NZ Level 8 (NZC) Level 3 (NCEA) [In development] Solve Applications Involving Square Root Functions

## Interactive practice questions

The distance a particular animal can see to the horizon is modelled by $d\left(x\right)=\sqrt{\frac{5x}{2}}$d(x)=5x2, where $x$x is the number of feet the animal is above sea level and $d\left(x\right)$d(x) is in miles.

a

If the animal is lying on a rock that is $32$32 feet above the water, how far can it see?

Give an exact answer in simplest form.

b

Hence find the distance that the animal can see to the nearest tenth of a mile.

Easy
Approx 3 minutes

The period $P$P, in seconds, of a pendulum is $P=2\pi\sqrt{\frac{l}{32}}$P=2πl32, where $l$l is the length of the pendulum in feet.

Find the period of a pendulum whose length is $2$2 feet. Give your answer to two decimal places.

The walking speed (in feet per second) of a particular creature is modelled by $W\left(x\right)=4\sqrt{3x}$W(x)=43x, where $x$x is the length of the creature's legs (in feet).

The length of a blue whale calf in its first few months is modelled approximately by the equation $l=1.5\sqrt{t+4}$l=1.5t+4, where $l$l represents its length in meters at $t$t months of age.

### Outcomes

#### M8-7

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

#### 91575

Apply trigonometric methods in solving problems