Integrated Math 3 / Unit 4: Radical Functions and Equations
4.6 Modeling with Radical Functions
Notes
Many formulas contain square roots, so you often solve a radical equation to use them.
- The distance to the horizon from a height of $h$ feet is about $\displaystyle d = \sqrt{1.5h}$ miles.
- The period of a pendulum is $\displaystyle T = 2\pi\sqrt{\frac{L}{g}}$, where $L$ is length and $g = 9.8 \text{ m/s}^2$.
- To find an input from an output, square both sides and solve.
Practice
Using $\displaystyle d = \sqrt{1.5h}$, how far is the horizon from a lookout at a height of 24 feet?
$\displaystyle d = \sqrt{1.5 \cdot 24} = \sqrt{36} = 6$.
Using $\displaystyle d = \sqrt{1.5h}$, how high must you be to see a horizon 9 miles away?
$81 = 1.5h$, so $h = 54$.
A pendulum is 2.45 m long. Using $\displaystyle T = 2\pi\sqrt{\frac{L}{9.8}}$, its period is about:
$\displaystyle \frac{2.45}{9.8} = 0.25$, so $T = 2\pi(0.5) = \pi \approx 3.14$ seconds.
Ready for more? Take the Unit 4 test.