Write the statement as a power function equation. Use k for constant of variation if one is not given.
a. Charles's law states the volume V of an enclosed ideal gas at a constant pressure varies directly as the absolute temperature T.
b. The volume V of a circular cylinder with a fixed height is proportional to the square of its radius.
c. the current I in an electrical circuit is inversely proportional to the resistance R, with constant of variation V.
I can't figure out how to do this. I was looking at my old notes but can't seem to come up with something.
No problem! I'll guide you through the process of writing each statement as a power function equation.
a. Charles's law states the volume V of an enclosed ideal gas at a constant pressure varies directly as the absolute temperature T.
To write this as a power function equation, we need to express the relationship between V and T using an equation of the form V = kt^n, where k is the constant of variation and n is the exponent. In this case, the statement says the volume varies directly with the absolute temperature, which means the exponent n is 1.
So, the power function equation for Charles's law can be written as V = kT.
b. The volume V of a circular cylinder with a fixed height is proportional to the square of its radius.
Again, we want to express the relationship between V and the radius (let's call it r) as a power function. The statement says that the volume is proportional to the square of the radius, which means the exponent n is 2.
Therefore, the power function equation for this statement can be written as V = kr^2.
c. The current I in an electrical circuit is inversely proportional to the resistance R, with a constant of variation V.
When a variable is inversely proportional to another, it means their product is constant. We can express this relationship using the equation I * R = V, where V is the constant of variation.
To write it as a power function equation, we can solve the equation for I by dividing both sides by R:
I = V/R
In this case, since there is no specific exponent mentioned, we can assume it's 1. Therefore, the power function equation becomes I = kR^-1.
Remember that in power function equations, the constant of variation (k) might be given in the original problem statement, but if it's not provided, we use the letter k to represent the constant.
No problem! I can help you with that. Let's write the statements as power function equations:
a. Charles's law: V = k * T
Here, V represents the volume of the gas, T represents the absolute temperature, and k represents the constant of variation.
b. Volume of a circular cylinder: V = k * r^2
In this equation, V represents the volume of the cylinder, r represents the radius, and k represents the constant of variation.
c. Current in an electrical circuit: I = k / R
Here, I represents the current, R represents the resistance, and k represents the constant of variation.
Keep in mind that the statements above are written as power function equations, where the variables are raised to a certain power (T in equation a, r in equation b) in a direct or inverse relationship.