8.05 Solve quadratics using appropriate methods
Interactive practice questions
Software engineers are designing a self-serve checkout system for a supermarket. They notice that the traffic through the store during the day is described by the function $C=-t\left(t-15\right)$C=−t(t−15), where $C$C is the number of customers and $t$t is the number of hours after the store opens.
To meet the peak demand, the engineers allow for an extra checkout machine to be on when the number of customers is at $44$44 people or more.
Find the times $t$t when the number of customers is equal to $44$44 people. Write both solutions on the same line, separated by a comma.
Therefore, the extra checkout machine will turn on $\editable{}$ hours after opening, and it will then turn off $\editable{}$ hours later.
The Widget and Trinket Emporium has released the forecast of its revenue for the next year. The revenue $R$R (in dollars) at any point in time $t$t (in months) is described by the equation $R=-\left(t-18\right)^2+16$R=−(t−18)2+16.
An object is launched from a height of $90$90 feet with an initial velocity of $131$131 feet per second, and after $x$x seconds its height (in feet) is given by $h=-16x^2+131x+90$h=−16x2+131x+90.
Solve for the number of seconds $x$x after which the object is $20$20 feet above the ground. Give your answer to the nearest tenth of a second.
Mae throws a stick vertically upwards. After $t$t seconds its height $h$h meters above the ground is given by the formula $h=25t-5t^2$h=25t−5t2.