Mathematics: Jimmy owns a small engine repair business. the revenue in dollars can be modeled by the equation y=420+72x. where x is the number of hours spentrepairing small engines. the overhead cost in dollars can be modeled by the equation y=2x^2+180 where x is the number of hours spent repairing bikes. after about how many hours does the company break even?

how do youm do manStep-by-step explanation:...

Jimmy owns a small engine repair business. the revenue

Ответ:

nany1982

13.03.2022

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:
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}
\\
\\=\frac{--72\pm \sqrt{(-72)^2-4(2)(-240)}}{2(2)}
\\
\\=\frac{72\pm \sqrt{5184--1920}}{4}
\\
\\=\frac{72\pm \sqrt{7104}}{4}
\\
\\=\frac{72\pm 84.29}{4}=\frac{72+84.29}{4}\text{ or }\frac{72-84.29}{4}
=\frac{-12.29}{4}\text{ or }\frac{156.29}{4}
=-3.07\text{ or }39.07$

Since negative time makes no sense, the answer is 39.07, or about 39 hours.

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