Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. If we measure temperature in degrees Celsius and time in minutes, the constant of proportionality k equals 0.4. Suppose the ambient temperature TA(t) is equal to a constant 68 degrees Celsius. Write the differential equation that describes the time evolution of the temperature T of the object.

Explanation:

Let T be the temperature of an object at time t , then

dT / dt will be rate of change of temperature

According to newton's law of cooling

dT / dt = k ( T - T₂ )

where T₂ is temperature of surrounding , T is temperature of object , k is a constant .

dT / dt = k ( T - T₂ )

Given k = .4 , ambient temperature T₂ = 68⁰C

dT / dt = .4 ( T - 68 )

dT / ( T - 68 )  = .4 dt .

This is required differential equation .

show the wavelengths of a wave. show the crests of a wave.

gpe = mass x gravity constant x height or… gpe = mgh

where… mass: measured in kilograms (kg)

gravity: gravity constant on earth = 10.00 m/s2

height: measured in meters (m)

gpe: measured in joules (j) or kilojoules (kj)

how do you solve gpe?

gravitational potential energy (gpe) is the energy an object has because of its position above the. ground.

gpe = mass x gravity constant x height or… gpe = mgh.

mass:

note: to earn full marks when solving science word problems, you must show your work:

formula.

example:

given values:

mass = 0.3 kg.