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 part remain below 141°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T=0.005x^2+0.45x+125. Will the temperature of the part ever reach or exceed 141°F? Use the discriminant of a quadratic equation to decide.​

Answer 1

Answer:

The temperature of the part won’t reach or exceed 141℉

Step-by-step explanation:

Substituting the value of T= 141 the given equation becomes

$\begin{array}{l}{141=-0.005 x^{2}+0.45 x+125} \\ {-0.005 x^{2}+0.45 x+125-141=0} \\ {-0.005 x^{2}+0.45 x-16=0}\end{array}$

we know that discriminant D = $b^{2}-4 a c$

Three conditions: - D < 0: imaginary roots, D = 0: real and equal roots,

D > 0: two real and unequal roots Substituting  a = -0.005, b = 0.045 and c = -16, $\mathrm{D}=0.045^{2}-4(-0.005)(-16) \mathrm{D}=-0.317975 \mathrm{D}=-0.32(\text { approx. })$ Therefore, it won't reach the temperature.

Answer 2

Answer:

No

Step-by-step explanation:

Just wanted to make it a little bit more clear on the matter of the answer