Respuesta :
The company breaks even at about 39 hours.
We will set both functions equal to each other, since we want to know when they break even:
420+72x = 2x²+180
We want to write this as a quadratic in standard form, so we will subtract 72x from both sides first:
420+72x-72x = 2x²+180-72x
420 = 2x²-72x+180
Now we subtract 420 from both sides:
420-420 = 2x²-72x+180-420
0 = 2x²-72x-240
We will now use the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\=\frac{--72\pm \sqrt{(-72)^2-4(2)(-240)}}{2(2)} \\ \\=\frac{72\pm \sqrt{5184--1920}}{4} \\ \\=\frac{72\pm \sqrt{7104}}{4} \\ \\=\frac{72\pm 84.29}{4}=\frac{72+84.29}{4}\text{ or }\frac{72-84.29}{4} =\frac{-12.29}{4}\text{ or }\frac{156.29}{4} =-3.07\text{ or }39.07[/tex]
Since negative time makes no sense, the answer is 39.07, or about 39 hours.
We will set both functions equal to each other, since we want to know when they break even:
420+72x = 2x²+180
We want to write this as a quadratic in standard form, so we will subtract 72x from both sides first:
420+72x-72x = 2x²+180-72x
420 = 2x²-72x+180
Now we subtract 420 from both sides:
420-420 = 2x²-72x+180-420
0 = 2x²-72x-240
We will now use the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\=\frac{--72\pm \sqrt{(-72)^2-4(2)(-240)}}{2(2)} \\ \\=\frac{72\pm \sqrt{5184--1920}}{4} \\ \\=\frac{72\pm \sqrt{7104}}{4} \\ \\=\frac{72\pm 84.29}{4}=\frac{72+84.29}{4}\text{ or }\frac{72-84.29}{4} =\frac{-12.29}{4}\text{ or }\frac{156.29}{4} =-3.07\text{ or }39.07[/tex]
Since negative time makes no sense, the answer is 39.07, or about 39 hours.
