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3 September, 18:57

During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 132 ° F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T = - 0.005x^2 + 0.45x + 125. Will the temperature of the part ever reach or exceed 132 ° F? Use the discriminant of a quadratic equation to decide.

A. no

B. yes

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  1. 3 September, 20:49
    0
    T = - 0.005x^2 + 0.45x + 125

    T = 132 = > - 0.005x^2 + 0.45x + 125 = 132

    => - 0.005x^2 + 0.45x + 125 - 132 = 0

    => - 0.005x^2 + 0.45x - 7 = 0

    Discriminant: b^2 - 4ac = (0.45) ^2 - 4 ( - 0.005) (-7) = 0.2025 - 0.14 = 0.0625

    Discriminant > 0 = > the equation has two real and different solutions.

    Answer: yes
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