Radioactive decay is given by:
N = No x e^(-λt)
We know that N/No has to be 0.05
λ = 0.15
0.05 = e^(-0.15t)
t = ln(0.05)/(-0.15)
t = 19.97 days
The density of the nugget is 
and is made of gold
Explanation:
The density of an object can be calculated as
where
d is the density
m is the mass
V is the volume of the object
We have to note that density of an object actually depends on the material the object is made of (therefore, two objects made of the same material can have different mass and different volume, but they have same density).
For the nugget in this problem, we have:
mass: m = 38 g
volume: 
So, its density is
And by looking at the table, we see that this value corresponds approximately to the density of gold, so the nugget is made of gold.
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vf ^2 = kx^2/m = 56(0.75)^2 / 2.5 = 12.6
Therefore, v= 3.5 m/s.
Without an external agent doing work, heat will always flow from a hotter to a cooler object. Two objects of different temperature always interact. There are three different ways for heat to flow from one object to another. They are conduction, convection, and radiation.
Answer:
Explanation:
Given that,
Mass of block
M = 2kg
Spring constant k = 300N/m
Velocity v = 12m/s
At t = 0, the spring is neither stretched nor compressed. Then, it amplitude is zero at t=0
xo = 0
It velocity is 12m/s at t=0
Then, it initial velocity is
Vo = 12m/s
Then, amplitude is given as
A = √[xo + (Vo²/ω²)]
Where
xo is the initial amplitude =0
Vo is the initial velocity =12m/s
ω is the angular frequency and it can be determine using
ω = √(k/m)
Where
k is spring constant = 300N/m
m is the mass of object = 2kg
Then,
ω = √300/2 = √150
ω = 12.25 rad/s²
Then,
A = √[xo + (Vo²/ω²)]
A = √[0 + (12²/12.5²)]
A = √[0 + 0.96]
A = √0.96
A = 0.98m
