Question

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 141°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by
T = 0.005x² + 0.45x + 125.
Will the temperature of the part ever reach or exceed 141F? Use the discriminant of a quadratic equation to decide.
A. yes
B. no

Answer 1

Answer:

Yes, it will reach or exceed 141 degree F

Step-by-step explanation:

Given equation that shows the temperature T in degrees Fahrenheit x minutes after the machine is put into operation is,

$T = 0.005x^2 + 0.45x + 125$

Suppose T = 141°F,

$\implies 141 = 0.005x^2 + 0.45x + 125$

$\implies 0.005x^2 + 0.45x + 125 - 141 =0$

$\implies 0.005x^2 + 0.45x - 16=0$

Since, a quadratic equation $ax^2 + bx + c =0$ has,

Real roots,

If Discriminant, $D = b^2 - 4ac \geq 0$

Imaginary roots,

If D < 0,

Since, $0.45^2 - 4\times 0.005\times -16 = 0.2025 + 32 > 0$

Thus, roots of -0.005x² + 0.45x + 125 are real.

Hence, the temperature can reach or exceed 141 degree F.