Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope of 6.2.
With 52 gallons of fuel in its tank, the airplane has a weight of 2222.4 pounds. What is the weight of the plane with 26 gallons of fuel in its tank?
y = 6.2x + b
2222.4 = 6.2*52 + b, so b = 1900
So, we now know that
y = 6.2x + 1900
Just plug in x=26
Or, without even finding b, we know that each gallon of fuel weighs 6.2 pounds, so just subtract 26*6.2 from 2222.4
To find the weight of the plane with 26 gallons of fuel in its tank, we can use the information given about the slope of the linear function.
Let's denote the weight of the plane as W (in pounds) and the amount of fuel in the tank as F (in gallons). We can express the linear function as:
W = mF + b
where m is the slope and b is the y-intercept.
Given that the slope of the function is 6.2, we have:
W = 6.2F + b
Next, we can use the information that with 52 gallons of fuel the weight of the plane is 2222.4 pounds. Substituting these values into the equation, we get:
2222.4 = 6.2(52) + b
Solving for b, we have:
2222.4 = 322.4 + b
b = 2222.4 - 322.4
b = 1900
Now we can substitute the slope and y-intercept into the equation to find the weight of the plane with 26 gallons of fuel:
W = 6.2F + 1900
Plugging in F = 26, we get:
W = 6.2(26) + 1900
W = 161.2 + 1900
W = 2061.2
Therefore, the weight of the plane with 26 gallons of fuel in its tank is 2061.2 pounds.
To find the weight of the plane with 26 gallons of fuel in its tank, we can use the information given about the linear function and the weight of the plane with 52 gallons of fuel.
Let's break down the problem step by step:
1. Identify the variables:
- Let x represent the total amount of fuel in gallons.
- Let y represent the weight of the plane in pounds.
2. Understand the given information:
- The weight of the plane is a linear function of the total amount of fuel in the tank.
- The slope of the function is 6.2, which means that for every additional gallon of fuel, the weight of the plane increases by 6.2 pounds.
- With 52 gallons of fuel in its tank, the plane's weight is 2222.4 pounds.
3. Formulate the equation of the linear function:
- The equation of a line can be written as y = mx + b, where m is the slope and b is the y-intercept.
- In this case, the slope is 6.2, so the equation becomes y = 6.2x + b.
4. Use the given information to find the y-intercept (b):
- We know that when x = 52 (52 gallons of fuel), y = 2222.4 (weight of the plane).
- Plugging these values into the equation, we get 2222.4 = 6.2(52) + b.
- Solving this equation, we find b = 2222.4 - 321.4.
- Therefore, the equation of the line is y = 6.2x + 1901.
5. Find the weight of the plane with 26 gallons of fuel:
- We want to find the weight of the plane when x = 26 (26 gallons of fuel).
- Plugging this value into the equation y = 6.2x + 1901, we get y = 6.2(26) + 1901.
- Simplifying the equation, we find y = 161.2 + 1901.
- Therefore, the weight of the plane with 26 gallons of fuel in its tank is 2062.2 pounds.
So, the weight of the plane with 26 gallons of fuel in its tank is 2062.2 pounds.