Suppose that the weight in pounds Of an airplane is a linear function of the amount of fuel in gallons in its tank when caring 14 gallons of fuel the airplane weight is 2091 Pounds when caring 46 gallons of fuel it weighs 2299 pounds how much does the airplane way if its carrying 50 gallons of fuel
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
Wf = 8Lbs/gal.
Wa + 8x = Wt
Wa + 8*14 = 2091
Wa = 1979 Lbs. = weight of airplane without fuel.
Wa + 8x = 1979 + 8*50 =
To find out how much the airplane weighs when carrying 50 gallons of fuel, we can use the given information to determine the equation of the linear function relating weight to fuel.
Let's start by identifying the variables:
- Weight of the airplane (in pounds): W
- Amount of fuel in the tank (in gallons): F
We are given two data points:
1. When carrying 14 gallons of fuel, the airplane weighs 2091 pounds.
So, the first data point is (F₁, W₁) = (14, 2091).
2. When carrying 46 gallons of fuel, the airplane weighs 2299 pounds.
The second data point is (F₂, W₂) = (46, 2299).
We can use these two points to find the equation of the line.
First, let's find the slope (m):
m = ΔW / ΔF
m = (W₂ - W₁) / (F₂ - F₁)
m = (2299 - 2091) / (46 - 14)
m = 208 / 32
m = 6.5
Now that we have the slope (m), we can find the equation of the line using the point-slope form:
W - W₁ = m(F - F₁)
Plugging in the values:
W - 2091 = 6.5(F - 14)
Simplifying the equation:
W - 2091 = 6.5F - 91
W = 6.5F - 91 + 2091
W = 6.5F + 2000
Now we can find the weight (W) when carrying 50 gallons of fuel (F = 50):
W = 6.5(50) + 2000
W = 325 + 2000
W = 2325
Therefore, the airplane weighs 2325 pounds when carrying 50 gallons of fuel.