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 141°F? Use the discriminant of a quadratic equation to decide.

Question

(1 point)
Responses

yes
yes

no
no

Answer 1

To determine if the temperature of the part will ever reach or exceed 141°F, we can use the discriminant of the quadratic equation.

The quadratic equation representing the temperature T in degrees Fahrenheit is:

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

We can rewrite this equation in the form ax^2 + bx + c = 0:

-0.005x^2 + 0.45x + 125 - 141 = 0

Simplifying this equation, we get:

-0.005x^2 + 0.45x - 16 = 0

Now we can calculate the discriminant:

Discriminant = b^2 - 4ac = (0.45)^2 - 4(-0.005)(-16)

Discriminant = 0.2025 - 1.28

Discriminant = -1.0775

Since the discriminant is negative, it means that the quadratic equation has no real roots. In other words, the temperature of the part will never reach or exceed 141°F.

Therefore, the correct answer is: no.