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

Question

Kirby

Mathematics

20 October, 02:53

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

+2

Answers (1)

Know the Answer?

Sonny Lam · Answer 1

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