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 5.9. see the figure below. with 53 gallons of fuel in its tank, the airplane has a weight of 2212.7 pounds. what is the weight of the plane with 20 gallons of fuel in its tank?

Question

27-10-2022
Mathematics

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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 5.9. see the figure below. with 53 gallons of fuel in its tank, the airplane has a weight of 2212.7 pounds. what is the weight of the plane with 20 gallons of fuel in its tank?

Answer :

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BhawnaKumari BhawnaKumari · Answer 1 · 2022-11-04T10:11:37-04:00

The weight of the plane with 20 gallons of fuel in its tank 2218 pounds. using a linear function.

what is linear function?
A straight line makes up the graph of a linear function. The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one.

Let y be the weight of the airplane and x be the amount of fuel

And we know that the general form of a linear

function is

(1) And given that the slope of the line is

y = mx + c

m = 5.9

Then (1) becomes

y = 5.9x + c

And given that for x = 53 , y = 2212.7

Then from (2), we have

2212.7 = 5.9 (53) + c

⇒ 2212.7 = 312.7 + c

c = 2212.7 - 312.7

c = 1900

Thus, (2) becomes

y = 5.9x + 1900

Then for x=22, from (3) y = 118 + 2100

= w = 2218

The weight of the plane with 20 gallons in its fuel tank is 2218 pounds

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