy as a function of tt.

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Mathematics

Kenzie Mcclain

2 April, 10:44

Ice is forming on a pond at a rate given by dydt=kt√, dydt=kt, where yy is the thickness of the ice in centimeters at time tt measured in hours since the ice started forming, and kk is a positive constant. find yy as a function of tt.

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Cullen Villegas · Answer 1

Answer: Multiply both sides by dt, yielding ... dy = kt^ (1/2) * dt. Integrate both sides, left with respect to y and right with respect to t, using the power rule. y = k (2/3) t^ (3/2). y = (2k/3) * t^ (3/2).