Solve applications involving hyperbolas
Interactive practice questions
rA group of architecture students are given the task of designing the layout of a house with a rectangular floorplan. There are no restrictions on the length and the width of the house, but the floor area must be $120$120 square metres. Each student will be allocated a rectangle with a different pair of dimensions to any other student's.
Complete the table for the various widths given:
| Width in metres ($x$x) | $5$5 | $10$10 | $15$15 | $20$20 | $25$25 |
|---|---|---|---|---|---|
| Length in metres ($y$y) | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ | $\editable{}$ |
Form an equation for $y$y in terms of $x$x.
As the width of the house increases, what happens to the length of the house?
It increases.
It decreases.
It stays the same.
If the width is $24$24 metres, what will be the length of the floor area?
Graph the relationship relating the width and length of the house.
Theoretically, how many students could be given unique dimensions, if the dimensions do not have to be whole number values?
$67$67
$10$10
$100$100
An infinite number.
Suppose you attend a fundraiser where each person in attendance is given a ball, each with a different number. The balls are numbered $1$1 through $x$x. Each person in attendance places his or her ball in an urn. After dinner, a ball is chosen at random from the urn. The probability that your ball is selected is $\frac{1}{x}$1x. Therefore, the probability that your ball is not chosen is $1-\frac{1}{x}$1−1x.
A truck driver is to cover a $480$480 km journey.
A group of people are trying to decide whether to charter a yacht for a day trip to the Great Barrier Reef. The total cost of chartering a yacht is $\$1200$$1200. The cost per person if $n$n people embark on the trip is $C=\frac{1200}{n}$C=1200n