Answer:
3.6 hours
Step-by-step explanation:
Alan's revenue function is given by:
[tex]r(h) = 47 + 2h[/tex]
for every h hours he spends repairing televisions.
His overhead cost is modeled by the function:
[tex]c(h) = 5 {h}^{2} - 25[/tex]
To find the number of hours Alan breaks even, we need to equate the functions and solve for h.
[tex]47 + 2h = 5 {h}^{2} - 25[/tex]
We rewrite in standard form:
[tex]5 {h}^{2} - 2h - 25 - 47 = 0[/tex]
This gives:
[tex]5 {h}^{2} - 2h - 72= 0[/tex]
Using the quadratic formula:
[tex]h = \frac{ - - 2 \pm \sqrt{( - {2)}^{2} - 4(5)( - 72) } }{2 \times 5} [/tex]
This gives:
[tex]h = 3.6 \: or \: h = - 4[/tex]
Since time is not negative, he breaks even after 3.6 hours.
