Answer:
Step-by-step explanation:
Expression for the rectangular area and perimeter are, respectively:
After some algebraic manipulation, area expression can be reduce to an one-variable form:
The first derivative of the previous equation is:
Let the expression be equalized to zero:
The second derivative is:
According to the Second Derivative Test, the critical value found in previous steps is a maximum. Then:
The maximum area is:
Answer:
h = a + b * t, this equation gives you the height of the candle after t hours, where:
h = height of the candle
t = hours of burning
a = the y intercept
b = the slope
Step-by-step explanation:
In your problem says that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. This means that the independent variable is t (hours of burning) and the dependent variable is h (height of the candle).
A linear function has the following form:
y = f(x) = a + bx
a is the constant term or the y intercept. It is the value of the dependent variable when x = 0.
b is the coefficient of the independent variable. It is also known as the slope and gives the rate of change of the dependent variable.
NOTE:
In order to find numerical values you need at least two points in order to find the slope (t1,h1), (t2,h2), with this equation:
b =
Next you find a when x = 0, y = a, where y is one of the points that you want to evaluate.
With these values you put them in this equation h = a + b * t and that's it! You will find the height of the candle after t hours.