91Ó°ÊÓ

In a certain wildlife refuge, the population of field mice can be modelled by $y=3000+1250\sin \left(\frac{\mathrm{Ï€}t}{6}\right)$, where (y) represents the number of mice and (t) represents the number of months past March 1 of a given year then what is the maximum number of mice and when does this occur?

State the vertical shift, amplitude, period and phase shift of the function $y=\frac{1}{2}\sec \left[4\left(\mathrm{θ}-\frac{\mathrm{π}}{4}\right)\right]+1$ and then graph the function.

Find the amplitude if it exists and period of the function $y=3\sin \left(\mathrm{θ}\right)$ and then graph the function.

State the vertical shift, amplitude, period and phase shift of the function $y=\frac{2}{3}\cos \left[\frac{1}{2}\left(\mathrm{θ}+\frac{\mathrm{π}}{6}\right)\right]-2$ and then graph the function.

PHYSICS

For Exercises $16-18$, use the following information.

A weight is attached to a spring and suspended from the ceiling. At equilibrium, the weight is located 4 feet above the floor. The weight is pulled down 1 foot and released.

Determine the vertical shift, amplitude, and period of a function that represents the height of the weight above the floor if the weight returns to its lowest position every 4 seconds.

Find the amplitude if it exists and period of the function $y=5\cos \left(\mathrm{θ}\right)$ and then graph the function.

PHYSICS

For Exercises $16-18$, use the following information.

A weight is attached to a spring and suspended from the ceiling. At equilibrium, the weight is located 4 feet above the floor. The weight is pulled down 4 foot and released.

Write the equation for the height h of the weight above the floor as a function of

time $t$ seconds.

Find the amplitude if it exists and period of the function $y=2\csc \left(\mathrm{θ}\right)$ and then graph the function.

Find the amplitude if it exists and period of the function $y=2\tan \left(\mathrm{θ}\right)$ and then graph the function.

PHYSICS

For Exercises $16-18$, use the following information.

A weight is attached to a spring and suspended from the ceiling. At equilibrium, the weight is located 4 feet above the floor. The weight is pulled down 4 foot and released.

Draw a graph of the function you wrote in Exercise 17.