Interactive practice questions
The Gateway Arch in St. Louis, Missouri, is $190$190 m tall.
We can model the behaviour of objects falling from the arch using Galileo's formula for falling objects: $d=16t^2$d=16t2, where $d$d is distance fallen in metres and $t$t is time in seconds since the object was dropped. The graph of this relationship is drawn here.
What does the point at $\left(0,0\right)$(0,0) represent?
The height of the arch.
The position of the object after it has fallen to to the ground.
The initial distance fallen by the object.
The sum of the series $1+2+3+\ldots+n$1+2+3+…+n is given by the function $S$S=$\frac{n\left(n+1\right)}{2}$n(n+1)2.
In a room of $n$n people, if everyone shakes hands with everyone else, the total number of handshakes is given by $H=\frac{n\left(n-1\right)}{2}$H=n(n−1)2.
An object is released $700$700 metres above ground and falls freely. The distance the object is from the ground is modelled by the formula $d=700-16t^2$d=700−16t2, where $d$d is the distance in metres that the object falls and $t$t is the time elapsed in seconds. This equation is graphed below.