# Power vs Resistance: 2.35(9+.05)^2-2(r+.5)/(r+0.5)^4

• sammiyahc0
In summary, the conversation discusses the correct application of the quotient rule to find the rate of change of power with respect to resistance. The correct formula is P = 2.35R /(R + 0.5)^2 watts and the rate of change should be calculated using the formula \frac{vdu-udv}{v^2} with appropriate substitution of values.
sammiyahc0
1.
The power delivered by a battery to an apparatus of resistance R (in ohms) is P = 2.35R /(R + 0.5)^2
watts.Find the rate of change of power with respect to resistance for R = 9.(Round your answer to four decimal places

2. quotient rule
3. 2.35(9+.05)^2-2(r+.5)/(r+0.5)^4

You've not applied the quotient rule correctly. You dropped a factor in the second term, and a 2.35 has been reduced to 2. it would help if you included all appropriate parentheses. Why have you substituted r = 9 in some places but not in others?

What you have written is (I think - you appear to have substituted R=9 in some places but not others):$$2.35(R+0.5)^2-\frac{2(R+0.5)}{(R+0.5)^4}$$which I don't think is right. Even assuming that you meant $$\frac{2.35(R+0.5)^2-2(R+0.5)}{(R+0.5)^4}$$I still don't think this is right. I was taught that the quotient rule as$$d\frac{u}{v}=\frac{vdu-udv}{v^2}$$Perhaps you could show us what you think $u, v, du, dv$ are?

## What is the formula for "Power vs Resistance"?

The formula for "Power vs Resistance" is 2.35(9+.05)^2-2(r+.5)/(r+0.5)^4.

## What does "r" represent in the formula?

"r" represents the resistance value in the formula.

## What is the significance of the exponent in the formula?

The exponent in the formula is used to calculate the power value in the equation.

## How can this formula be applied in real life?

This formula can be used in various fields such as electrical engineering, physics, and chemistry to calculate the relationship between power and resistance in a specific system.

## What are the units for the values in the formula?

The units for the values in the formula will depend on the specific application and system being analyzed. Typically, the units for power are watts and the units for resistance are ohms.

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