A) 
The total energy of the system is equal to the maximum elastic potential energy, that is achieved when the displacement is equal to the amplitude (x=A):
(1)
where k is the spring constant.
The total energy, which is conserved, at any other point of the motion is the sum of elastic potential energy and kinetic energy:
(2)
where x is the displacement, m the mass, and v the speed.
We want to know the displacement x at which the elastic potential energy is 1/3 of the kinetic energy:
Using (2) we can rewrite this as
And using (1), we find
Substituting 
into the last equation, we find the value of x:
B) 
In this case, the kinetic energy is 1/10 of the total energy:
Since we have
we can write
And so we find:
Answer: D(t)= 50(4/5)^t
Explanation: If 1/5 of the temperature difference is lost each minute, that means 4/5 of the difference remains each minute. So each minute, the temperature difference is multiplied by a factor of 4/5 (or 0.8).
If we start with the initial temperature difference, 50° Celsius, and keep multiplying by 4/5, this function gives us the temperature difference t minutes after the cake was put in the cooler.
Answer:
Putting your partner first means his or her needs, feelings, and wellbeing take priority over other people or things. A “sense of we” forms as you maintain this priority on purpose each day. You protect your relationship from being destroyed or damaged. You tend to your connection so it feels good to you b
Answer:
Tangential speed=5.4 m/s
Radial acceleration=
Explanation:
We are given that
Angular speed=2.59 rev/s
We know that
1 revolution=
2.59 rev=
By using 
Angular velocity=
Distance from axis=r=0.329 m
Tangential speed=
Radial acceleration=
Radial acceleration=
Answer:
88.2 N
Explanation:
Datos
Lcubo = 10 cm = 0.1 m
Vcubo = Vfluido desalojado= 0.1 m x 0.1 m x 0.1 m = 10-3 m
mcubo = 10 kg
dfluido = 1000 kg/m3
g = 9.8 m/s2
Sabemos que el peso aparente de un cuerpo que se sumerge en un fluido es:
Paparente=Preal−Pfluido
Teniendo en cuenta que:
Preal = mcubo⋅gPfluido=E= dfluido⋅Vfluido⋅g
Como el cuerpo se sumerge completamente en el fluido, el volumen de fluido desalojado es exactamente el volumen del cubo. Por lo tanto si sustituimos los datos que nos proporcionan en el enunciado en la primera ecuación:
Paparente=mcubo⋅g−dfluido⋅Vfluido⋅g ⇒Paparente=10 kg ⋅9.8 m/s2 − 1000 kg/m3 ⋅10−3 m ⋅9.8 m/s2 ⇒Paparente = 88.2 N
