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------------------------------------------------ Consider the two scenarios:

A. A machine is able to perform 3000 Joules of work in 10 seconds.
B. A machine is able to perform 3000 Joules of work in 5 seconds.

What equation expresses the relative power of the two machines?

A. [tex]A = 2B[/tex]
B. [tex]2A = B[/tex]
C. No answer text provided.
D. [tex]A = B[/tex]

Let's solve this problem by understanding how to calculate the power of each machine and determine their relative power.

1. Understanding Power:
- Power is defined as the rate at which work is done. It is calculated by dividing the work done by the time it takes to do that work.
- The formula for power [tex]$ P $[/tex] is:
[tex]\[
P = \frac{\text{Work}}{\text{Time}}
\][/tex]

2. Calculate Power for Machine A:
- Machine A performs 3000 Joules of work in 10 seconds.
- Using the formula for power:
[tex]\[
P_A = \frac{3000 \text{ Joules}}{10 \text{ seconds}} = 300 \text{ Watts}
\][/tex]

3. Calculate Power for Machine B:
- Machine B performs the same 3000 Joules of work but in 5 seconds.
- Using the formula for power:
[tex]\[
P_B = \frac{3000 \text{ Joules}}{5 \text{ seconds}} = 600 \text{ Watts}
\][/tex]

4. Determine the Relation Between Powers:
- Now we compare the power of the two machines. We have to express power [tex]$ P_A $[/tex] relative to power [tex]$ P_B $[/tex].
- Comparing the values, we see:
- If [tex]$ 2 \times P_A = P_B $[/tex], then:
[tex]\[
2 \times 300 = 600
\][/tex]
- This is true, which matches the equation [tex]$ 2A = B $[/tex].

Therefore, the equation that expresses the relative power of the two machines is:
[tex]\[
2A = B
\][/tex]