Answer:
2440.24 J
Explanation:
Moment of inertia, I1 = 5 kg m^2
frequency, f1 = 3 rps
ω1 = 2 x π x f1 = 2 x π x 3 = 6 π rad/s
Moment of inertia, I2 = 2 kg m^2
Let the new frequency is f2.
ω2 = 2 x π x f2
here no external torque is applied, so the angular momentum remains constant.
I1 x ω1 = I2 x ω2
5 x 6 π = 2 x 2 x π x f2
f2 = 7.5 rps
ω2 = 2 x π x 7.5 = 15 π
Initial kinetic energy, K1 = 1/2 x I1 x ω1^2 = 0.5 x 5 x (6 π)² = 887.36 J
Final kinetic energy, K2 = 1/2 x I2 x ω2^2 = 0.5 x 3 x (15 π)² = 3327.6 J
Work done, W = Change in kinetic energy = 3327.6 - 887.36 = 2440.24 J
Answer:
530.93 units squared
Explanation:
The formula for the area of a circle is pi*r^2. The radius is half the diameter. So, 26/2 = 13.
pi*13^2 = ?
pi*169 = 530.93
The area is 530.93 units squared.
The present value (PV) of $15,254.24 is the most James bennett can consume in his youth.
<u>Given the following data:</u>
- Investment opportunity (youth) = $12,000
- Investment opportunity (old age) = $15,000
To calculate the most James bennett can consume in his youth:
First of all, we would determine the future value of James bennett from his investment and inheritance as follows:

FV = $18000
Mathematically, the most James bennett can consume in his youth is given by this formula:

Substituting the given parameters into the formula, we have;

PV = $15,254.24
Therefore, the present value (PV) of $15,254.24 is the most James bennett can consume in his youth.
Read more on present value here: brainly.com/question/24341207