5. A cup of warm coffee at 80°C is cooling off outdoors according to the equation dy = k(y – 20) - dt where y(t) is the temperature (in °C) of the coffee at time t minutes. If the temperature of the coffee is 60°C after 10 minutes, what is (i) the value of k, and (ii) the temperature when t = 15 minutes?

Q: Solve for y: x/4 + y/9 = 1

A:

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Q: A factory is dumping pollutants into a river at a rate given by dx/dt = t3/4/600 tons per week,…

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Q: dy Find for each equation and simplify fully. dx (17x² + B) (11x – A)° (а). у- (5x+4)°

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Q: 1 y = x²-1 Using differential, draw the function

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Q: A cold drink is poured out at 55°F. After 2 minutes of sitting in a 60°F room, its temperature has…

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Q: (a) If y varies directly with x2 and y = 144 when x = 4, find an equation to represent this…

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Q: Q2: find y' y= 33xelnx²

A: We have the given function : y=33xelnx2 We have to find the derivative of this function.

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A: Given:- Runner' speed sh=2h Time th=34h Let dh represents distance of runner travel

Q: (b) Find the differential for y = -5 %3D

A: Giveny=4x-53   ...(1)

Q: SSx = 172.5, SSY = 80.6, and ∑[(X – Mx) (Y – MY)] = 95.33, r =  A. .08. B. .01 C. –.81. D. .81.

A: SSx = 172.5 SSY = 80.6 and ∑[(X – Mx) (Y – MY)] = 95.33

Q: The time, in minutes, for a student to run L laps is T(L). What is the meaning of T'(3)=2? O When…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.