Alan repairs televisions. his revenue is modeled by the function r(h)=10+30h for every h hours he spends repairing televisions. his overhead cost is modeled by the function c(h)=5h^2−25 dollars.

after how many hours does he break even?

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ANSWER

Alan breaks even after 7 hours.

EXPLANATION

Alan's revenue is modeled by the function

His overhead cost function is modeled by the function

Alan will break even when his cost is equal to his revenue.

Factorize:

or

We discard the negative value.

He breaks even after 7 hours.

during a tunnel construction project, engineers used explosives to excavate partway into a mountain. but due to constraints and environmental concerns, they later introduced a tunnel boring machine (tbm) to excavate the rest of the tunnel. the length and of the completed tunnel (in feet) is based on the number of days since the tbm started working. the length can be calculated using the equation y = 25x + 225. what does the y-intercept represent in this scenario?

105ft

is the anwser to the question