The term "autonomous" refers to an ordinary differential equation that relates the derivatives of the dependent variable as a function *only* of the dependent variable. In other words, the ODE doesn't explicitly depend on the independent variable.
Examples:
is autonomous
is *not* autonomous
Let x = cost of one cheese pizza.
Let y = cost of one pepperoni pizza.
Set up a system of equations.
6x + 7y = 153.50
2x + 2y = 47.00.
Multiply the second equation by -3
6x + 7y = 153.50
-6x - 6y = -141.00.
Add the equations together
y = $12.00.
Plug 12 into one of our original equations.
2x + 2(12) = 47.
Simplify the left side.
2x + 24 = 47.
Subtract 24 from each side.
2x = 23.
Divide each side by 2
x = $11.50
In conclusion, one pepperoni pizza costs $12.00
Your answer would be $1.89
You take 11.34 and divide it by 6. After that you’ll be 1.89 as your unit price.
1.89 is how much for 1 pound
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➷ Substitute in the value:
840 - 52.5(14) = 105
Since e(14) = 105, the elevation of the cable car would be 105 meters from the ground 14 minutes after it begins descending from the top of the hill
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➶ Hope This Helps You!
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