Question 1099735: Write a system of three equations to solve applied problems
The concentration of dissolved oxygen in water varies with temperature. Between 0∘C−50∘C0∘C−50∘C , the relationship can be modeled as a quadratic function. Use the data in the table below to write a system of equations that, if solved, would help you find the quadratic function.
T ( ∘C)∘C) Dissolved oxygen (mgL)(mgL)
10 11.27
20 9.07
30 7.54
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! 10 11.27
20 9.07
30 7.54
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since it's a quadratic, find the parabola thru the 3 points.
y = ax^2 + bx + c
---
11.27 = 100a + 10b + c
9.07 = 400a + 20b + c
7.54 = 900a + 30b + c
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Eliminate c
9.070 = 400a + 20b + c
11.27 = 100a + 10b + c
--------------------------- Subtract
-2.2 = 300a + 10b Eqn A
---
7.54 = 900a + 30b + c
9.07 = 400a + 20b + c
--------------------------- Subtract
-1.53 = 500a + 10b Eqn B
10b = -1.53 - 500a
10b = -2.2 - 300a --- From Eqn A
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Since both = 10b:
-1.53 - 500a = -2.2 - 300a
200a = 0.67
a = 0.00335
Sub for a, find b, then find c
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There's a "shortcut" when the x values are evenly spaced, but this always works.
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