Adifferential equation for the velocity v of a falling mass m subjected to air resistance proportional to the square of the instantaneous velocity is m dv dt = mg − kv2, where k > 0 is a constant of proportionality. the positive direction is downward. (a) solve the equation subject to the initial condition v(0) = v0. v(t) = (b) use the solution in part (a) to determine the limiting, or terminal, velocity of the mass. lim t→[infinity] v(t) = (c) if the distance s, measured from the point where the mass was released above ground, is related to velocity v by ds/dt = v(t), find an explicit expression for s(t) if s(0) = 0. s(t) =

false

step-by-step explanation:

step-by-step explanation:

the answer is 128

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.

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step-by-step explanation: