A model airplane reaches a maximum altitude and then begin to descend at a constant rate in feet per second. After falling for 12 seconds, the model airplane has an altitude of 212 feet. After falling for 25 second, the model airplane’s altitude is 95 feet. Write an equation that represents the altitude of the model airplane, y, after x seconds of falling.
treat it as two ordered pairs of the form (t, h)
they would be (12, 212) and (25,95)
find the slope and find the equation using the method you
must have learned to do this type of problem.
find the rate of fall ... (change in altitude) / (change in time)
... this is the slope of the line ... y = m x + b
plug in one of the time/altitude points to find the y-intercept (b)
To write an equation that represents the altitude of the model airplane, we can use the slope-intercept form of a linear equation, which is y = mx + b.
Given that the airplane descends at a constant rate, we know that the altitude decreases linearly with time. Let's find the slope (m) of the line.
The altitude after falling for 12 seconds is 212 feet, and after falling for 25 seconds, it is 95 feet. We can use these two points to calculate the slope as follows:
slope (m) = (y2 - y1) / (x2 - x1)
= (95 - 212) / (25 - 12)
= -13
Now that we have the slope, we need to find the y-intercept (b) of the line. We can choose any point on the line, such as (12, 212). Substituting these values into the slope-intercept form, we can solve for b:
y = mx + b
212 = -13 * 12 + b
212 = -156 + b
b = 212 + 156
b = 368
Therefore, the equation that represents the altitude of the model airplane after x seconds of falling is:
y = -13x + 368
To write the equation, let's analyze the given information. We know that the model airplane descends at a constant rate in feet per second. Let's denote this rate as r.
Given that after 12 seconds, the altitude is 212 feet, we can create an equation:
12r + initial altitude = 212
Similarly, after 25 seconds, the altitude is 95 feet, leading to another equation:
25r + initial altitude = 95
To find the equation that represents the altitude of the model airplane after x seconds, we need to find the value of the initial altitude.
First, let's subtract the initial altitude from both equations to isolate the constant rate:
12r = 212 - initial altitude
25r = 95 - initial altitude
Now, we can equate the equations to solve for the initial altitude:
212 - initial altitude = 95 - initial altitude
Simplifying, we find that the initial altitude cancels out, giving us:
212 = 95
Since 212 is not equal to 95, these equations are inconsistent. This implies that there may be an error in the given information or a mistake in the problem statement. Please recheck the problem and provide accurate information to find the equation accurately.