Given:
The given value is
.
To find:
The value of the given expression by using the Binomial approximation.
Explanation:
We have,

It can be written as:

![[\because (1+x)^n=1+nx]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%281%2Bx%29%5En%3D1%2Bnx%5D)


Therefore, the approximate value of the given expression is 1.0002.
Answer:
The final temperature of the gas is <em>114.53°C</em>.
Explanation:
Firstly, we calculate the change in internal energy, ΔU from the first law of thermodynamics:
ΔU=Q - W
ΔU = 1180 J - 2020 J = -840 J
Secondly, from the ideal gas law, we calculate the final temperature of the gas, using the change in internal energy:


Then we make the final temperature, T₂, subject of the formula:



Therefore the final temperature of the gas, T₂, is 114.53°C.
Answer:
t=2.10 s
u= 47.40 m/s
Explanation:
given that
h= 21.8 m
x= 101 m
g=9.8 m/s²
Lets take horizontal speed of ball = u m/s
The vertical speed of the car at initial condition is zero ( v= 0).
We know that

v= 0 m/s

now by putting the values
21.8 = 1/2 x 9.8 x t²
t=2.10 s
This is time when ball was in motion.
Now in horizontal direction
x = u .t
101 = u x 2.1
u= 47.40 m/s