A weight is attached to a spring that is fixed to the floor. The equationh= 7 cos (pi/3 t) models the height, h, in centimeters after t seconds of the weight being stretched and released.a. Solve the equation for t.b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Round your answers to the nearest hundredth.

Respuesta :

The given equation is:

[tex]h=7\cos(\frac{\pi}{3}t)[/tex]

Divide both sides of the equation by 7:

[tex]\begin{gathered} \cos(\frac{\pi}{3}t)=\frac{h}{7} \\ \frac{\pi}{3}t=\cos^{-1}(\frac{h}{7}) \\ t=\frac{3}{\pi}\cos^{-1}(\frac{h}{7}) \\ \end{gathered}[/tex][tex]t=\frac{3}{\pi}\cos^{-1}(\frac{h}{7})[/tex]

When h = 1

[tex]t=78.10s[/tex]

When h = 3:

[tex]t=61.71s[/tex]

When h=5

[tex]t=42.41s[/tex]

h=1, t =78.10;

h=3, t=61.71;

h=5, t=42.41

.