Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 10 gallons of fuel, the airplane weighs 2026 pounds. When carrying 25 gallons of fuel, it weighs 2155 pounds. How much does the airplane weigh if it is carrying 35 gallons of fuel?
Well, if the relationship between weight and fuel is linear, we can use the given data to find the slope (rate of change) of the function.
First, let's find the change in weight when the fuel changes from 10 gallons to 25 gallons:
Change in weight = 2155 pounds - 2026 pounds = 129 pounds
Change in fuel = 25 gallons - 10 gallons = 15 gallons
Therefore, the slope of the function is:
Slope = Change in weight / Change in fuel = 129 pounds / 15 gallons = 8.6 pounds per gallon
Now, we can use the slope to find the weight when the fuel is 35 gallons:
Change in fuel = 35 gallons - 10 gallons = 25 gallons
Change in weight = Slope * Change in fuel = 8.6 pounds per gallon * 25 gallons = 215 pounds
So, the airplane would weigh 2,026 pounds (starting weight) + 215 pounds = 2,241 pounds when carrying 35 gallons of fuel.
Just remember, I'm just a clown bot, so don't take my answer too seriously!
To solve this problem, we need to find the equation of the linear function that relates the weight of the airplane to the amount of fuel in its tank.
Let's denote the weight of the airplane as W (in pounds) and the amount of fuel in the tank as F (in gallons).
From the problem statement, we have two sets of data points:
1) When carrying 10 gallons of fuel, the airplane weighs 2026 pounds. This can be written as W = 2026 pounds when F = 10 gallons.
2) When carrying 25 gallons of fuel, it weighs 2155 pounds. This can be written as W = 2155 pounds when F = 25 gallons.
To find the equation of the linear function, we can use the slope-intercept form: W = mF + b, where m is the slope and b is the y-intercept.
To find the slope (m), we can use the formula:
m = (W2 - W1) / (F2 - F1), where (F1, W1) and (F2, W2) are two data points.
Substituting the values from the given data points, we have:
m = (2155 - 2026) / (25 - 10)
m = 129 / 15
m = 8.6
Now, let's find the y-intercept (b) using one of the data points. We'll use the first data point (10 gallons, 2026 pounds):
2026 = 8.6 * 10 + b
2026 = 86 + b
b = 2026 - 86
b = 1940
So the equation of the linear function relating the weight of the airplane (W) to the amount of fuel in its tank (F) is:
W = 8.6F + 1940
To find out how much the airplane weighs when carrying 35 gallons of fuel, we plug F = 35 into the equation above:
W = 8.6 * 35 + 1940
W = 301 + 1940
W = 2241
Therefore, the airplane weighs 2241 pounds when carrying 35 gallons of fuel.
To find out how much the airplane weighs when carrying 35 gallons of fuel, we can use the concept of a linear function. A linear function represents a straight line on a graph, where the relationship between two variables (in this case, weight and fuel) can be expressed using an equation of the form y = mx + b.
In this case, let's assign the weight of the airplane as y (dependent variable) and the amount of fuel as x (independent variable). We need to determine the values of m and b in the equation.
Given that the airplane weighs 2026 pounds when carrying 10 gallons of fuel and 2155 pounds when carrying 25 gallons of fuel, we have two data points: (10, 2026) and (25, 2155).
To find the slope (m) of the line, we use the formula:
m = (change in y) / (change in x)
m = (2155 - 2026) / (25 - 10)
m = 129 / 15
m = 8.6
Now we have the slope of the line.
To find the y-intercept (b), we can substitute one of the points into the equation y = mx + b and solve for b.
Using the point (10, 2026), we have:
2026 = 8.6 * 10 + b
2026 = 86 + b
b = 1940
Now we have the slope (m = 8.6) and the y-intercept (b = 1940).
So, the equation that represents the relationship between the weight of the airplane (y) and the amount of fuel (x) is:
y = 8.6x + 1940
To find out how much the airplane will weigh when carrying 35 gallons of fuel, we substitute x = 35 into the equation:
y = 8.6 * 35 + 1940
y = 301 + 1940
y = 2241
Therefore, the airplane will weigh 2241 pounds when carrying 35 gallons of fuel.
25 g - 10 g = 2155 - 2026
15 g = 129 ... g = 129 / 15
add the weight of 10 gallons to the 25 gallon total weight