The price of a steel rod varies jointly as the length and square of the diameter. If a 12 ft rod with a 2 in of diameter cost 480.00 pesos then what is the price of an 18 ft rod with a 3 in of diameter?
this is just like the gas problem in your last post, but P=kLD^2
give it a try, and show us what you've tried if you get stuck.
To find the price of an 18 ft rod with a 3 in diameter, we can use the concept of joint variation. Joint variation states that when two variables are related to a third variable, the expression relating them is of the form y = kx₁x₂, where y is the dependent variable, x₁ and x₂ are the independent variables, and k is the constant of variation.
In this case, the price of the steel rod (y) varies jointly as the length (x₁) and square of the diameter (x₂). Let's set up the equation using the given information:
480.00 = k * 12 * (2²)
480.00 = k * 12 * 4
480.00 = k * 48
Now, we can solve for k by dividing both sides of the equation by 48:
k = 480.00 / 48
k = 10.00
Now that we have the value of k, we can find the price of the 18 ft rod (y₂) with a 3 in diameter (x₂₂) using the joint variation equation:
y₂ = k * x₁₂ * (x₂₂)²
y₂ = 10.00 * 18 * (3²)
y₂ = 10.00 * 18 * 9
y₂ = 1620.00 pesos
Therefore, the price of an 18 ft rod with a 3 in diameter would be 1620.00 pesos.