NZ Level 8 (NZC) Level 3 (NCEA) [In development] 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. a

Complete the table for the various widths given:

 Width in metres ($x$x) Length in metres ($y$y) $5$5 $10$10 $15$15 $20$20 $25$25 $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$
b

Form an equation for $y$y in terms of $x$x.

c

As the width of the house increases, what happens to the length of the house?

It increases.

A

It decreases.

B

It stays the same.

C

It increases.

A

It decreases.

B

It stays the same.

C
d

If the width is $24$24 metres, what will be the length of the floor area?

e

Graph the relationship relating the width and length of the house.

f

Theoretically, how many students could be given unique dimensions, if the dimensions do not have to be whole number values?

$67$67

A

$10$10

B

$100$100

C

An infinite number.

D

$67$67

A

$10$10

B

$100$100

C

An infinite number.

D
Easy
Approx 5 minutes

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}$11x.

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 $\$12001200. The cost per person if $n$n people embark on the trip is $C=\frac{1200}{n}$C=1200n

### Outcomes

#### M8-7

Form and use trigonometric, polynomial, and other non-linear equations

#### 91575

Apply trigonometric methods in solving problems