# data[].attributes.headline
The power factor is decreasing at a rate of 0.01249 per hour at 10 am when the rate of change of reactive power is 300 MVAR/hr and the power factor is 0.99

# data[].attributes.subject
The power factor is decreasing at a rate of 0.01249 per hour at 10 am when the rate of change of reactive power is 300 MVAR/hr and the power factor is 0.99

# data[].attributes.body
The real power b is a constant, so its derivative is 0.

# data[].attributes.body
First we need to find a

# data[].attributes.body
We need to find c (or apparent power) and the rate of change of c to get the answer

# data[].attributes.headline
Derive the power factor equation explicitly

# data[].attributes.subject
Derive the power factor equation explicitly

# data[].attributes.headline
Set the derivative to 0 to find local extremas

# data[].attributes.subject
Set the derivative to 0 to find local extremas

# data[].attributes.headline
Write a function to represent the total cost and simplify

# data[].attributes.subject
Write a function to represent the total cost and simplify

# data[].attributes.headline
Now that we have c and the rate of change of c, we can find the rate of change of the power factor!

# data[].attributes.subject
Now that we have c and the rate of change of c, we can find the rate of change of the power factor!

# data[].attributes.headline
Using Pythagorean Theorem, we can find a as we know b and c

# data[].attributes.subject
Using Pythagorean Theorem, we can find a as we know b and c

# data[].attributes.body
Find the rate at which the power factor is changing when the reactive power is increasing at a rate of 300 MVAR/hr and the power factor is 0.99.

# data[].attributes.headline
The total real power from the Shearon-Harris nuclear plant and the Roxboro coal plant

# data[].attributes.subject
The total real power from the Shearon-Harris nuclear plant and the Roxboro coal plant

# data[].attributes.headline
The distance down the cart path for minimum cost:

# data[].attributes.subject
The distance down the cart path for minimum cost:

# data[].attributes.headline
There is a local min at x = 60.678 since C' changes from negative to positive

# data[].attributes.subject
There is a local min at x = 60.678 since C' changes from negative to positive

# data[].attributes.attachment_link.entities[].name
Finance Optimization Research on Solar Electricity

# data[].attributes.attachment_link.entities[].name
Duke University Bass Connections Energy Efficiency

# data[].attributes.attachment_link.entities[].name
VP Research and Technologies and Innovation

# data[].attributes.body
- The power line needs to run from the transformer (the green dot) to the light (the red dot) .

- The blue path will be done by the trench-digging device, which costs $15/ft while the orange path will be done by the horizontal boring machine at $40/ft.

- Determine the location where the horizontal boring machine should be placed to minimize cost.

# data[].attributes.body
Find the rate of change of the power factor

# data[].attributes.body
Minimize the total cost of underground wiring