Question 821710: Oil Leak
A tractor has an oil leak. The amount of oil, L(t), in milliliters per hour that leaks out is a function of the tractors operating temperature,t, in degrees Celsius. The function is L(t)=0.0004t^2+0.16t+20,100 degrees Celsius<=160 Celsius
a) How many milliliters of oil will leak out in 1 hour if the operating temperature of the tractor is 100 C?
b) If oil is leaking out at 53 milliliters per hour, what is the operating temperature of the tractor?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
L(t) = 0.0004t^2 + 0.16t + 20
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answer a:
t = 100 degrees C:
L(1) = 0.0004(100)^2 + 0.16(100) + 20
L(1) = 4 + 16 + 20
L(1) = 40 ml per hour
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answer b:
L(t) = 53 = 0.0004t^2 + 0.16t + 20
0.0004t^2 + 0.16t - 33 = 0
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the above quadratic equation is in standard form, with a=0.0004, b=0.16, and c=-33
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
0.0004 0.16 -33
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
t = 150
t = -550
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negative operating temperature doesn't make sense for this problem, so use the positive root:
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operating temperature is 150 degrees C
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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