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

No

Explanation:

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

Answer 2

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

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.