QuestionFind the weight of an airplane with 70 gallons of fuel, given it weighs 2012 lbs at 20 gallons and 2208 lbs at 55 gallons.

Studdy Solution

STEP 1

Assumptions1. The weight of the airplane is a linear function of the amount of fuel in its tank. . When carrying20 gallons of fuel, the airplane weighs201 pounds.
3. When carrying55 gallons of fuel, it weighs2208 pounds.
4. We need to find the weight of the airplane when carrying70 gallons of fuel.

STEP 2

We can write the weight of the airplane as a linear function in the form $y = mx + b$ , where $y$ is the weight of the airplane, $x$ is the amount of fuel, $m$ is the slope of the function, and $b$ is the y-intercept.

STEP 3

First, we need to find the slope of the function. The slope is the change in $y$ divided by the change in $x$ . $m = \frac{\Delta y}{\Delta x}$

STEP 4

Substitute the given values into the formula to find the slope.
$m = \frac{2208 -2012}{55 -20}$

STEP 5

Calculate the slope.
$m = \frac{196}{35} =5.$

STEP 6

Now that we have the slope, we can find the y-intercept, $b$ . We can do this by rearranging the equation of the line and substituting one of the given points. Let's use the point (20,2012).
$b = y - mx$

STEP 7

Substitute the values into the formula to find $b$ .
$b =2012 -5.6 \times20$

STEP 8

Calculate the y-intercept.
$b =2012 -112 =1900$

STEP 9

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y =5.6x +190$

STEP 10

We can now find the weight of the airplane when it is carrying70 gallons of fuel by substituting $x =70$ into the equation.
$y =5.6 \times70 +1900$

STEP 11

Calculate the weight of the airplane.
$y =392 +1900 =229$ The airplane weighs229 pounds when it is carrying70 gallons of fuel.

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QuestionFind the weight of an airplane with 70 gallons of fuel, given it weighs 2012 lbs at 20 gallons and 2208 lbs at 55 gallons.

Studdy Solution

STEP 1

Assumptions1. The weight of the airplane is a linear function of the amount of fuel in its tank. . When carrying20 gallons of fuel, the airplane weighs201 pounds.
3. When carrying55 gallons of fuel, it weighs2208 pounds.
4. We need to find the weight of the airplane when carrying70 gallons of fuel.

STEP 2

We can write the weight of the airplane as a linear function in the form $y = mx + b$ , where $y$ is the weight of the airplane, $x$ is the amount of fuel, $m$ is the slope of the function, and $b$ is the y-intercept.

STEP 3

First, we need to find the slope of the function. The slope is the change in $y$ divided by the change in $x$ . $m = \frac{\Delta y}{\Delta x}$

STEP 4

Substitute the given values into the formula to find the slope.
$m = \frac{2208 -2012}{55 -20}$

STEP 5

Calculate the slope.
$m = \frac{196}{35} =5.$

STEP 6

Now that we have the slope, we can find the y-intercept, $b$ . We can do this by rearranging the equation of the line and substituting one of the given points. Let's use the point (20,2012).
$b = y - mx$

STEP 7

Substitute the values into the formula to find $b$ .
$b =2012 -5.6 \times20$

STEP 8

Calculate the y-intercept.
$b =2012 -112 =1900$

STEP 9

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y =5.6x +190$

STEP 10

We can now find the weight of the airplane when it is carrying70 gallons of fuel by substituting $x =70$ into the equation.
$y =5.6 \times70 +1900$

STEP 11

Calculate the weight of the airplane.
$y =392 +1900 =229$ The airplane weighs229 pounds when it is carrying70 gallons of fuel.

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QuestionFind the weight of an airplane with 70 gallons of fuel, given it weighs 2012 lbs at 20 gallons and 2208 lbs at 55 gallons.

Studdy Solution

STEP 1

Assumptions1. The weight of the airplane is a linear function of the amount of fuel in its tank. . When carrying20 gallons of fuel, the airplane weighs201 pounds.3. When carrying55 gallons of fuel, it weighs2208 pounds.4. We need to find the weight of the airplane when carrying70 gallons of fuel.

STEP 2

We can write the weight of the airplane as a linear function in the form y=mx+by = mx + by=mx+b, where yyy is the weight of the airplane, xxx is the amount of fuel, mmm is the slope of the function, and bbb is the y-intercept.

STEP 3

First, we need to find the slope of the function. The slope is the change in yyy divided by the change in xxx.m=ΔyΔxm = \frac{\Delta y}{\Delta x}m=ΔxΔy​

STEP 4

Substitute the given values into the formula to find the slope.m=2208−201255−20m = \frac{2208 -2012}{55 -20}m=55−202208−2012​

STEP 5

Calculate the slope.m=19635=5.m = \frac{196}{35} =5.m=35196​=5.

STEP 6

Now that we have the slope, we can find the y-intercept, bbb. We can do this by rearranging the equation of the line and substituting one of the given points. Let's use the point (20,2012).b=y−mxb = y - mxb=y−mx

STEP 7

Substitute the values into the formula to find bbb.b=2012−5.6×20b =2012 -5.6 \times20b=2012−5.6×20

STEP 8

Calculate the y-intercept.b=2012−112=1900b =2012 -112 =1900b=2012−112=1900

STEP 9

Now that we have the slope and the y-intercept, we can write the equation of the line.y=5.6x+190y =5.6x +190y=5.6x+190

STEP 10

We can now find the weight of the airplane when it is carrying70 gallons of fuel by substituting x=70x =70x=70 into the equation.y=5.6×70+1900y =5.6 \times70 +1900y=5.6×70+1900

STEP 11

Calculate the weight of the airplane.y=392+1900=229y =392 +1900 =229y=392+1900=229The airplane weighs229 pounds when it is carrying70 gallons of fuel.

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Assumptions1. The weight of the airplane is a linear function of the amount of fuel in its tank. . When carrying20 gallons of fuel, the airplane weighs201 pounds.
3. When carrying55 gallons of fuel, it weighs2208 pounds.
4. We need to find the weight of the airplane when carrying70 gallons of fuel.

We can write the weight of the airplane as a linear function in the form $y = mx + b$ , where $y$ is the weight of the airplane, $x$ is the amount of fuel, $m$ is the slope of the function, and $b$ is the y-intercept.

First, we need to find the slope of the function. The slope is the change in $y$ divided by the change in $x$ . $m = \frac{\Delta y}{\Delta x}$

Substitute the given values into the formula to find the slope.
$m = \frac{2208 -2012}{55 -20}$

Calculate the slope.
$m = \frac{196}{35} =5.$

Now that we have the slope, we can find the y-intercept, $b$ . We can do this by rearranging the equation of the line and substituting one of the given points. Let's use the point (20,2012).
$b = y - mx$

Substitute the values into the formula to find $b$ .
$b =2012 -5.6 \times20$

Calculate the y-intercept.
$b =2012 -112 =1900$

Now that we have the slope and the y-intercept, we can write the equation of the line.
$y =5.6x +190$

We can now find the weight of the airplane when it is carrying70 gallons of fuel by substituting $x =70$ into the equation.
$y =5.6 \times70 +1900$

Calculate the weight of the airplane.
$y =392 +1900 =229$ The airplane weighs229 pounds when it is carrying70 gallons of fuel.