Answer:
Explanation:
In first case we are interested in one time 6 in six rolls
Thus probability = number of chances required/Total chances
= 1/6
Similarly in the second case probability = 2/12 = 1/6
In the same way in last case probability = 100/600 = 1/6
The probability is the same . Thus all the cases has equal chances
Answer:
|v| = 8.7 cm/s
Explanation:
given:
mass m = 4 kg
spring constant k = 1 N/cm = 100 N/m
at time t = 0:
amplitude A = 0.02m
unknown: velocity v at position y = 0.01 m

1. Finding Ф from the initial conditions:

2. Finding time t at position y = 1 cm:

3. Find velocity v at time t from equation 2:

Answer:
t ’=
, v_r = 1 m/s t ’= 547.19 s
Explanation:
This is a relative velocity exercise in a dimesion, since the river and the boat are going in the same direction.
By the time the boat goes up the river
v_b - v_r = d / t
By the time the boat goes down the river
v_b + v_r = d '/ t'
let's subtract the equations
2 v_r = d ’/ t’ - d / t
d ’/ t’ = 2v_r + d / t
In the exercise they tell us
d = 1.22 +1.45 = 2.67 km= 2.67 10³ m
d ’= 1.45 km= 1.45 1.³ m
at time t = 69.1 min (60 s / 1min) = 4146 s
the speed of river is v_r
t ’=
t ’=
In order to complete the calculation, we must assume a river speed
v_r = 1 m / s
let's calculate
t ’=
t ’= 547.19 s
Since the temperature of the gas remains constant in the process, we can use Boyle's law, which states that for a gas transformation at constant temperature, the product between the gas pressure and its volume is constant:

which can also be rewritten as

(1)
where the labels 1 and 2 mark the initial and final conditions of the gas.
In our problem,

,

and

, so the final pressure of the gas can be found by re-arranging eq.(1):

Therefore the correct answer is
<span>1. 0.75 atm</span>