The function y = 125 + 75x can be used to determine the cost in dollars for a painting job of x hours. What is the rate of change of the cost in dollars with respect to the number of hours spent painting? *
These are examples of a dependent variable and an independent variable. Because y is the variable which is changing, it is considered the dependent variable (as its value DEPENDS on the independent variable). By process of elimination, x is the independent variable (make sure you see why before reading on).
With the knowledge that x is the independent variable in mind, look at the coefficient of x in the equation (y = 125 + 75x). If the coefficient of the linear term (with x) is 75, then the rate of change you're looking for is... 75.
Please try to learn from this solution.
Well, the rate of change of the cost in dollars with respect to the number of hours can be found by taking the derivative of the function. But who needs calculus when we can just use some good old clown magic?
*poof*
Abracadabra! The rate of change is 75 dollars per hour. So for every hour you spend painting, it'll cost you an extra 75 dollars. Now that's what I call an expensive masterpiece!
The rate of change of the cost in dollars with respect to the number of hours spent painting can be found by calculating the derivative of the given function.
To find the derivative, take the derivative of the term with x, which in this case is 75x. Since the derivative of a constant multiplied by x is just the constant, the derivative of 75x is 75.
Therefore, the rate of change of the cost in dollars with respect to the number of hours spent painting is 75 dollars per hour.
To find the rate of change of the cost in dollars with respect to the number of hours spent painting, we need to take the derivative of the given function.
The given function is y = 125 + 75x, where y represents the cost in dollars and x represents the number of hours spent painting.
To find the derivative, we need to apply the power rule of differentiation. According to the power rule, the derivative of x^n, where n is a constant, is nx^(n-1).
Applying the power rule to the given function, the derivative of 125 + 75x is 75, since the derivative of 125 is 0 (as it is a constant) and the derivative of 75x is 75 (using the power rule).
Therefore, the rate of change of the cost in dollars with respect to the number of hours spent painting is 75.
In summary, the rate of change (derivative) of the cost in dollars with respect to the number of hours spent painting is 75.