An object, whose temperature is 100 degrees Fahrenheit is thrown into a swimming pool where the water is 50 degrees Fahrenheit. According to Newton's Law of cooling the rate at which the temperature of the object changes is proportional to the difference between the temprature of the object and the temprature of the water. (A) Write the differential equation for this problem and solve it  I know that the formula is dT/dt=K(T-Tm) How do I solve the differential equation? (B) It is observed that 5 seconds after the object enters the pool, the temprature of the object is 90 degrees Fahrenheit. When will the object's temprature be at 60 degrees Fahrenheit?

An object attached to a spring undergoes simple harmonic motion modeled by the differential equation d?y + ky dt? mass of the object, and k is the spring constant. A mass of 17 kilograms stretches the spring 0.2 meters. 0 where y(t) is the displacement of the mass (relative to equilibrium) at time t, m is the m Use this information to find the spring constant. (Use g = 9.8 meters/second?) k = The previous mass is detached from the spring and a mass of 12 kilograms is attached. This mass is displaced 0.15 meters above equilibrium (above is positive and below is negative) and then launched with an initial velocity of 0.5 meters/second. Write the equation of motion in the form y(t) = c1 cos(wt) + c2 sin(wt). Do not leave unknown constants in your equation, and round all values to exactly 3 decimal places. y(t)

A force of 720 newtons stretches a spring 4 meters. A mass of 45 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 6 m/s. Give the initial conditions. x(0) = x'(0) = Find the equation of motion. x(t) = Need Help? m m/s Read It Watch It

For this problem T is the variable for the temperature, k is the growth constant (or constant of proportionality) and is positive.Newton's Law of cooling states that the temperature of an object changes at a rate proportional to the difference of the temperature of the surrounding medium and the temperature of the object. If the temperature of the surrounding medium is 340∘� write a differential equation to model the situation.