B !! Is the correct answer
Answer:
ω=314.15 rad/s.
0.02 s.
Explanation:
Given that
Motor speed ,N= 3000 revolutions per minute
N= 3000 RPM
The speed of the motor in rad/s given as
Now by putting the values in the above equation
ω=314.15 rad/s
Therefore the speed in rad/s will be 314.15 rad/s.
The speed in rev/sec given as
ω= 50 rev/s
It take 1 sec to cover 50 revolutions
That is why to cover 1 revolution it take

Answer:


Explanation:
Given
--- Initial altitude
-- Altitude after 16.5 seconds
--- Acceleration (It is negative because it is an upward movement i.e. against gravity)
Solving (a): Final Speed of the rocket
To do this, we make use of:

The final altitude after 16.5 seconds is represented as:

Substitute the following values:
and 
So, we have:



Collect Like Terms


Make u the subject



Solving (b): The maximum height attained
First, we calculate the time taken to attain the maximum height.
Using:

At the maximum height:
--- The final velocity

So, we have:

Collect Like Terms

Make t the subject


The maximum height is then calculated as:

This gives:





Hence, the maximum height is 1141.07ft
Answer:
20 years
Explanation:
You do 2,000,000 ÷ 100,000 but you can simplify that to 20 ÷ 1 = 20
During those 20 years, the profits you earn will be 80,000 since when you do 2,000,000 x 0.04 but you can simplify that to 20,000 x 4 getting 80,000 and that quite doesn't reach 100,000 dollars
Answer:
The answer is 960 kg
Explanation:
Solution
Given that:
Assume the initial dye concentration as A₀
We write the expression for the dye concentration for one hour as follows:
ln (C₁) = ln (A₀) -kt
Here
C₁ = is the concentration at 1 hour
t =time
Now
Substitute 480 g for C₁ and 1 hour for t
ln (480) = ln (A₀) -k(1) ------- (1)
6.173786 = ln (A₀) -k
Now
We write the expression for the dye concentration for three hours as follows:
ln (C₃) = ln (A₀) -k
Here
C₃ = is the concentration at 3 hour
t =time
Thus
Substitute 480 g for C₃ and 3 hour for t
ln (120) = ln (A₀) -k(3) ------- (2)
4.787492 = ln (A₀) -3k
Solve for the equation 1 and 2
k =0.693
Now
Calculate the amount of blue present initially using the expression:
Substitute 0.693 for k in equation (2)
4.787492 = ln (A₀) -3 (0.693)
ln (A₀) =6.866492
A₀ =e^6.866492
= 960 kg
Therefore, the amount of the blue dye present from the beginning is 960 kg