Modelling non-linear Relationships
Interactive practice questions
A rectangle is to be constructed with $80$80 metres of wire. The rectangle will have an area of $A=40x-x^2$A=40x−x2, where $x$x is the length of one side of the rectangle.
Using the equation, state the area of the rectangle if one side is $12$12 metres long.
The graph below displays all the possible areas that can be obtained using this amount of wire. From the graph, determine the nearest value for the longer side of a rectangle that has an area of $256$256 square metres.
$33$33 m
$9$9 m
$8$8 m
$32$32 m
Using the graph, what is the greatest possible area of a rectangle that has a perimeter of $80$80 m?
Using the graph, state the dimensions of the rectangle with the maximum area.
Length $=$=$\editable{}$ m
Width $=$=$\editable{}$ m
The height $h$h, in metres, reached by a ball thrown in the air after $t$t seconds is given by the equation $h=10t-t^2$h=10t−t2.
The formula for the surface area of a sphere is $S=4\pi r^2$S=4πr2, where $r$r is the radius in centimetres.
The volume of a sphere has the formula $V=\frac{4}{3}\pi r^3$V=43πr3. The graph relating $r$r and $V$V is shown.